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B @ j3o?Line 10"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDOj0fh"(slW?plmXsRT//?zƱqrpxAuL `z~ZbݍwtZ*hb )CՐ0vq[ Zjn[gLZ4賡w[e׶[Sn.QeX4ć]4>d3+HD\PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK-,$D  m%   F ?Text Box 9#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! e&drs/downrev.xmlDMK1EBCx;iAiRb8?'I2$˹~(;e\u4vޑ"w-ڏF$9*0}.e YKߓKbh8&:֥= _UztޞFwX)us=6 &?eYVqy?C LAArKPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! e&drs/downrev.xmlPK D,$m <C = 1 2 3 4 5 6 7 8 9== =    F@?Text Box 9#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0drs/downrev.xmlDQK0Co.c"u6kʚ$׵ >÷X g ^t@i|=H`+#.<*%(D' =-o6Bdissolve*<3<*D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*C%(D' =-o6Bdissolve*<3<*CD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*CK%(D' =-o6Bdissolve*<3<*CKD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*K%(D' =-o6Bdissolve*<3<*KD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*%(D' =-o6Bdissolve*<3<*D' = @B%(Dh' =A@BB BB0B%()))D' =1:Bvisible*o3>+#.<*%(D' =-g6B fade*<3<*D9' =4@BBBB%( D' =1:Bvisible*o3>+#.<*%(D' =-u6Bwipe(right)*<3<*D' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*%(D' =-o6Bdissolve*<3<*D' = @B%(Dh' =A@BB BB0B%()))D' =1:Bvisible*o3>+#.<* %(D' =-g6B fade*<3<* D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*%(D' =-o6Bdissolve*<3<*D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*%(D' =-o6Bdissolve*<3<*D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*%(D' =-o6Bdissolve*<3<*D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* %(D' =-o6Bdissolve*<3<* +P+0+ ++0+ ++0+ ++0+ ++0+  ++0+  +")48  (   +   x0e0e?Rectangle 2  `0  m _Colon Operator vs. linspace()$    x0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Addrs/downrev.xmlDOK1G!fmSצEzPnAM7f$i .iõu9Yc)lzz2\_Z$ 41vjb8c:}-CVFZ4象k 6f\dn>/}xRo_RF"y)0& rPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Addrs/downrev.xmlPK gH$m m What will the following do? D=0 : 3 : 10 F=linspace(0, 10, 11) Observations about the two methods: both methods produce vectors with equally spaced elements colon operator method allows you to specify the first element and the interval spacing between elements, but not the number of elements If just start : end, then spacing is 1 linspace method allows you to specify the first and last elements of the vector, but not the spacing between elements0Z#Z$ZZ'ZvZ#$"w  U D  N`?Rectangle 5#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Q%drs/downrev.xmlDN0EH5Hlu(nxꢏECSh8y7"y)0& rPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Q%drs/downrev.xmlPK h,$m base : increment : limitH3 3  9  N?Rectangle 6#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!idrs/downrev.xmlDMO1@&fLhE1R1(⁏0ntӖe68&o5g CrL@ĄlL.a>baR%cBX0}K)&9]#GJ=I[zޝǏzaƺ joo>]<_asWf1QА797cPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!idrs/downrev.xmlPK  ,$m start : end : nH33   }ff___PPT10. PB+RD' = @B Df' = @BA?%,( < +O%,( < +D*' = @B%(%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* %(D' =-o6Bdissolve*<3<* D' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* )%(D' =-o6Bdissolve*<3<* )D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* )?%(D' =-o6Bdissolve*<3<* )?D' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* %(D' =-o6Bdissolve*<3<* D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* %(D' =-o6Bdissolve*<3<* D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* ?c%(D' =-o6Bdissolve*<3<* ?cD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* c%(D' =-o6Bdissolve*<3<* cD' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* %%(D' =-o6Bdissolve*<3<* %D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* %L%(D' =-o6Bdissolve*<3<* %LD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* L%(D' =-o6Bdissolve*<3<* L++0+  ++0+  ++0+  +"=8 $(  $+ $  x0e0e?Rectangle 2  `0  m _Review of length() and size()( ^ $  x0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!%.drs/downrev.xmlDn0xkz+DMApmۑm kWOX cr^Y#`:IT|@#j9[`.t)Câ!9nI؞Ld4xK(%ɜkT&.ӦTm9T׫a,MjU2dOwJ910F |PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!%.drs/downrev.xmlPK  H$m m ~What will the following do? length(ones(1,3)) length returns the number of elements of the vector size(zeros(2,3)) size returns the size of the dimensions of its argument483   3      }ff___PPT10. PB+ D`' = @B D' = @BA?%,( < +O%,( < +D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*$%(D' =-o6Bdissolve*<3<*$D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*$.%(D' =-o6Bdissolve*<3<*$.D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*$.b%(D' =-o6Bdissolve*<3<*$.bD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*$bs%(D' =-o6Bdissolve*<3<*$bsD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*$s%(D' =-o6Bdissolve*<3<*$s+8+0+$ +",8 ) ! ( (  ( (  x0e0e?Rectangle 2  `0  m BReview of Array Manipulation  (  x0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!mеdrs/downrev.xmlDn0xkz+NJ+sB!\z[%v6zhYͧ/ӱ3O2`d'mJ%W \nXJweIbCT}yh דMNr,+Amӂž553}X!?wXU2+<vxH^@ L _PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!mеdrs/downrev.xmlPK `H$m m "Given G=[2 4 6; 8 10 12], what is: G(2,3) G(: , 2) G(4) G(1,1)=0 G(1, :)=0 Observations: Array indexing begins with 1 (contrast with C) : means  all of the elements in that dimension Extract elements by indexing Extract sub-arrays using vectors as the indexing arguments z#P(PPP(V Y  @ }ffX#P#___PPT100#. `B+ D"' = @B D"' = @BA?%,( < +O%,( < +D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(#%(D' =-o6Bdissolve*<3<*(#D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(#*%(D' =-o6Bdissolve*<3<*(#*D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(*3%(D' =-o6Bdissolve*<3<*(*3D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(38%(D' =-o6Bdissolve*<3<*(38D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(8A%(D' =-o6Bdissolve*<3<*(8AD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(AK%(D' =-o6Bdissolve*<3<*(AKD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(KY%(D' =-o6Bdissolve*<3<*(KYD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(Y%(D' =-o6Bdissolve*<3<*(YD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(%(D' =-o6Bdissolve*<3<*(D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(%(D' =-o6Bdissolve*<3<*(D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*(%(D' =-o6Bdissolve*<3<*(+8+0+( +"mC8 ,(  ,  ,  x0e0e?Rectangle 2  `0  m =More Array Manipulation z ,  x`0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDn0D֭]qJ(I1e]tw/!#ۀ.G3:3[D=98ɀiTiV0H!̰lj:C !IؑLvi )Kϳl5*ziS{X7S7o.WO36wXWZ><+{l5@N@LIPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK `GH$m m gSuppose H=1:9 (what will this produce?) How could we form into a 3x3 matrix? Reshape function I=reshape(H,3,3) How to transpose the rows to be the columns? Reverse the order of the rows of I J=I(3:-1:1,:) Reverse the order of the columns of I (how?) K=I(:, 3:-1:1) Reverse the order of all the elements of I (how?) Pseudocode: Index I in reverse order Reshape(%>#-2 !%>  #-2 !   h , T@?Rectangle 4#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!pdrs/downrev.xmlDN0DHHܨMUV -m7qDlG6MggFo]' ^L _FDbID ˋ5"C|*Pe )Sea|r&9]'J-=-UǓ02?NIJ)Z__w Fd4rN]N_5LLQCdݬ rPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!pdrs/downrev.xmlPK S ],$Dm pL = reshape(I(9:-1:1),3,3)   , T?Rectangle 5#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDMk1E DѩOB;.Jw7t Ig}Cuys9`ZѳӉpDd525e]sDؐBcI ئtPLWR{&iL4PS k ˮ) "o0C4L-Wj o! &ݤ r PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK ,$Dm F I = I    }ff00___PPT10/. bB+BD/' = @B D.' = @BA?%,( < +O%,( < +D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,(%(D' =-o6Bdissolve*<3<*,(D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,(M%(D' =-o6Bdissolve*<3<*,(MD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,M^%(D' =-o6Bdissolve*<3<*,M^D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,^o%(D' =-o6Bdissolve*<3<*,^oD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,o%(D' =-o6Bdissolve*<3<*,oD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,%(D' =-o6Bdissolve*<3<*,D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,%(D' =-o6Bdissolve*<3<*,D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,%(D' =-o6Bdissolve*<3<*,D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,%(D' =-o6Bdissolve*<3<*,D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*, %(D' =-o6Bdissolve*<3<*, D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*, ;%(D' =-o6Bdissolve*<3<*, ;D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,;G%(D' =-o6Bdissolve*<3<*,;GD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,G`%(D' =-o6Bdissolve*<3<*,G`D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,`h%(D' =-o6Bdissolve*<3<*,`hD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,%(D' =-o6Bdissolve*<3<*,++0+, ++0+, ++0+, +" 8 HH00H(  0  0  x0e0e?Rectangle 2  `0  m AMatrix and Array Arithmetic Z  0  x0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! drs/downrev.xmlDQO0M%M:ݤA1^.m᯷AOwؑW$V*V˛{`>YCa1]ͰdJ:nB"!nI؞Li 1KOd5*Z驥{sv*OY$:_fmB\`?>꯼VR@]lz9%K􁜀(u*/PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! drs/downrev.xmlPK  HH$Dm m vArithmetic operators: + - * / \ ^  addition and subtraction are done element-by-element (same for matrix and array arithmetic) Unless one is a scalar, the operands must be of the same size scalar (matrix or array) --> ? (matrix or array) (matrix or array) --> ? (matrix or arrays) must be of the same size For the other operators, need to distinguish between matrix and array operation Matrix arithmetic operations per rules of linear algebra rows and columns must conform For example, A x B: must have column and row agreement Array arithmetic operations element-by-element Denote with dot operator: .* ./ .\ .^ . (array transpose)ZWZ\0Zd?ZMZ,ZPZZZUZZZBZW D?  +,P    7  $$((B,,  0 L`?Text Box 4#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!#FRdrs/downrev.xmlDAN0EH$6:  08$#۴)b?b5^؇Y$v u"DzgVmŇ]lDPq( fCa;o(<2ϲ;iiAku2Ef^ns===c6lSBMtϧߪBd.I7\PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!#FRdrs/downrev.xmlPKE,$m >add.   0 L?Text Box 5#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDMO0DHkQ'Ci[[iA8$^GIS~=8fFol/Fu e k[n>^ BD;&G Z,[w ¡B&ơ2Ԇ,SwbL7R{<$ee7b@kCu nn^{_{>:?nADxA쟎[ $t*PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK&,$m >sub.   0 L?Text Box 6#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! .drs/downrev.xmlDN0HHܨӔ4ԭP7hx6icqhF[Fۉ|h+N2ĕ ߞ !"kX-Xjw XPc_J*Cĩ;8o1k=v2ϲ[i`YEf_v{=1G*uy1>܃4qnWZAgE9}F0D `M ?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! .drs/downrev.xmlPK,,$m ?mult.   0 L@?Text Box 7#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!o4drs/downrev.xmlDN1&CsMI0R L/:vV|z<9'7[eA;+`8ȀԶp<=BD+u(b~7Rek 6(@ؕJ0pԝ7S5 nZgل6=(hj_F@mL`gZSLJ~,RShWޥ<vZ0D`M?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!o4drs/downrev.xmlPK ,$m D right div.   0 L?Text Box 8#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!4Zdrs/downrev.xmlDN0DHHܨPPV uqHlӦ|=8fFom/vCXt nQzwVYc(jy|R=WF$RP&n Ny1EHq඗y]J- *(2u%¬ox}"O;/A+y1?|VW"yI0&UPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!4Zdrs/downrev.xmlPK ,$m C left div.    0 L?Text Box 9#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!iFdrs/downrev.xmlDQO0M5M:1)Qo .[ۥlm|Ǔs|`Zv$jgG0U^ `!:KN`c)]o7tFĆPi2F#c^qOp<˦`mӃƎ֚fchYyI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!4Kdrs/downrev.xmlD]K0U]]6d*@ܗۦk$n^9*.4ĮNѱ:I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0\drs/downrev.xmlDOk@ouDĊP#Lٷ!͟o-zf76M#z\mYA@V\*?pYccL ͞h;'g_a6tKn;>Ȯ!M#WQ* *li_Q8lqO5I|6 i+nPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!0\drs/downrev.xmlPK )! ,$Dm 0 JA b??Object 12 0   bB 0 d3o?Line 20   0 \A c??Object 17"@# M  cBv  X  0C *Group 30#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!|drs/downrev.xmlDA0oVQEd]<ȂUXhmy)M,Yo{SWZVO"ę% x ydeR `M}.] DJdMlMm \7FB,9,XӾ_vYٞ29ŤhV <~Z  7OPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!|drs/downrev.xmlPK X,$Dm   0C *Group 27"# X 0 \A `??Object 18"@C   ` 0 JA a??Object 14  a 4 n 0C *Group 24" 9 B 0 jZ3o?Line 214  0 \A _??Object 19"@ n  _  0 T@?Text Box 28#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!ۯdrs/downrev.xmlDQO0M5@BD&(& >^ְK[a6>9N ;QLi2z4kH@O3i/&s*!g(8eMȶdbwNcU\:Dnx$\2ƖV5G X~m6w@]6}) MgdN} ' Fݨ | PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!ۯdrs/downrev.xmlPK  ,$Dm WA   0 T ?Text Box 29#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!ۮ~drs/downrev.xmlDQK0C/ZEqu06$%ɶ|9|oL'va:@ҶA|.AHVQ,#`1??QɮXF$ !1nPm)F*O7̳N6=sr] BrUu[]kg//G?ʿ&_;՚BdnR9PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!ۮ~drs/downrev.xmlPK  ,$Dm WB   }ffQQ___PPT10Q. B+θUD^O' = @B DO' = @BA?%,( < +O%,( < +D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0D' = @B%(D' = @B%(D!' =4@BBBB@HB%()))D' =1:Bvisible*o3>+#.<*0m%(DF' =+4 8?pCB#9999cc [5]BCB#666699 [6]B*z3>!Bstyle.color= `B<*0mD-' =+4 8?pCB#9999cc [5]BCB#666699 [6]B*a3><*0mD' =1:B solid*a3>.<*0mD' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0D' = @B%(|D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0D' = @B%(dD@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0D' = @B%(LD@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0D' = @B%(4!D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* 0%(D' =-o6Bdissolve*<3<* 0D' = @B%(%D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* 0%(D' =-o6Bdissolve*<3<* 0D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0m%(D' =-o6Bdissolve*<3<*0mD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0)%(D' =-o6Bdissolve*<3<*0)D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0)U%(D' =-o6Bdissolve*<3<*0)UD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0U%(D' =-o6Bdissolve*<3<*0UD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0 %(D' =-o6Bdissolve*<3<*0 D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0 (%(D' =-o6Bdissolve*<3<*0 (D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0(_%(D' =-o6Bdissolve*<3<*0(_D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<* 0%(D' =-o6Bdissolve*<3<* 0D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* 0%(D' =-o6Bdissolve*<3<* 0D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<* 0%(D' =-o6Bdissolve*<3<* 0D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0_|%(D' =-o6Bdissolve*<3<*0_|D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0|%(D' =-o6Bdissolve*<3<*0|D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*0%(D' =-o6Bdissolve*<3<*0++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+0 +" N 8 "!P4!(  42 4  x0e0e?Rectangle 2  `0  m f$Matrix and Array Arithmetic Examples%%% % 4  x`0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!}6ddrs/downrev.xmlDQO0M5M:Wb4(>.ez|'t>Ql픶u Yp N*6,Al(PBc_p ɦnoxJp<AmC=TFNk.<.DU X!_Z* w{`kUb%$T~PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!}6ddrs/downrev.xmlPK `H$Dm m :Scalar and matrix operands If L=ones(1,5) and M=ones(1,4) N = 2*L --> ? N  1 --> ? Non-scalar operations If O = [ 1:5 ] O + M --> ? L * O --> ? L* O --> ?    $ * 4 H?Rectangle 4#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!`gdrs/downrev.xmlDN0DHH\uhBݪ* Bo =p4mZ8q47ze;w Je{`>YC\\^̱ltB!nIٞLi )KgY5*ZiR}t[nY},U\= x_WJ)` + Matrix dimensions must agree.443 4 1 4 H?Rectangle 5#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!2drs/downrev.xmlDn0D֭MU"mAR5nHK|I l,G3:3uagr^Y#K)Tx~5$Jf f^̆EX:6ܗ5i=ے:!FWq$sć[ZT-`)OK!@]Wy/P0Gi ly9%79Q0FU_PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!2drs/downrev.xmlPK g ,$ m 9??? Error using ==> * Inner matrix dimensions must agree.::3 :   4 H?Rectangle 6#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!1Ldrs/downrev.xmlDn0ET*AbPK[% b;]_]{^D+k  02ʟ`>ZC.ac*t*B"4!t)jH؎Li t5[>J)רLlhUCձ6ɶ\ep|UO٬Hn%C,Pm)-2)`4Ofq~}9%s􁜀(u*PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!1Ldrs/downrev.xmlPK ,$m m15 Same as sum(L .* O)   4 L@?Text Box 7#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!jdrs/downrev.xmlDN0DHHܨӤ@VXmۑ _[ۉx`:@n\b"2:w`KnK"A\,QaK)ceb\>-c۱Y%-6.=ijɳI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!/drs/downrev.xmlDN0EH5HӴ4ԭP]ix 8MX,`yYo'3#9YV0% +;n=d |@8X&g\^1{:B#"} \J_dH:!FHfiIDžG*Z×Q%f՛-J8~*u}5=܃4碬yU ],Yԩ{􁜂xQPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!/drs/downrev.xmlPK SO,$m |B(1x5 * 5x1 works! Inner matrix dimensions agree. Results in a 1x1) C  }ff, ,___PPT10+. 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Pseudocode: Calculate avg. speeds: speed[i] = distance[i] / time[i], for i=1 to 4 Determine maximum speed M/O/F (vectorize!): distances=[120, 213, 87, 35] (in miles) times=[ 2, 3.8, 0.9, 0.6] (in hours) speeds=distances ./ times %( note:  dot / divide element-by-element) max_speed=max(speeds) To get the maximum speed and its index: [max_speed, i] = max(speeds)*#Y(^#Y(E   j  313   }ff[$S$___PPT103$. %B+ D#' = @B D#' = @BA?%,( < +O%,( < +D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8#%(D' =-o6Bdissolve*<3<*8#D' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8#|%(D' =-o6Bdissolve*<3<*8#|D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8|%(D' =-o6Bdissolve*<3<*8|D' = @B%(DU' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8%(D' =-o6Bdissolve*<3<*8D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8%(D' =-o6Bdissolve*<3<*8D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8%(D' =-o6Bdissolve*<3<*8D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8%(D' =-o6Bdissolve*<3<*8D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8?%(D' =-o6Bdissolve*<3<*8?D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8?e%(D' =-o6Bdissolve*<3<*8?eD@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8e%(D' =-o6Bdissolve*<3<*8eD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8%(D' =-o6Bdissolve*<3<*8D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8%(D' =-o6Bdissolve*<3<*8D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*8 %(D' =-o6Bdissolve*<3<*8 +8+0+8 +"c 8 tNlN<TN(  <  <  x &0e0e?Rectangle 2  `0  m @Circuit Analysis Equations  <  x`0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!ͅdrs/downrev.xmlDAO1F&fLI`PV 1V=.۰v+vX68y-Vؙ|J)m js,D ;gI•]lImlXؐ6><- cדMNp!fܠiŞ^[ۓד~U!|3Cu\Kyw;<4gSd.]x=;]^C$/!܄/PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!ͅdrs/downrev.xmlPK   H$m m cMatrix operations Matrix division Recall the circuit 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_rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!rdrs/downrev.xmlDOk0 Mi5J2I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!`Ydrs/downrev.xmlDO=o0+CV*JAuk`a;G6>¿ HO{|zbt".2p<^@ńl La=,1_R1G.6:I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!+?xGdrs/downrev.xmlDOMk1ze]Jof]L$;BX S7 la<2Z-ovƒO ,]V©D M}uF',0EK1SeihmCeww:}S1ݣ0`}}sP/s9?3#_PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!+?xGdrs/downrev.xmlPKe " 8 l$D mK < H` &?Text Box 12#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDN0EH5Hlˣ@[M C<#b;&{,ѹ:Zq5L' *- ,Gs,L[ETRʒ4 !:|Z}V^(5,vh~; f5gSoUu֧'g&ܩ51PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPKaSs,$m >If we had iR = V instead, we d use  right division to solve for i: ( i = R / V ) Think of it like inverting R and multiplying on the right side of V: i = VR-10  S < N&?Text Box 12#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!ġdrs/downrev.xmlDQk06FYu A7|6׶$%/a{*x$ N׶T0YRSfvW˞K!6bnS)CQ0p-؝71Rj7&Xm|eEym6|x~Z!39S{`<~6+QZ?Z00y-FKPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!ġdrs/downrev.xmlPK  c,$Dm CThink of it like inverting R and multiplying on the left side of V 0D4  D  }ff77___PPT10_7. sB+~OD6' = @B DF6' = @BA?%,( < +O%,( < +D' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*<%(D' =-o6Bdissolve*<3<*<D' = @B%(D@' =A@BB BB0B%( D' =1:Bvisible*o3>+#.<*<"%(D' =-o6Bdissolve*<3<*<"D' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*<">%(D' =-o6Bdissolve*<3<*<">D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<* <%(D' =-o6Bdissolve*<3<* <D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<* <%(D' =-o6Bdissolve*<3<* <D' = @B%(D@' =A@BB BB0B%( D' =1:Bvisible*o3>+#.<*<>E%(D' =-o6Bdissolve*<3<*<>ED' = @B%( D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*<EN%(D' =-o6Bdissolve*<3<*<END' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*<NT%(D' =-o6Bdissolve*<3<*<NTD' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*<%(D' =-o6Bdissolve*<3<*<D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*<%(D' =-o6Bdissolve*<3<*<D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*<%(D' =-o6Bdissolve*<3<*<D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*<%(D' =-o6Bdissolve*<3<*<D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*<Td%(D' =-o6Bdissolve*<3<*<TdD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<* <%(D' =-o6Bdissolve*<3<* <D' = @B%(D' = @B%(D7' =4@BBBB%(D' =1:Bvisible*o3>+#.<* <%(D' =-s6Bwipe(left)*<3<* <D' = @B%(D7' =4@BBBB%(D' =1:Bvisible*o3>+#.<* <%(D' =-s6Bwipe(left)*<3<* <D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*<%(D' =-o6Bdissolve*<3<*<D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*<%(D' =-o6Bdissolve*<3<*<D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*<%(D' =-o6Bdissolve*<3<*<++0+< ++0+< ++0+< +"J 8  @(  @  @  x 0e0e?Rectangle 2  `0  m ?Circuit Analysis Solution j @  xl 0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Xhdrs/downrev.xmlDOO@G&~͘x,@PI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0\drs/downrev.xmlDOk@ouDĊP#Lٷ!͟o-zf76M#z\mYA@V\*?pYccL ͞h;'g_a6tKn;>Ȯ!M#WQ* *li_Q8lqO5I|6 i+nPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!0\drs/downrev.xmlPK /5 ,$Dm @ NA m??Object 4X t m @ NA n??Object 5[#  n @ NA o??Object 6A  o  @ NA p??Object 72A  p @ R`&?Text Box 8#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!̞pdrs/downrev.xmlD1O0Fw$uHl V- e;k6>Gi~=wzl1Nɇֱ| nQpUYc`1??a݉tF$ JP&'NlŘNH䶓YVH-=- Շ͗U@t̕nAD~X'Znʢ=k r9PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!̞pdrs/downrev.xmlPK9R,$Dm mR1=10k R2=R3=5k V=10V   }ff4z4___PPT10Z4. ’B+D3' = @B Dy3' = @BA?%,( < +O%,( < +DW' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@%(D' =-o6Bdissolve*<3<*@D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@%(D' =-o6Bdissolve*<3<*@D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*@%(D' =-o6Bdissolve*<3<*@D1' = @B%(D' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<*@9%(D' =-s6Bwipe(left)*<3<*@9D' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@9A%(D' =-o6Bdissolve*<3<*@9AD' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@AM%(D' =-o6Bdissolve*<3<*@AMD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@Ml%(D' =-o6Bdissolve*<3<*@MlD' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@lo%(D' =-o6Bdissolve*<3<*@loD' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@o%(D' =-o6Bdissolve*<3<*@oD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@%(D' =-o6Bdissolve*<3<*@D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@%(D' =-o6Bdissolve*<3<*@D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@%(D' =-o6Bdissolve*<3<*@D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@%(D' =-o6Bdissolve*<3<*@D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@%(D' =-o6Bdissolve*<3<*@D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@%(D' =-o6Bdissolve*<3<*@D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@ %(D' =-o6Bdissolve*<3<*@ D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*@ %(D' =-o6Bdissolve*<3<*@ +p+0+@ ++0+@ +"?8 &&D&(  D D  x` 0e0e?Rectangle 2  `0  m 9Dot Product Example  D  x 0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!4G"drs/downrev.xmlL1o0FJ؊CPbPU-BX񑸍6ku:}ze[v!5&Jejr}4[kH<,9^MA}Y&.W icۑdOWsiI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Rldrs/downrev.xmlDO]k0}?+mi5Q Aa*>_k[ln$7{gr`4L@V7\)>' |@Z&W/i{/:oC%b !tɠڎ8rG ]%K 7LUl86QQSy.oi|:_h>mz3/s8Go';PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Rldrs/downrev.xmlPKz8 r$D m}w ` Y DC *Group 21#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0\drs/downrev.xmlDOk@ouDĊP#Lٷ!͟o-zf76M#z\mYA@V\*?pYccL ͞h;'g_a6tKn;>Ȯ!M#WQ* *li_Q8lqO5I|6 i+nPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!0\drs/downrev.xmlPK ,$@mB  D X?Line 13 `* `  D \A x??Object 15"@ F  x  D \A y??Object 16"@7  y  D \A z??Object 18"@ V e zB D ^7!?Line 14`   D \A {??Object 19"@ZPYv { D b ?Rectangle 22#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!tȱdrs/downrev.xmlDAO@F&͘x(+ 1FSBwxMޗ7GqV0Atv"0ZL3NvE5W"JlPAeR&a:7OQnZ9JTll\ך(IBnkQHޏsVy&:< vy1/PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!tȱdrs/downrev.xmlPK  L$Dmt8 2  ~ D BA u?Object 2"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!j(drs/downrev.xmlD[k1 |)UF'A[6g/tsMn }f&wr`8H@V\*\' |@X&a>{|0[B)"} TJWdlK:!JWJᦑ$yk (ޝM59>OqJ@]?1ܯ g7PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!j(drs/downrev.xmlPK k 8 u$D m D NA v?33Object 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Pcdrs/downrev.xmlDAk@F-%D-lhmȮ&n030|Q qtõsJAuL !L֘i7nPaBI+Cure_Kᶕ$y ;OWxpgS.\˷G*z D1گZ3^7@n~PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Pcdrs/downrev.xmlPK 7~ 8 v$D m  D BA w?Object 4"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!,,wdrs/downrev.xmlDj@ rM-VM]E һC4̞ ٭InafaF+x% +.O kǤ<u|1"BاФRE?r q>]k1DٖRE8I^Ŋ U0ռ&fGVM D>`W ;PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!,,wdrs/downrev.xmlPK 8 w$D  m }ff___PPT10~.  B+a׈D' = @B D' = @BA?%,( < +O%,( < +D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*D1%(D' =-o6Bdissolve*<3<*D1D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*D1L%(D' =-o6Bdissolve*<3<*D1LD1' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*D%(D' =-o6Bdissolve*<3<*DD' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*D%(D1' = @B%(D' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<*D%(D' =-s6Bwipe(down)*<3<*DD1' = @B%(D' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<*D%(D' =-s6Bwipe(down)*<3<*DD1' = @B%(D' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<*D%(D' =-s6Bwipe(down)*<3<*DD1' = @B%(D' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<* D%(D' =-s6Bwipe(down)*<3<* D+p+0+D ++0+D +" E8   H (  H& H  p 0e0e?Title 4  `0  m b Dot Product Function Development!!( ! H   0e0e?,Content Placeholder 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0O|drs/downrev.xmlDKK@p7NTR% ؗk6 ęi ];|ՠѱ5wªڔ(ja=Wef."B ͤEŚ̶lbwNSѕR9#\7>ӳ-Vv0=㾱gۧtDz=<<:գK_ԻB8㷫Ֆ|`ݢiPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!0O|drs/downrev.xmlPK  `H$m m Define the problem Create a function that will take two vectors as arguments and will return their vector dot product Inputs v1, v2 (three-element row vectors) Outputs z (the dot product) Algorithm Multiply v1 and v2 element-by-element Sum the element-by-element products Return the sumc# Yc#  Y  @ H HA |?Object 6"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!^{drs/downrev.xmlDAk@B nJUDPzk%}|L睭ą_:V>L@gN\(ݯ> k+y^zSLkyK](DOQ N!~j宱l l#V#IŒ*XoU{1Rn "PGG+JrvPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!^{drs/downrev.xmlPK ; z8 |$D m }ff8 8___PPT107. 0Q+D7' = @B DA7' = @BA?%,( < +O%,( < +D7' = @B%(D' = @B%(Dm' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =+4 8?HCBBBCBB*k3>'.<*HD' =-g6B fade*<3<*HD' = @B%(Dp' = @B%(D ' =A@BBBB0B%()))D' =1:Bvisible*o3>+#.<*Hv%(D!' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*a3>B ppt_x=<*HvD' =+4 8?\CB#ppt_yBCB#ppt_yB*a3>B ppt_y=<*HvD7' = @B%(D' = @B%(Dm' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*Hv}%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*Hv}D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*Hv}D' =+4 8?HCBBBCBB*k3>'.<*Hv}D' =-g6B fade*<3<*Hv}D' = @B%(Dp' = @B%(D ' =A@BBBB0B%()))D' =1:Bvisible*o3>+#.<*H}%(D!' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*a3>B ppt_x=<*H}D' =+4 8?\CB#ppt_yBCB#ppt_yB*a3>B ppt_y=<*H}D7' = @B%(D' = @B%(Dm' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =+4 8?HCBBBCBB*k3>'.<*HD' =-g6B fade*<3<*HD' = @B%(Dp' = @B%(D ' =A@BBBB0B%()))D' =1:Bvisible*o3>+#.<*H%(D!' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*a3>B ppt_x=<*HD' =+4 8?\CB#ppt_yBCB#ppt_yB*a3>B ppt_y=<*HD7' = @B%(D' = @B%(Dm' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =+4 8?HCBBBCBB*k3>'.<*HD' =-g6B fade*<3<*HD>' = @B%(D' = @B%(Dt' =A@BBBB0B%()))D' =1:Bvisible*o3>+#.<*H%(D' =-s6Bwipe(left)*<3<*HD>' = @B%(D' = @B%(Dt' =A@BBBB0B%()))D' =1:Bvisible*o3>+#.<*H%(D' =-s6Bwipe(left)*<3<*HD>' = @B%(D' = @B%(Dt' =A@BBBB0B%()))D' =1:Bvisible*o3>+#.<*H%(D' =-s6Bwipe(left)*<3<*HD' = @B%(D' = @B%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+#.<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =-g6B fade*<3<*H+8+0+H +"w68 3+L(  L L  p` 0e0e?Title 1  `0  m CDot Product Function in M/O/F u L  @ 0e0e?,Content Placeholder 2"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!q+drs/downrev.xmlDMK@Eax7NjJ초 __3IhM&wp˽˙-zS,+Ĺ G> k- yX̯fjm(DOQABJ mcw`R;".I`Ć^JO۳Q0gi-ZA"PcۭL@Uz>Sݢi9PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!q+drs/downrev.xmlPK  `H$ m m |Write the function Test it out   0@ L L ?Text Box 4#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDJ1EЍVEM]kܽN'/C;SЅ./r.g\+v@X57 bB6z& '\\^̱0-w±@ MJ]!e,rǾ#]Ôc gkDr~hUCiZnzqR4hH7j2Dr:k -fK_PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK H$ ,$Dm Dfunction [z] = dot_prod(v1, v2) % dot_prod(v1,v2) computes the vector dot product between vectors v1 and v2 % Function dot_prod(v1,v2) computes and returns the vector dot product between vectors v1 and v2 z = sum(v1.*v2);$3  h L R@ 00?Text Box 4"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!,drs/downrev.xmlDOO1&~xJ B?p!cq?=Nf鼷8Ʊ| 6\+x; !"kl+noXjw ¡DM])e#Ny1I_KඕY6 ;Z4T}l= Xo͸7JO^qX~_ԫV0qz; -=MxPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!,drs/downrev.xmlPK  } ,$D m [A = [ 1 2 3 ]; B = [ 4 5 6 ]; % what should A dot B result in? A_dot_B = dot_prod(A,B).C\ \  }ff##___PPT10#.( pW+g,>D"' = @B D"' = @BA?%,( < +O%,( < +D' = @B%(D' = @B%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*L%(D' =-s6Bwipe(left)*<3<*LD' = @B%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*L%(D' =-g6B fade*<3<*LD1' = @B%(D' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<*L %(D' =-s6Bwipe(left)*<3<*L D1' = @B%(D' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<*L l%(D' =-s6Bwipe(left)*<3<*L lD1' = @B%(D' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<*Ll%(D' =-s6Bwipe(left)*<3<*LlD1' = @B%(D' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<*L%(D' =-s6Bwipe(left)*<3<*LD' = @B%(D' = @B%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*L%(D' =-s6Bwipe(left)*<3<*LD' = @B%(D' = @B%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*L%(D' =-g6B fade*<3<*LD' = @B%(D' = @B%(D7' =4@BBBB%(D' =1:Bvisible*o3>+#.<*L%(D' =-s6Bwipe(left)*<3<*LD' = @B%(D' = @B%(D7' =4@BBBB%(D' =1:Bvisible*o3>+#.<*LC%(D' =-s6Bwipe(left)*<3<*LCD' = @B%(D' = @B%(D7' =4@BBBB%(D' =1:Bvisible*o3>+#.<*LD\%(D' =-s6Bwipe(left)*<3<*LD\++0+L ++0+L ++0+L +" *8 P(  Pq P0  A }?5%8c8c    ?Object 73"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDOj0cV2,v8$Ƕ؜&j`VLW}Xr t(8쫗w> ;y(Sq7kCا aH%~h1D86ҌxᶗI; -ْ>@J:?ͥUmLezOD)_&x[7'PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK \T }$D m m P  x 0e0e?Rectangle 2  `0  m 9Review of Functions   P  x 0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!`gQdrs/downrev.xmlDAO1F&fHI (Bp6lݴeY68y-ViXG>hg%)m+ b},D gI•7 ̔؜mXؐ:6<5 CגMN_qc!ܠiƖ^j*g#;΋7afI*ݠ^U}2{xNޯGU!Sn?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!`gQdrs/downrev.xmlPK H$m m Functions Like script M-files, but several differences: first line (function declaration) must be of the form: function [output args] = function_name(input args) variables generated in the function are local to the function, whereas for script files, variables are global must be named,  function_name.m (same as file name) Make sure you add comments at the start that describe what the function does (see example code) Example: root-mean-square function, rms.m0 .k0  .5G3C C C(   :          M*  }ff___PPT10. 0B+I1DZ' = @B D' = @BA?%,( < +O%,( < +D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*P %(D' =-o6Bdissolve*<3<*P D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*P 8%(D' =-o6Bdissolve*<3<*P 8D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*P8%(D' =-o6Bdissolve*<3<*P8DR' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*P%(D' =-o6Bdissolve*<3<*PD@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*PF%(D' =-o6Bdissolve*<3<*PFD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*PF%(D' =-o6Bdissolve*<3<*PFD' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*P%(D' =-o6Bdissolve*<3<*PD' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*P%(D' =-o6Bdissolve*<3<*P+8+0+P +" F8 UM0T5(  T3 T  x 0e0e?Rectangle 2  `0  m g%Root Mean-Square Function Development&&  & T  x 0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!ևPdrs/downrev.xmlDN0DHVbGh[!Py,X*oClGӦ|= XftFgMǎvVB6NiHV;`!U9K`\,PdK:nbĆ%1n`l)+7υM-Rη]Vm>')/=Hc;$ٍ/תKHI7_PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!ևPdrs/downrev.xmlPK  H$m m Functions, cont. Example: root-mean-square function, cont. Pseudocode: square each element of x sum the squares divide by N take the square root Square each element xs = x .^2 Sum the squares sums = sum(xs) Divide by N N = length(x) ms = sums/NZ*Z ZJZZ ZZZ ZZ* J      s T0  A ~?5%8c8c    ?Object 43"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!}Bdrs/downrev.xmlDˊ0C8lDSKGEf'񭷃iDOזg Kt deRGsm|JG稠 ͥEE̶ѻ[g0DJ>id$ iPaKǹ3 vǟ\Vt:;k׉Rah,I#A, 7PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!}Bdrs/downrev.xmlPKIB AT ~$Dm mN T H` ?Rectangle 7"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!]-1drs/downrev.xmlDQK0C/Uˆ dEN-67m|9|oL+r`>K@V7\)x?]߃Yckjy~Lۑw4>Cu]&/k2g#:!FWIpp4ICk*o`,a۫Cnu"Gk6Io@7O@NAQPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!]-1drs/downrev.xmlPKjJ #,$m Take the square root rms = sqrt(ms) Before you write the function, make sure the name you propose is not already used! Use: which name to check (nK(<S(nK(<SE3AAAA  }ff2 2___PPT101. @7B++#.<*T%(D' =-o6Bdissolve*<3<*TD' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T;%(D' =-o6Bdissolve*<3<*T;D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*T%(D' =-o6Bdissolve*<3<*TD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T;G%(D' =-o6Bdissolve*<3<*T;GD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*TG`%(D' =-o6Bdissolve*<3<*TG`D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T`p%(D' =-o6Bdissolve*<3<*T`pD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*Tp|%(D' =-o6Bdissolve*<3<*Tp|D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T|%(D' =-o6Bdissolve*<3<*T|D ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T%(D' =-o6Bdissolve*<3<*TD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T%(D' =-o6Bdissolve*<3<*TD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T%(D' =-o6Bdissolve*<3<*TD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T%(D' =-o6Bdissolve*<3<*TD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T%(D' =-o6Bdissolve*<3<*TD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T%(D' =-o6Bdissolve*<3<*TD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T%(D' =-o6Bdissolve*<3<*TD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*T%(D' =-o6Bdissolve*<3<*T+p+0+T ++0+T +" -h8 11P X0(  X6 X  xa 0e0e?Rectangle 2  `0  m j(Root Mean-Square Function Implementation))  ) X  x 0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!F#drs/downrev.xmlDMO1E&晸11RQܐ ÆcNI[`۰ͽ97gyF-l8vkU`%$dLOPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!F#drs/downrev.xmlPK  H$Dm m :Functions, cont. Example: root-mean-square function, cont.*** ; @: X L ?Text Box 4#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! )&drs/downrev.xmlDMK1!ElJY;-"'m7ɒ_o}!#]q5a;F8qlAqj!.ФRƲaKq;v9|jn[9QVZ2.74C"ܼM 3aD@$᥮^_ԳFg*N-!el rPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! )&drs/downrev.xmlPKY ,$Dm function [y] = rms(v) % RMS(v) root mean square of the elements of the column vector v % Function rms(v) returns the root mean square of the elements % of the column vector, v vs = v.^2; % what does this line do? Also note semicolon. s = length(v); y = sqrt(sum(vs)/s);H3a-b   X L ?Text Box 5#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!ڸ=drs/downrev.xmlDMO1E&摸v&b`En|׏c:δ ]ܛss޴D>JFҩV7`!U:K.`\ͱPltŊ% J1vd0\G6uG }ŕsBqM;Zi*ݗ0i&lWzπEx+QJBrb%$dL/~PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!ڸ=drs/downrev.xmlPK ,$m :Let v=sin([0: 0.01*pi: 2*pi] ), one period of a sine wave. The RMS value of a sine wave is its amplitude*1/sqrt(2)ss s ) X L ?Text Box 6#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!W drs/downrev.xmlDN0EH5H쨓VU }CI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDN0DHHܨHEVPQ$. mqDlG$ŁG3zL' NA@k\~܁Nc))f}yRTq+桔26,ƅȥEN1RȲ[is@*`|mLoOɚ%J]_MLǻOw_VP˼q|Bl)/PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK zM,$m {#H1 comment line (used in lookfor)$$ $ B X  t3o??Line 9"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!K/drs/downrev.xmlDMK1!fE)kӢQV =$$v7ųXWy6PN Pĵ7>?n栒 [=3%X-//XY [iTTV$TZ%iq>:,cmSwŝvq~h1кv\zua6^~A kX򶜁:I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!VhHdrs/downrev.xmlDKK@a;;IZbGKy`f&wp9|oM'uVA:I@-nm AFs)jyyLpZD *hLP6d0L\O6v9F_Kᦓ$[鹡m7iOqY{siq]yW^iz@ToWm4PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!VhHdrs/downrev.xmlPK ,$D  m 2    X F ?Text Box 6#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!~drs/downrev.xmlDMO0DHkQ'P[UD\چ6Qc;X8f(;"Au"2:w` KGwȍHKT`RX'9HpLpe=KK{ǛU\۸FVJ=>LWL|_k˼ Z}$dLAPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!~drs/downrev.xmlPK  Y ,$m /Comments that will be displayed by help command00 0 B  X  v3o??Line 12"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!kdrs/downrev.xmlDMK@aݤhR B[M1M{<_+#.<*X%(D' =-o6Bdissolve*<3<*XD' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*X;%(D' =-o6Bdissolve*<3<*X;D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*X%(D' =-o6Bdissolve*<3<*XDZ' = @B%(D' = @B%(D.' =A@BBBB0B@HB%()))D' =1:Bvisible*o3>+#.<*X%(DF' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*z3>!Bstyle.color= `B<*XD-' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*a3><*XD' P=1:B solid*a3>.<*XD' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<*X%(D' =-s6Bwipe(left)*<3<*XD' = @B%(D!' =4@BBBB@HB%()))D' =1:Bvisible*o3>+#.<*XW%(DF' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*z3>!Bstyle.color= `B<*XWD-' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*a3><*XWD' P=1:B solid*a3>.<*XWD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<* X%(D' =-o6Bdissolve*<3<* XD' = @B%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+#.<* X%(D' =-s6Bwipe(left)*<3<* XD' = @B%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<* X%(D' =-s6Bwipe(left)*<3<* XD' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*XW%(D' =-o6Bdissolve*<3<*XWD' = @B%( D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*X%(D' =-o6Bdissolve*<3<*XD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*X%(D' =-o6Bdissolve*<3<*XD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*X%(D' =-o6Bdissolve*<3<*XD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*X%(D' =-o6Bdissolve*<3<*XD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*X%(D' =-o6Bdissolve*<3<*XD ' = @B%(D' = @B%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*X%(D' =-o6Bdissolve*<3<*X++0+X ++0+X ++0+X ++0+ X ++0+ X +"q?8 Z R p\: (  \3 \  x@":0e0e?Rectangle 2  `0  m g%More Robust Root Mean-Square Function&&  & \  x 0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Ȓdrs/downrev.xmlDQO0M5M:F40)(/]V]ۥ-lm|Ǔs|Ev&5FJe*bu?5$Bۛfv&6T,BP@Bq˚4mhtEnx$\2Ɩ^j*'-^-8bp?? ԇf_a<v|9@N@PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Ȓdrs/downrev.xmlPK z FH$Dm m vFunctions, cont. Make rms function more robust to work with row or column vector or matrix with column vectors of dataBZZHZ$H w \ L":?Text Box 8#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Hpdrs/downrev.xmlDN0DHH\uH(Bn* %$x٦Iz,pb5^X,A\;mU\߃Yc(jy~Rwtb+C RPwd1@y1EJqLp+#.<*\%(D' =-o6Bdissolve*<3<*\D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*\/%(D' =-o6Bdissolve*<3<*\/D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*\/w%(D' =-o6Bdissolve*<3<*\/wD' = @B%(DV' = @B%(D' =4@BBBB@HB%(D' =1:Bvisible*o3>+#.<*\%(DF' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*z3>!Bstyle.color= `B<*\D-' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*a3><*\D' P=1:B solid*a3>.<*\D' = @B%(DV' = @B%(D' =4@BBBB@HB%(D' =1:Bvisible*o3>+#.<*\;%(DF' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*z3>!Bstyle.color= `B<*\;D-' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*a3><*\;D' P=1:B solid*a3>.<*\;Dw' = @B%(DV' = @B%(D' =4@BBBB@HB%(D' =1:Bvisible*o3>+#.<*\;j%(DF' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*z3>!Bstyle.color= `B<*\;jD-' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*a3><*\;jD' P=1:B solid*a3>.<*\;jDV' = @B%(@D' =4@BBBB@HB%(D' =1:Bvisible*o3>+#.<*\j%(DF' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*z3>!Bstyle.color= `B<*\jD-' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*a3><*\jD' P=1:B solid*a3>.<*\jDV' = @B%(D' =4@BBBB@HB%(D' =1:Bvisible*o3>+#.<*\%(DF' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*z3>!Bstyle.color= `B<*\D-' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*a3><*\D' P=1:B solid*a3>.<*\D' = @B%(DV' = @B%(D' =4@BBBB@HB%(D' =1:Bvisible*o3>+#.<*\%(DF' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*z3>!Bstyle.color= `B<*\D-' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*a3><*\D' P=1:B solid*a3>.<*\D' = @B%(DV' = @B%(D' =4@BBBB@HB%(D' =1:Bvisible*o3>+#.<*\%(DF' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*z3>!Bstyle.color= `B<*\D-' P=+4 8?pCB#9999cc [5]BCB#666699 [6]B*a3><*\D' P=1:B solid*a3>.<*\+"R'8 c [ `C (  ` `  x$:0e0e?Rectangle 2  `0  m 9File I/O with M/O/F  `  x#:0e0e?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!hzdrs/downrev.xmlDN0DHuNR J[V#I7nۑ6)_YFݱ39N`dj+ih$v֐ yX-K;ehX6>-iSۓ:!Fppp,IFeC=mZʓpP9YxV,e>7/U Ȳ4;\N} ' Fݨ |PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!hzdrs/downrev.xmlPK `H$Dm m <Data Input - simplest method load command Ex: load( data_file.txt ) reads on a row-by-row basis data values separated by spaces or commas and rows terminated by new line columns must have the same number of elements data is stored in workspace in an array with same name as the argument used in the load function Ex. Portland International Airport monthly rainfall load ( PDXprecip.dat ) % must be in search path! C2E3 E3  _  .   }ff___PPT10_. ӓB+MC D3' = @B D' = @BA?%,( < +O%,( < +D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*`%(D' =-o6Bdissolve*<3<*`D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*`*%(D' =-o6Bdissolve*<3<*`*D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*`*D%(D' =-o6Bdissolve*<3<*`*DD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*`D`%(D' =-o6Bdissolve*<3<*`D`D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*``%(D' =-o6Bdissolve*<3<*``D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*`%(D' =-o6Bdissolve*<3<*`D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*`9%(D' =-o6Bdissolve*<3<*`9D' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*`9m%(D' =-o6Bdissolve*<3<*`9mD' = @B%(D' = @B%(D3' =4@BB BB%(D' =1:Bvisible*o3>+#.<*`m%(D' =-o6Bdissolve*<3<*`m+"8 d(  d d  p $:0e0e?Title 1  `0  m @File I/O with M/O/F, cont. V d  !:0e0e?,Content Placeholder 2 ` m pData Output - simplest method Save command Ex: save( data_file_name ) Saves all the variables into a .mat file named  data_file_name Many other commands are available for special purpose file I/O  @?E3E3@?   }ff___PPT10i.v 18)+D=' = @B +"8 h(  h h  x 0e0e?Rectangle 2  `0  m CFile I/O and Plotting Example  h R@%:?Text Box 4"@7  % read data into PDXprecip matrix load('PDXprecip.dat'); % copy first column of PDXprecip into month month = PDXprecip(:,1); % and second column into precip precip = PDXprecip(:,2); % plot precip vs. month with circles plot(month,precip,'o'); % add axis labels and plot title xlabel('month of the year'); ylabel('mean precipitation (inches)'); title('Mean monthly precipitation at Portland International Airport');($-!&!   h N%:?Rectangle 5"@? cAdapted from: http://web.cecs.pdx.edu/~gerry/MATLAB/plotting/loadingPlotData.html visited 15NOV2009dd C8Q  h Z$:@@?Rectangle 4 *2  Kfile_io_example.m   }ff___PPT10i. 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O% plot precip vs. month with circles plot(month,precip,'o',month,precip,'-r');*P(&* P A l T':?Rectangle 5"@ T %General Format: plot (x, y, fmt, ...)H& & N l R&:?Text Box 6"@   % copy first column of PDXtemperature into month month = PDXtemperature(:,1); % and second column into high_temp high_temp = PDXtemperature(:,2); % and third column into low temp low_temp = PDXtemperature(:,3); % and fourth column into avg temp avg = PDXtemperature(:,4); % generate the plot plot(month,high_temp,'ko',month,low_temp,'k+',month,avg, r-'); % add axis labels and plot title xlabel('Month'); ylabel('temperature (degrees F)'); title('Monthly average temperature for PDX'); % add a plot legend using labels read from the file legend('High','Low','Avg');W2  $ " " ! #   @ ! y 5   W  l N`#:?Rectangle 6< F multi_plot.m   }ff___PPT10. 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(2009, November 6). In Wikipedia, the free encyclopedia. Retrieved November 6, 2009, from http://en.wikipedia.org/wiki/Matlab Matlab tutorials: http://www.mathworks.com/academia/student_center/tutorials/launchpad.html GNU Octave. (2009, October 31). In Wikipedia, the free encyclopedia. Retrieved November 6, 2009, from http://en.wikipedia.org/wiki/GNU_Octave Octave main page: http://www.gnu.org/software/octave/ (http://octave.sourceforge.net/ access to pre-built installers) Octave tutorials: http://homepages.nyu.edu/~kpl2/dsts6/octaveTutorial.html, http://smilodon.berkeley.edu/octavetut.pdf FreeMat. http://freemat.sourceforge.net/index.html ftp://www.chabotcollege.edu/faculty/bmayer/ChabotEngineeringCourses/ENGR-25.htmZ\ZZZZ GJ# #(fdb#Ig'#38* )O8b88Ho888284^8_`8i8 @ }ff___PPT10i.e^>+D=' = @B +"m um U(    f x x?Rectangle 7i-   j*   _   rdOdO|?Rectangle 2   mJ    x x5%|?Rectangle 35 ,  m N    3380___PPT10.a`m um@U(    f@ x x?Rectangle 7i-   j*   _   rdOdO|?Rectangle 2   mJ   `a x x5%|?Rectangle 35 ,  m N    3380___PPT10.`00m um`U(    f x x?Rectangle 7i-   j*   _   rdOdO|?Rectangle 2   mJ   ` x x5%|?Rectangle 35 ,  m N    3380___PPT10.cm @8 (     rdOdO|?Rectangle 2   m.   ` x x5%|?Rectangle 35 ,  m 2   3380___PPT10.Y m @8 (     rdOdO|?Rectangle 2   m.     x x5%|?Rectangle 35 ,  m 2   3380___PPT10.`r<m (     rdOdO|?Rectangle 2   m   @ x x5%|?Rectangle 35 ,  m Note: format for creating a vector using the colon operator: start : increment : limit This allows you to specify the first element of the vector and the increment between elements of the vector, but not the number of elements. If the difference between the ending value divided by the increment is an integral value, then the limit value will be the last element in the vector created. If not, the ending value in the vector will be within (limit - increment). Thus, the colon operator method allows you to specify the first element and the interval spacing between elements, but not the number of elements. The format for creating a vector using the linspace method: linspace(start, limit, num_elem) The linspace method allows you to specify the first and last elements of the vector, but not the spacing between elements num_intervals == num_elem - 1 size_interval == (last_elem - first_elem)/num_intervals > " $m  U U ! W    3380___PPT10.H_ oO m @8 (     rdOdO|?Rectangle 2   m.   ': x x5%|?Rectangle 35 ,  m 2   3380___PPT10.d>!m @8 (     rdOdO|?Rectangle 2   m.   /: x x5%|?Rectangle 35 ,  m 2   3380___PPT10.d>"m @8  (     rdOdO|?Rectangle 2   m.   `/: x x5%|?Rectangle 35 ,  m 2   3380___PPT10.je L#m  @(     rdOdO|?Rectangle 2   m   @+: x x5%|?Rectangle 35 ,  m The algebraic transpose involves taking the complex conjugate transpose of a matrix. If the elements of the matrix are not complex, it results in the same thing as ( . ), the array transpose (which does not involve conjugation).   3380___PPT10. 8^$m @8` (     rdOdO|?Rectangle 2   m.    x x5%|?Rectangle 35 ,  m 2   3380___PPT10.`p`%m (     rdOdO|?Rectangle 2   m   f x x5%|?Rectangle 35 ,r  mZR___PPT94, pNote that distances vector and time vector must have the same length. In C, how would you do this? Create an array of distances and an array of speeds. Use a FOR loop to index the arrays and calculate the average speeds. Capture the speed and its index, compare to the next calculated speed, and hold the highest speed Print out the maximum speed and its index You can use a FOR loop in Matlab to essentially do the same thing, but using array operations like in this example is MUCH faster@d" d  3380___PPT10.ve)&m ~v^(     rdOdO|?Rectangle 2   ml    x x5%|?Rectangle 35 ,  m pLeft division is equivalent to inverting the matrix R, but does not actually take the inverse. The case for right division would have to have i as a row vector, [i1 i2 i3], R as = [1 -1 -1; 0 0 10e3; 0 10e3 0] , and V= [0 10 10] H<"'   3380___PPT10.H_ oO''m (     rdOdO|?Rectangle 2   m    x x5%|?Rectangle 35 ,  m _Left division is equivalent to inverting the matrix R, but does not actually take the inverse.  `  3380___PPT10.d>B(m (     rdOdO|?Rectangle 2   m   ` x x5%|?Rectangle 35 ,  m NDot products used often in vector mechanics: statics, dynamics, kinematics. Often used to find the component of a vector in a particular direction. Click on the vector diagram to go to an example showing the dot product in more detail. sum() is a built-in function that will sum the elements of the vector passed to it as an argument.$O O  3380___PPT10.H_ oO&)m  (     rdOdO|?Rectangle 2   m   a x x5%|?Rectangle 35 ,  m ^Left division is equivalent to inverting the matrix R, but does not actually take the inverse. _  3380___PPT10.H_ oO*m d\@D(     rdOdO|?Rectangle 2   mR   @b x x5%|?Rectangle 35 ,  m VTry x = sin(0:0.1*pi : 2*pi)   3380___PPT10.eP+m 80`(     rdOdO|?Rectangle 2   m&   b x x5%|?Rectangle 35 ,  m *For v=sin([0: 0.01*pi: 2*pi] ), I get Vrms=0.7053 For v=sin([0: 0.001*pi: 2*pi] ), I get Vrms=0.7069 Exact answer=0.7071 y  3380___PPT10.pfPra,m kcK(     rdOdO|?Rectangle 2   mY   c x x5%|?Rectangle 35 ,  m ]function rmsout=rms2(v) %rms Root Mean Square %rms(v) returns the root mean square of the elements of %a column vector v. If v is a matrix, then rms(v) returns %a row vector such that each element is the root mean square %of the elements in the corresponding column of v. vs=v.^2; s=size(v); rmsout=sqrt(sum(vs,1)/s(1)); % sum(X, 1) sums down each column Pseudocode: Test for size of v if > 2, print error message else if row vector transpose calculate rmsbd !*d ! *  3380___PPT10.pfPran-m (     rdOdO|?Rectangle 2   m   `c x x5%|?Rectangle 35 ,  m bData file PDXprecip.dat from: http://web.cecs.pdx.edu/~gerry/MATLAB/plotting/loadingPlotData.html   L8   3380___PPT10.ufP4Ue.m @8 (     rdOdO|?Rectangle 2   m.   c x x5%|?Rectangle 35 ,  m 2   3380___PPT10._< 4 /m (     rdOdO|?Rectangle 2   m    d x x5%|?Rectangle 35 ,  m lIf more than one argument is given, they are interpreted as plot (x, y, fmt, ...) or as plot (x, y, property, value, ...) where y, fmt, property and value are optional, and any number of argument sets may appear. 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Part 2The Plan for TodayLearning Objectives Last LectureArrays, Vectors, and MatricesColon Operator vs. linspace()Review of length() and size()Review of Array ManipulationMore Array ManipulationMatrix and Array Arithmetic%Matrix and Array Arithmetic ExamplesArray OperationsCircuit Analysis EquationsCircuit Analysis SolutionDot Product Example!Dot Product Function DevelopmentDot Product Function in M/O/FReview of Functions&Root Mean-Square Function Development)Root Mean-Square Function Implementation&More Robust Root Mean-Square FunctionFile I/O with M/O/FFile I/O with M/O/F, cont.File I/O and Plotting ExampleMore on PlottingVector Dot Product ExampleReview References  Fonts UsedThemeEmbedded OLE Servers Slide Titlest(PXl _PID_HLINKSVersionA "304,24,Vector Dot Product Example 367,11,Matlab/Octave Basics - 9Fhttp://web.cecs.pdx.edu/~gerry/MATLAB/plotting/examples/PDXprecip.datDhttp://web.cecs.pdx.edu/~gerry/MATLAB/plotting/loadingPlotData.html$http://en.wikipedia.org/wiki/MatlabJhttp://www.mathworks.com/academia/student_center/tutorials/launchpad.html(http://en.wikipedia.org/wiki/GNU_Octave$http://www.gnu.org/software/octave/http://octave.sourceforge.net/9http://homepages.nyu.edu/~kpl2/dsts6/octaveTutorial.html+http://smilodon.berkeley.edu/octavetut.pdfPftp://www.chabotcollege.edu/faculty/bmayer/ChabotEngineeringCourses/ENGR-25.htm*http://freemat.sourceforge.net/index.htmlPftp://www.chabotcollege.edu/faculty/bmayer/ChabotEngineeringCourses/ENGR-25.htm"304,24,Vector Dot Product ExampleDhttp://web.cecs.pdx.edu/~gerry/MATLAB/plotting/loadingPlotData.html 367,11,Matlab/Octave Basics - 9$http://en.wikipedia.org/wiki/MatlabJhttp://www.mathworks.com/academia/student_center/tutorials/launchpad.html(http://en.wikipedia.org/wiki/GNU_Octave$http://www.gnu.org/software/octave/http://octave.sourceforge.net/9http://homepages.nyu.edu/~kpl2/dsts6/octaveTutorial.html+http://smilodon.berkeley.edu/octavetut.pdfPftp://www.chabotcollege.edu/faculty/bmayer/ChabotEngineeringCourses/ENGR-25.htm*http://freemat.sourceforge.net/index.htmlPftp://www.chabotcollege.edu/faculty/bmayer/ChabotEngineeringCourses/ENGR-25.htmFhttp://web.cecs.pdx.edu/~gerry/MATLAB/plotting/examples/PDXprecip.dat_n8BuffBuff  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~    Root EntrydO)Picturese=Current UserSummaryInformation(4PowerPoint Document(DocumentSummaryInformation8T