david/ECE_456_Reports
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

commit

Browse Source
This commit is contained in:
pkirwin 2021-03-01 15:43:09 -07:00
parent c046bc1b64
commit e55e364adc
6 changed files with 53 additions and 24 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

19
PS2/doc.fdb_latexmk
View File

@ -1,8 +1,8 @@
# Fdb version 3 # Fdb version 3
["pdflatex"] 1614637883 "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf" "doc" 1614637886 ["pdflatex"] 1614638543 "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf" "doc" 1614638561
"C:/Users/speed/AppData/Local/MiKTeX/fonts/pk/ljfour/jknappen/ec/dpi600/tcrm1000.pk" 1614620319 11548 693fc704971bedc6e913b37b081cf40e "" "C:/Users/speed/AppData/Local/MiKTeX/fonts/pk/ljfour/jknappen/ec/dpi600/tcrm1000.pk" 1614620319 11548 693fc704971bedc6e913b37b081cf40e ""
"C:/Users/speed/AppData/Local/MiKTeX/miktex/data/le/pdftex/pdflatex.fmt" 1612675286 9293900 83195ab665706b6f706823352908aa95 "" "C:/Users/speed/AppData/Local/MiKTeX/miktex/data/le/pdftex/pdflatex.fmt" 1612675286 9293900 83195ab665706b6f706823352908aa95 ""
"C:/Users/speed/AppData/Local/MiKTeX/pdftex/config/pdftex.map" 1614626913 80909 eab91d9745dd2edfd62a31d53cd5fe15 "" "C:/Users/speed/AppData/Local/MiKTeX/pdftex/config/pdftex.map" 1614638559 80909 eab91d9745dd2edfd62a31d53cd5fe15 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/jknappen/ec/tcrm1000.tfm" 993058908 1436 c7f957a372ef2fbe93c0982f96625e12 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/jknappen/ec/tcrm1000.tfm" 993058908 1436 c7f957a372ef2fbe93c0982f96625e12 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1233951848 1004 54797486969f23fa377b128694d548df "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1233951848 1004 54797486969f23fa377b128694d548df ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1233951848 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1233951848 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 ""
@ -43,7 +43,9 @@
"C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr7.pfb" 1247593067 32762 7fee39e011c23b3589931effd97b9702 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr7.pfb" 1247593067 32762 7fee39e011c23b3589931effd97b9702 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr9.pfb" 1247593066 33993 9b89b85fd2d9df0482bd47194d1d3bf3 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr9.pfb" 1247593066 33993 9b89b85fd2d9df0482bd47194d1d3bf3 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1247593067 32569 5e5ddc8df908dea60932f3c484a54c0d "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1247593067 32569 5e5ddc8df908dea60932f3c484a54c0d ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy7.pfb" 1247593066 32716 08e384dc442464e7285e891af9f45947 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmti10.pfb" 1247593067 37944 359e864bd06cde3b1cf57bb20757fb06 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmti10.pfb" 1247593067 37944 359e864bd06cde3b1cf57bb20757fb06 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/latxfont/line10.pfb" 1247593053 11493 4f5ed183a47d3197cf8cd322325db6de ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/context/base/mkii/supp-pdf.mkii" 1580390158 71627 94eb9990bed73c364d7f53f960cc8c5b "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/context/base/mkii/supp-pdf.mkii" 1580390158 71627 94eb9990bed73c364d7f53f960cc8c5b ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/generic/iftex/iftex.sty" 1583523400 6501 4011d89d9621e0b0901138815ba5ff29 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/generic/iftex/iftex.sty" 1583523400 6501 4011d89d9621e0b0901138815ba5ff29 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/generic/iftex/ifvtex.sty" 1583523400 1057 525c2192b5febbd8c1f662c9468335bb "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/generic/iftex/ifvtex.sty" 1583523400 1057 525c2192b5febbd8c1f662c9468335bb ""
@ -61,6 +63,7 @@
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/base/article.cls" 1610120746 20145 aad8c3dd3bc36e260347b84002182bc2 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/base/article.cls" 1610120746 20145 aad8c3dd3bc36e260347b84002182bc2 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/base/omscmr.fd" 1610120746 2470 59e43b502a8bea3a12f4954945302e40 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/base/omscmr.fd" 1610120746 2470 59e43b502a8bea3a12f4954945302e40 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/base/size10.clo" 1610120746 8449 a72d5d4e612221b46000c3d71724e0ef "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/base/size10.clo" 1610120746 8449 a72d5d4e612221b46000c3d71724e0ef ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/cancel/cancel.sty" 1388370247 7592 dd751af313a16a0308545d5bfd7aaaa2 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/caption/caption.sty" 1603736996 51746 e89c4da670ba533e6ab38e045ce6d1d9 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/caption/caption.sty" 1603736996 51746 e89c4da670ba533e6ab38e045ce6d1d9 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/caption/caption3.sty" 1603736996 67929 d50ae850e1d9604065e8337a75a41029 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/caption/caption3.sty" 1603736996 67929 d50ae850e1d9604065e8337a75a41029 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/caption/subcaption.sty" 1603736996 6133 46bea384e36e9b74bd53a238fc2d0654 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/caption/subcaption.sty" 1603736996 6133 46bea384e36e9b74bd53a238fc2d0654 ""
@ -93,15 +96,15 @@
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/parskip/parskip.sty" 1592833306 4414 25631f9679adf750bac898538ededd61 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/parskip/parskip.sty" 1592833306 4414 25631f9679adf750bac898538ededd61 ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/setspace/setspace.sty" 1324294077 22913 a27d7908fc6f0385466454a966a316eb "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/setspace/setspace.sty" 1324294077 22913 a27d7908fc6f0385466454a966a316eb ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/titlesec/titlesec.sty" 1571240058 48596 2b6a95da931c07a430b1a61904aaa42d "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/titlesec/titlesec.sty" 1571240058 48596 2b6a95da931c07a430b1a61904aaa42d ""
"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.aux" 1614637886 334 906353ae3fc5daad100ce8b921730ac7 "" "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.aux" 1614638561 334 906353ae3fc5daad100ce8b921730ac7 ""
"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" 1614637882 10279 f262bef4de2ea276f6d0acd4c1d77d63 "" "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" 1614638542 10889 00e896f1f98c88bd40320d9e83a777cb ""
"doc.aux" 1614637886 334 906353ae3fc5daad100ce8b921730ac7 "pdflatex" "doc.aux" 1614638561 334 906353ae3fc5daad100ce8b921730ac7 "pdflatex"
"doc.tex" 1614637882 10279 f262bef4de2ea276f6d0acd4c1d77d63 "" "doc.tex" 1614638542 10889 00e896f1f98c88bd40320d9e83a777cb ""
"q1a_1and50.png" 1614636283 34155 72f34c6abf061325ae1f162db0ffd06b "" "q1a_1and50.png" 1614636283 34155 72f34c6abf061325ae1f162db0ffd06b ""
"q1a_eigenvals.png" 1614637266 23078 9c99a5505761d0b964e665e35fd9c02a "" "q1a_eigenvals.png" 1614637266 23078 9c99a5505761d0b964e665e35fd9c02a ""
(generated) (generated)
"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf"
"doc.log"
"doc.pdf" "doc.pdf"
"doc.log"
"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf"
"doc.aux" "doc.aux"
"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.log" "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.log"

15
PS2/doc.fls
View File

@ -416,6 +416,17 @@ INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\enumitem\enumitem.s
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\enumitem\enumitem.sty INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\enumitem\enumitem.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\enumitem\enumitem.sty INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\enumitem\enumitem.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\enumitem\enumitem.sty INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\enumitem\enumitem.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\cancel\cancel.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\lstlang1.sty INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\lstlang1.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\lstlang1.sty INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\lstlang1.sty
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\lstlang1.sty INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\tex\latex\listings\lstlang1.sty
@ -534,5 +545,9 @@ INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\c
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmr9.pfb INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmr9.pfb
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmsy10.pfb INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmsy10.pfb
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmsy10.pfb INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmsy10.pfb
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmsy7.pfb
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmsy7.pfb
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmti10.pfb INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmti10.pfb
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmti10.pfb INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmti10.pfb
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\latxfont\line10.pfb
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\latxfont\line10.pfb

18
PS2/doc.log
View File

@ -1,4 +1,4 @@
This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 21.1) (preloaded format=pdflatex 2021.2.6) 1 MAR 2021 15:31 This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 21.1) (preloaded format=pdflatex 2021.2.6) 1 MAR 2021 15:42
entering extended mode entering extended mode
**d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex **d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex
(d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex (d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex
@ -230,6 +230,8 @@ Package: enumitem 2019/06/20 v3.9 Customized lists
\enit@inbox=\box55 \enit@inbox=\box55
\enit@count@id=\count281 \enit@count@id=\count281
\enitdp@description=\count282 \enitdp@description=\count282
) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/cancel\cancel.sty
Package: cancel 2013/04/12 v2.2 Cancel math terms
) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/listings\lstlang1.sty ) (C:\Users\speed\AppData\Local\Programs\MiKTeX\tex/latex/listings\lstlang1.sty
File: lstlang1.sty 2020/03/24 1.8d listings language file File: lstlang1.sty 2020/03/24 1.8d listings language file
) (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux) ) (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux)
@ -332,17 +334,17 @@ Package pdftex.def Info: q1a_eigenvals.png used on input line 163.
(pdftex.def) Requested size: 202.3529pt x 151.76526pt. (pdftex.def) Requested size: 202.3529pt x 151.76526pt.
[3 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1a_1and50.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1a_eigenvals.png (PNG copy)>] [4] [5] [6] [7] [8] (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux) ) [3 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1a_1and50.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1a_eigenvals.png (PNG copy)>] [4] [5] [6] [7] [8] (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux) )
Here is how much of TeX's memory you used: Here is how much of TeX's memory you used:
8302 strings out of 479618 8334 strings out of 479618
124686 string characters out of 2865027 125207 string characters out of 2865027
980964 words of memory out of 3000000 981750 words of memory out of 3000000
25370 multiletter control sequences out of 15000+200000 25398 multiletter control sequences out of 15000+200000
413212 words of font info for 65 fonts, out of 3000000 for 9000 413212 words of font info for 65 fonts, out of 3000000 for 9000
1141 hyphenation exceptions out of 8191 1141 hyphenation exceptions out of 8191
68i,12n,75p,1278b,2408s stack positions out of 5000i,500n,10000p,200000b,50000s 68i,12n,75p,1278b,2408s stack positions out of 5000i,500n,10000p,200000b,50000s
<C:\Users\speed\AppData\Local\MiKTeX\fonts/pk/ljfour/jknappen/ec/dpi600\tcrm1000.pk><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmbx10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmbx12.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmex10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi9.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr12.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr17.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr5.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr9.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmti10.pfb> <C:\Users\speed\AppData\Local\MiKTeX\fonts/pk/ljfour/jknappen/ec/dpi600\tcrm1000.pk><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmbx10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmbx12.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmex10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi9.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr12.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr17.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr5.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr9.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmti10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/latxfont/line10.pfb>
Output written on d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.pdf (8 pages, 234173 bytes). Output written on d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.pdf (8 pages, 248293 bytes).
PDF statistics: PDF statistics:
93 PDF objects out of 1000 (max. 8388607) 101 PDF objects out of 1000 (max. 8388607)
0 named destinations out of 1000 (max. 500000) 0 named destinations out of 1000 (max. 500000)
11 words of extra memory for PDF output out of 10000 (max. 10000000) 11 words of extra memory for PDF output out of 10000 (max. 10000000)

BIN
PS2/doc.pdf
View File

Binary file not shown.

BIN
PS2/doc.synctex.gz
View File

Binary file not shown.

25
PS2/doc.tex
View File

@ -14,8 +14,8 @@
\usepackage{fancyhdr} \usepackage{fancyhdr}
\usepackage{titlesec} \usepackage{titlesec}
\usepackage{lipsum} \usepackage{lipsum}
\usepackage{enumitem} \usepackage{enumitem}
\usepackage{cancel}
\titleformat{\subsection}[runin]{\normalfont \large \bfseries} \titleformat{\subsection}[runin]{\normalfont \large \bfseries}
{\thesubsection}{1em}{} {\thesubsection}{1em}{}
@ -171,29 +171,30 @@ legend({'Numerical','Analytical'},'Location','northwest');
The analytical solution is The analytical solution is
\begin{equation} \begin{equation}
\Phi(x) = A sin \left( \frac{n \pi}{L} x \right) \phi(x) = A sin \left( \frac{n \pi}{L} x \right)
\label{eq:analytical} \label{eq:analytical}
\end{equation} \end{equation}
In order to normalise this equation it must conform to the following: In order to normalise this equation it must conform to the following:
\begin{equation} \begin{equation}
\int_{0}^{L} \left| \Phi(x) \right| ^2 dx = 1 \int_{0}^{L} \left| \phi(x) \right| ^2 dx = 1.
\label{eq:normalise} \label{eq:normalise}
\end{equation} \end{equation}
Using the following identity: We use the following identity:
\begin{equation} \begin{equation}
foo \int\sin^2{(\alpha x)}\:dx = \frac{1}{2} x -\frac{1}{4\alpha}\sin{(2\alpha x)}.
\label{eq:integral_ident} \label{eq:integral_ident}
\end{equation} \end{equation}
Given that $sin$ of a real value is always real, we can disregard the norm operation, and directly relate to the above identity. Given that $sin$ of a real value is always real, we can disregard the norm operation, and directly relate (\ref{eq:analytical})
to the above identity.
Evaluating the integral gives us the following relationship Evaluating the integral gives us the following relationship
\begin{equation*} \begin{equation*}
\frac{1}{A^2} = \frac{1}{2} L - \frac{L}{4n \pi} sin \left( \frac{2n \pi}{L} L \right) - \frac{1}{2} \cdot 0 + \frac{L}{4n \pi} sin(0) \frac{1}{A^2} = \frac{1}{2} L - \cancel{\frac{L}{4n \pi} sin \left( \frac{2n \pi}{L} L \right)} - \cancel{\frac{1}{2} \cdot 0} + \cancel{\frac{L}{4n \pi} sin(0)}
\end{equation*} \end{equation*}
From this, we find: From this, we find:
@ -224,7 +225,15 @@ legend({'Numerical','Analytical'},'Location','northwest');
\item %1c \item %1c
\begin{enumerate}[align=left,leftmargin=*,labelsep=0em,label=(\roman*)] \begin{enumerate}[align=left,leftmargin=*,labelsep=0em,label=(\roman*)]
\item %1ci \item %1ci
\lipsum[1]
From the base form of $\phi _\ell = Bsin \left( \frac {n \pi}{L} a \ell \right)$, we can see that
$\phi _ {\ell + 1}$ and $\phi _ {\ell - 1}$ correspond to the trigonometric identities
$sin(\alpha + B) = sin(\alpha)cos(B) + cos(\alpha)sin(B)$ and
$sin(\alpha + B) = sin(\alpha)cos(B) + cos(\alpha)sin(B)$, respectively, where
$\alpha = \frac{n \pi \alpha \ell}{L}$ and $B = \frac{n \pi \ell}{L}$.
Fro
\item %1cii \item %1cii
\lipsum[1] \lipsum[1]
\item %1ciii \item %1ciii