MATH348 Advanced Engineering Mathematics

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==Instructor Information ==
 
==Instructor Information ==
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Instructor : [http://www.mines.edu/~sstrong Scott Strong]
 
  
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Office : [http://www.mines.edu/csm_maps/buildings/ChauvenetHall/ Chauvenet Hall 266]
 
  
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Office Phone : 303.384.2446
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==Textbook Information==
  
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email : math348@gmail.com
 
  
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*[[MATH-348 Advanced Engineering Mathematics - Textbook Usage |MATH 348 : Advanced Engineering Mathematics - Textbook Usage ]]
  
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==Textbook Information==
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I do not require a textbook for this course as the lecture notes should suffice. However, owning a post Calc/DiffEQ textbook may be useful. I provide some options below.
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===Kreyszig Abridged edition===
  
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The bookstore sells an abridged version of the following text. The abridged version contains the seven chapters and an appendix:
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The bookstore sells an abridged version of the Kreyszig text, which is now in its tenth edition -- all previous CSM abridged editions will be acceptable for this course. The abridged version contains the seven chapters and an appendix:
  
 
1. Chapter 5: Power Series Solutions to ODE and [http://en.wikipedia.org/wiki/Frobenius_method Frobenius method]
 
1. Chapter 5: Power Series Solutions to ODE and [http://en.wikipedia.org/wiki/Frobenius_method Frobenius method]
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While this will meet out needs, if you plan to continue in mathematics for a [http://mcs.mines.edu/Academic_Programs/mathminor.shtml minor] or [http://mcs.mines.edu/Academic_Programs/mathminor.shtml area of special interest] or seek an [http://engineering.mines.edu/graduate-program/5year/ advanced degree in your field] then you are advised to get the unabridged edition. [http://math348.wordpress.com/2011/08/20/i-never-work-a-day-in-my-life-i-just-lay-back-and-let-the-big-beat-lead-me/ Older editions are fine and relatively cheap from online retailers.]
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While this will meet out needs, if you plan to continue in mathematics for a [http://mcs.mines.edu/Degrees/math_minor_asi.php minor] or [http://mcs.mines.edu/Degrees/math_minor_asi.php area of special interest] or seek an [http://engineering.mines.edu/graduate-program/5year/ advanced degree in your field] then you are advised to get the unabridged edition.  
  
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*[http://www.amazon.com/Schaums-Advanced-Mathematics-Engineers-Scientists/dp/0071635408/ref=sr_1_4?s=books&ie=UTF8&qid=1326152552&sr=1-4 Schaums Outline Series - Advanced Mathematics for Engineers and Scientists.] There is a lot of overlap between this book and what we will cover.
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===Texts on Fourier Analysis===
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The following are some texts that you may want to consider for study of Fourier "Analysis" (AKA Fourier methods.)
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*[http://www.amazon.com/Fourier-Dover-Mathematics-Georgi-Tolstov/dp/0486633179/ref=pd_sim_b_3 Fourier Series by Tolstov and published by Dover]
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*[http://www.amazon.com/Schaums-Analysis-Applications-Boundary-Problems/dp/0070602190/ref=sr_1_1?s=books&ie=UTF8&qid=1326152160&sr=1-1 Schaum's Outline of Fourier Analysis with Applications to Boundary Value Problems]
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*[http://www.amazon.com/Schaums-Outline-Signals-Systems-Second/dp/007163472X/ref=sr_1_1?s=books&ie=UTF8&qid=1326152246&sr=1-1 Schaum's Outline of Signals and Systems, Second Edition]
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*[http://www.amazon.com/Schaums-Outline-Digital-Signal-Processing/dp/0071635092/ref=sr_1_2?s=books&ie=UTF8&qid=1326152246&sr=1-2 Schaums Outline of Digital Signal Processing, 2nd Edition (Schaum's Outline Series)]
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===Texts on PDE===
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The following are some texts that you may want to consider for study of linear PDE.
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*[http://www.amazon.com/Differential-Equations-Scientists-Engineers-Mathematics/dp/048667620X/ref=sr_1_1?s=books&ie=UTF8&qid=1326151805&sr=1-1 PDE for Scientists and Engineers Dover Text]
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*[http://www.amazon.com/Schaums-Outline-Partial-Differential-Equations/dp/0071756183/ref=sr_1_1?s=books&ie=UTF8&qid=1326152187&sr=1-1 Schaum's Outline of Partial Differential Equations (Schaum's Outline Series) ]
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*[http://www.amazon.com/Applied-Partial-Differential-Equations-4th/dp/0130652431 Applied PDE by Richard Haberman] This is the text used for MATH455-PDE, if you are considering a minor then you will be able to use it twice.
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===Texts on Linear Algebra===
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The following are some texts that you may want to consider for study of linear algebra.
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*[http://www.amazon.com/Linear-Algebra-Its-Applications-4th/dp/0321385179/ref=sr_1_1?s=books&ie=UTF8&qid=1326151883&sr=1-1 Linear Algebra by David C. Lay] This text used for MATH332-Linear Algebra, if you are considering a minor then you will be able to use it twice.
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*[http://www.amazon.com/Schaums-Outline-Linear-Algebra-Fourth/dp/007154352X/ref=sr_1_1?s=books&ie=UTF8&qid=1326152151&sr=1-1 Schaum's Outline of Linear Algebra Fourth Edition]
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*[http://www.amazon.com/Matrices-Linear-Algebra-Dover-Mathematics/dp/0486660141/ref=sr_1_1?s=books&ie=UTF8&qid=1326152331&sr=1-1 Matrices and Linear Algebra (Dover Books on Mathematics)]
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*[http://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X/ref=sr_1_2?s=books&ie=UTF8&qid=1326152331&sr=1-2 Linear Algebra (Dover Books on Mathematics - Mature)]
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===Continued use of your Differential Equations (MATH225) text===
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[http://www.cengagebrain.com/shop/en/US/storefront/US;CMGTJSESSIONID=hQZwPLyMtQY9XpyjpGq70Fz2c8pdlgcWD8yJ5pJGDxdHkN2bK22L!-1525080620!180763908?cmd=catProductDetail&gclid=CMG5-bO6xK0CFQ1ahwod-WTzBA&entryPoint=storefront&cid=CJ5&ISBN=9780495108368&messageType=catProductDetail Your MATH225 differential equations text] was chosen, partially, so that you could use it for topics in this course. The following will outline how the chapters in Differential Equations by Zill and Cullen matches up with AEM material.
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<ol>
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<li> First task is to review some concepts in ODE. Specifically, we will need to remember/learn how to: </li>
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  <ul>
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  <li>Constant Linear Problems: 4.3</li>
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  <li> Undetermined Coefficients: 4.4 </li>
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  <li> Variation of Parameters: 4.6 - this was likely not covered in your course, we will cover it in a homework problem.</li>
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  <li> Mass-spring Problems: 5.1 </li>
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  <li> Series Solutions to Linear Equations: 6.1 </li>
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  <li> Bessel's Equation: 6.3.1 </li>
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  <li> Boundary Value Problems and Sturm-Liouville Problems: 5.2 (example 2) and to some extend chapter 12-13 although this will come later with PDE, 11.4 (example 1) </li>
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  </ul>
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<li> Fourier Series: 11.1-11.3 </li>
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<li> Fourier integral/transforms: 14.3-14.4</li>
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<li> Linear Partial Differential Equations: Chapter 12 and Chapter 13 </li>
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<li> Linear Algebra: Appendix II, we will actually need far more than this appendix will cover but it will be a good start. </li>
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</ol>
  
 
=Course Materials=
 
=Course Materials=
  
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The following outlines materials specific to this course. The materials, as indicated, have been developed over time and have achieved a steady-state. An archive of [[MATH-348 Advanced Engineering Mathematics - Archive | older ticc pages ]] is available. There is also a binder available in the library of practically everything ever done since Fall 2006. The ticc websites pick up at Spring 2008 when I started presenting linear algebra first.   
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The following outlines materials specific to this course. The materials, as indicated, have been developed over time and have achieved a steady-state. An archive of [[MATH-348 Advanced Engineering Mathematics - Archive | older ticc pages ]] is available. The ticc websites pick up at Spring 2008 when I started presenting linear algebra first.   
  
 
==Syllabus==
 
==Syllabus==
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{{PDF Table Item|filename=AMath348syllabusF11.pdf | title=MATH348.Syllabus}}
 
  
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==Lecture Slides==
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==Lecture Pictures==
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This semester, Spring 2012, I will try to take pictures of the boards before I scrub them. One word of warning, these are not a substitute for lecture itself. The interactions and development are often important in understanding the material.
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===Spring 2012===
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[https://picasaweb.google.com/104969599060487036456/January112012?authuser=0&feat=directlink 1.11.2012], [https://picasaweb.google.com/104969599060487036456/January132012?authuser=0&feat=directlink 1.13.2012], [https://picasaweb.google.com/104969599060487036456/January162012?authuser=0&feat=directlink 1.16.2012], [https://picasaweb.google.com/104969599060487036456/January182012?authuser=0&feat=directlink 1.18.2012],[https://picasaweb.google.com/104969599060487036456/January202012?authuser=0&feat=directlink 1.20.2012], [https://picasaweb.google.com/104969599060487036456/January232012?authuser=0&feat=directlink 1.23.2012], [https://picasaweb.google.com/104969599060487036456/January252012?authuser=0&feat=directlink 1.25.2012],[https://picasaweb.google.com/104969599060487036456/January272012?authuser=0&feat=directlink 1.27.2012], [https://picasaweb.google.com/104969599060487036456/January302012?authuser=0&feat=directlink 1.30.2012], [https://picasaweb.google.com/104969599060487036456/February62012?authuser=0&feat=directlink 2.6.2012], [https://picasaweb.google.com/104969599060487036456/February82012?authuser=0&feat=directlink 2.8.2012], [https://picasaweb.google.com/104969599060487036456/February102012?authuser=0&feat=directlink 2.10.2012], [https://picasaweb.google.com/104969599060487036456/February132012?authuser=0&feat=directlink 2.13.2012], [https://picasaweb.google.com/104969599060487036456/February15201202?authuser=0&feat=directlink 2.15.2012], [https://picasaweb.google.com/104969599060487036456/February172012?authuser=0&feat=directlink 2.17.2012]. [https://picasaweb.google.com/104969599060487036456/February222012?authuser=0&feat=directlink 2.22.2012], [https://picasaweb.google.com/104969599060487036456/February242012?authuser=0&feat=directlink 2.24.2012], [https://picasaweb.google.com/104969599060487036456/February272012?authuser=0&feat=directlink 2.27.2012],[https://picasaweb.google.com/104969599060487036456/February292012?authuser=0&feat=directlink 2.29.2012], [https://picasaweb.google.com/104969599060487036456/March22012?authuser=0&feat=directlink 3.2.2012], [https://picasaweb.google.com/104969599060487036456/March62012?authuser=0&feat=directlink 3.5.2012], [https://picasaweb.google.com/104969599060487036456/March82012?authuser=0&feat=directlink 3.7.2012], [https://picasaweb.google.com/104969599060487036456/March192012?authuser=0&feat=directlink 3.19.2012], [https://picasaweb.google.com/104969599060487036456/March212012?authuser=0&feat=directlink 3.21.2012],[https://picasaweb.google.com/104969599060487036456/March232012?authuser=0&feat=directlink 3.23.2012], [https://picasaweb.google.com/104969599060487036456/March262012?authuser=0&feat=directlink 3.26.2012], [https://picasaweb.google.com/104969599060487036456/March282012?authuser=0&feat=directlink 3.28.2012], [https://picasaweb.google.com/104969599060487036456/April22012?authuser=0&feat=directlink 4.2.2012], [https://picasaweb.google.com/104969599060487036456/April42012?authuser=0&feat=directlink 4.4.2012], [https://picasaweb.google.com/104969599060487036456/April62012?authuser=0&feat=directlink 4.7.2012],
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[https://picasaweb.google.com/104969599060487036456/April92012?authuser=0&feat=directlink 4.9.2012], [https://picasaweb.google.com/104969599060487036456/April112012?authuser=0&feat=directlink 4.11.2012], [https://picasaweb.google.com/104969599060487036456/April132012?authuser=0&feat=directlink 4.13.2012], [https://picasaweb.google.com/104969599060487036456/April162012?authuser=0&feat=directlink 4.16.2012], [https://picasaweb.google.com/104969599060487036456/April202012?authuser=0&feat=directlink 4.20.2012], [https://picasaweb.google.com/104969599060487036456/April232012?authuser=0&feat=directlink 4.23.2012],
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[https://picasaweb.google.com/104969599060487036456/April252012?authuser=0&feat=directlink 4.25.2012], [https://picasaweb.google.com/104969599060487036456/April272012?authuser=0&feat=directlink 4.27.2012],
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[https://picasaweb.google.com/104969599060487036456/April302012?authuser=0&feat=directlink 4.30.2012], [https://picasaweb.google.com/104969599060487036456/May22012?authuser=0&feat=directlink 5.2.2012]
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===Fall 2012===
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[https://picasaweb.google.com/104969599060487036456/August222012?authuser=0&feat=directlink 8.22.2012], [https://picasaweb.google.com/104969599060487036456/August242012?authuser=0&feat=directlink 8.24.2012], [https://picasaweb.google.com/104969599060487036456/August272012?authuser=0&feat=directlink 8.27.2012], [https://picasaweb.google.com/104969599060487036456/August292012?authuser=0&feat=directlink 8.29.2012],[https://picasaweb.google.com/104969599060487036456/August312012?authuser=0&feat=directlink 8.31.2012], [https://picasaweb.google.com/104969599060487036456/September32012?authuser=0&feat=directlink 9.3.2012], [https://picasaweb.google.com/104969599060487036456/September52012?authuser=0&feat=directlink 9.5.2012], [https://picasaweb.google.com/104969599060487036456/September72012?authuser=0&feat=directlink 9.7.2012], [https://picasaweb.google.com/104969599060487036456/September102012?authuser=0&feat=directlink 9.10.2012],[https://picasaweb.google.com/104969599060487036456/September122012?authuser=0&feat=directlink 9.12.2012], [https://picasaweb.google.com/104969599060487036456/September142012?authuser=0&feat=directlink 9.14.2012], [https://dl.dropbox.com/u/31308033/9.17.2012.pdf 9.17.2012], [https://picasaweb.google.com/104969599060487036456/September192012?authuser=0&feat=directlink 9.19.2012],
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[https://picasaweb.google.com/104969599060487036456/September212012?authuser=0&feat=directlink 9.21.2012],
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[https://picasaweb.google.com/104969599060487036456/September242012?authuser=0&feat=directlink 9.24.2012],
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[https://picasaweb.google.com/104969599060487036456/September262012?authuser=0&feat=directlink 9.26.2012],
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[https://picasaweb.google.com/104969599060487036456/September282012?authuser=0&feat=directlink 9.28.2012],
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[https://picasaweb.google.com/104969599060487036456/October12012?authuser=0&feat=directlink 10.1.2012],
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[https://picasaweb.google.com/104969599060487036456/October32012?authuser=0&feat=directlink 10.3.2012],
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[https://picasaweb.google.com/104969599060487036456/October52012?authuser=0&feat=directlink 10.5.2012],
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[https://picasaweb.google.com/104969599060487036456/October82012?authuser=0&feat=directlink 10.8.2012],
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[https://picasaweb.google.com/104969599060487036456/October102012?authuser=0&feat=directlink 10.10.2012],
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[https://picasaweb.google.com/104969599060487036456/October122012?authuser=0&feat=directlink 10.12.2012],
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[https://picasaweb.google.com/104969599060487036456/October192012?authuser=0&feat=directlink 10.19.2012],
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[https://picasaweb.google.com/104969599060487036456/October222012?authuser=0&feat=directlink 10.22.2012],
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[https://picasaweb.google.com/104969599060487036456/October242012?authuser=0&feat=directlink 10.24.2012],
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[https://picasaweb.google.com/104969599060487036456/October292012?authuser=0&feat=directlink 10.29.2012],
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[https://picasaweb.google.com/104969599060487036456/October312012?authuser=0&feat=directlink 10.31.2012],
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[https://picasaweb.google.com/104969599060487036456/November22012?authuser=0&feat=directlink 11.2.2012],
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[https://picasaweb.google.com/104969599060487036456/November52012?authuser=0&feat=directlink 11.5.2012],
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[https://picasaweb.google.com/104969599060487036456/November72012?authuser=0&feat=directlink 11.7.2012],
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[https://picasaweb.google.com/104969599060487036456/November92012?authuser=0&feat=directlink 11.9.2012],
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[https://picasaweb.google.com/104969599060487036456/November122012?authuser=0&authkey=Gv1sRgCIWXycSF0ZWpRw&feat=directlink 11.12.2012],
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[https://picasaweb.google.com/104969599060487036456/November142012?authuser=0&feat=directlink 11.14.2012],
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[https://picasaweb.google.com/104969599060487036456/November162012?authuser=0&feat=directlink 11.16.2012],
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[https://picasaweb.google.com/104969599060487036456/November192012?authuser=0&feat=directlink 11.19.2012],
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[https://picasaweb.google.com/104969599060487036456/Novebmer262012?authuser=0&feat=directlink 11.26.2012],
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[https://picasaweb.google.com/104969599060487036456/November302012?authuser=0&feat=directlink 11.30.2012],
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[https://picasaweb.google.com/104969599060487036456/December32012?authuser=0&feat=directlink 12.3.2012],
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[https://picasaweb.google.com/104969599060487036456/December52012?authuser=0&feat=directlink 11.5.2012]
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===Spring 2013===
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[https://picasaweb.google.com/104969599060487036456/January92013?authuser=0&feat=directlink 1.9.2013], [https://picasaweb.google.com/104969599060487036456/January112013?authuser=0&feat=directlink 1.11.2013], [https://picasaweb.google.com/104969599060487036456/January142013?authuser=0&feat=directlink 1.14.2013],
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[https://picasaweb.google.com/104969599060487036456/January162013?authuser=0&feat=directlink 1.16.2013],
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[https://picasaweb.google.com/104969599060487036456/January182013?authuser=0&feat=directlink 1.18.2013],
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[https://picasaweb.google.com/104969599060487036456/January212013?authuser=0&feat=directlink 1.21.2013],
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[https://picasaweb.google.com/104969599060487036456/January232013?authuser=0&feat=directlink 1.23.2013],
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[https://picasaweb.google.com/104969599060487036456/January252013?authuser=0&feat=directlink 1.25.2013],
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[https://picasaweb.google.com/104969599060487036456/January282013?authuser=0&feat=directlink 1.28.2013],
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[https://picasaweb.google.com/104969599060487036456/Janurary302013?authuser=0&feat=directlink 1.30.2013],
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[https://picasaweb.google.com/104969599060487036456/February12013?authuser=0&feat=directlink 2.1.2013],
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[https://picasaweb.google.com/104969599060487036456/February42013?authuser=0&feat=directlink 2.4.2013],
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[https://picasaweb.google.com/104969599060487036456/February62013?authuser=0&feat=directlink 2.6.2013],
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[https://picasaweb.google.com/104969599060487036456/February82013?authuser=0&feat=directlink 2.8.2013],
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[https://picasaweb.google.com/104969599060487036456/Feb112013?authuser=0&feat=directlink 2.11.2013],
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[https://picasaweb.google.com/104969599060487036456/Feb132013?authuser=0&feat=directlink 2.13.2013],
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[https://picasaweb.google.com/104969599060487036456/February152013?authuser=0&feat=directlink 2.15.2013],
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[https://picasaweb.google.com/104969599060487036456/February202013?authuser=0&feat=directlink 2.20.2013],
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[https://picasaweb.google.com/104969599060487036456/February222013?authuser=0&feat=directlink 2.22.2013],
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[https://picasaweb.google.com/104969599060487036456/Feb252013?authuser=0&feat=directlink 2.25.2013],
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[https://picasaweb.google.com/104969599060487036456/Feb272013?authuser=0&feat=directlink 2.27.2013],
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[https://picasaweb.google.com/104969599060487036456/March12013?authuser=0&feat=directlink 3.1.2013], [https://picasaweb.google.com/104969599060487036456/March42013?authuser=0&feat=directlink 3.4.2013],
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[https://picasaweb.google.com/104969599060487036456/March62013?authuser=0&feat=directlink 3.6.2013],
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[https://picasaweb.google.com/104969599060487036456/March82013?authuser=0&feat=directlink 3.8.2013],
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[https://picasaweb.google.com/104969599060487036456/March182013?authuser=0&feat=directlink 3.18.2013],
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[https://picasaweb.google.com/104969599060487036456/March202013?authuser=0&feat=directlink 3.20.2013],
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[https://picasaweb.google.com/104969599060487036456/March252013ThroughApril3?authuser=0&feat=directlink 3.25.2013 -- 4.3.2013: Acoustics and Waves on a Circle], [https://picasaweb.google.com/104969599060487036456/April82013ThroughApril192013?authuser=0&feat=directlink 4.5.2013 -- 4.19.2013: Complex FS through FT],
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[https://picasaweb.google.com/104969599060487036456/April222013?authuser=0&feat=directlink 4.22.2013]
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 +
*[[MATH-348 Advanced Engineering Mathematics - Lecture Pictures |MATH 348 : Advanced Engineering Mathematics - Lecture Pictures: Archive ]]
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==Useful Blog Posts==
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Here you will find posts on the [http://math348.wordpress.com math348.wordpress.com blog] that typically get reposted semester after semester.
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*[https://math348.wordpress.com/2012/03/05/this-averages-to-more-than-one-use-of-profanity-every-two-seconds/ Post] about spectrograms and the b-side to the [http://en.wikipedia.org/wiki/Windowlicker Windowlicker single] by [http://en.wikipedia.org/wiki/Aphex_Twin Aphex Twin].
 +
 
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==Lecture Slides and Notes==
  
 
There are various lecture slides associated with the course. They were developed during the Spring of 2010 and are intended to deliver important bulk concepts while avoiding the desire to write down 'every little thing.' Specifically, the slides address:
 
There are various lecture slides associated with the course. They were developed during the Spring of 2010 and are intended to deliver important bulk concepts while avoiding the desire to write down 'every little thing.' Specifically, the slides address:
Line 65: Line 185:
  
 
*[[MATH-348 Advanced Engineering Mathematics - Lecture Slides |MATH 348 : Advanced Engineering Mathematics - Lecture Slides ]]
 
*[[MATH-348 Advanced Engineering Mathematics - Lecture Slides |MATH 348 : Advanced Engineering Mathematics - Lecture Slides ]]
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==Lecture Notes==
 
  
 
There is a set of lecture notes associated with the course. They were developed during the Fall of 2008 through the Spring of 2009 and are intended to outline key-points, objectives and goals from the text in the order we cover them. Listed in each set are:
 
There is a set of lecture notes associated with the course. They were developed during the Fall of 2008 through the Spring of 2009 and are intended to outline key-points, objectives and goals from the text in the order we cover them. Listed in each set are:
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*[[MATH-348 Advanced Engineering Mathematics - Lecture Notes |MATH 348 : Advanced Engineering Mathematics - Lecture Notes ]]
 
*[[MATH-348 Advanced Engineering Mathematics - Lecture Notes |MATH 348 : Advanced Engineering Mathematics - Lecture Notes ]]
  
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==Assignments==
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==Homework Assignments==
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Students learn by doing problems. Consequently, a course's assignments are critically important and is where the majority of student learning takes place. So, this raises an important question, "how should the assignments for a course like AEM be structured?" This is a tough question and to arrive at my 'answer,' we need some background.
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First, while the majority of students (>90%) in AEM are engineers their skill-sets are highly inhomogeneous. Specifically, you have all had two-years of post-secondary mathematics at different difficulty levels, pace and success. So, there isn't a standard assumption I can use about what you have seen, how well you remember it and, most importantly, how comfortable you are manipulating "it." Moreover, it is unclear where you are going from here. Some of you will find yourself in industry and some in academia, which means that your needs from the material are different. Clearly, any [http://en.wikipedia.org/wiki/Curve_fitting line of best fit] through the material will be poor. 
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Second, everyone in this course needs to understand that they have an '''fairly extensive''' mathematical background. Seriously, how many students do you know that will have had six semesters of course work, outside of their discipline, when they graduate? Those that do are typically awarded a [http://mcs.mines.edu/Academic_Programs/mathminor.shtml minor] in the field. The point is, you are moving past [http://en.wikipedia.org/wiki/Computer plug-and-chug] mathematics and into the conceptual framework of [http://en.wikipedia.org/wiki/Linear_algebra finite] and [http://www.math.ohio-state.edu/~gerlach/math/BVtypset/node2.html infinite] dimensional [http://en.wikipedia.org/wiki/Linear_system linear theory]. Finally, we address the question
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      How should the assignments for a course like AEM be structured?
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Based on the diverse background of the student audience and the growing sophistication of the material homework, assignments should be constructed to highlight both the algorithmic procedures and conceptual framework of linear mathematics. For quick practice skills the recommended homework problems and examples in the text should suffice. However, a student should only do this after replicating the work from class and deciding they wish to have more practice.
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On the other hand, the homework assignments are made to provide a deeper understanding of the course material and often take the student past a first-calculation and into a deeper concept. For example, using the power-series representation for the exponential function is a first-calculation, while using this power-series to show the deep connection between exponential functions and sinusoids is uses multiple pieces of math to arrive at a deeper concept. All students should be able to handle the first-calculations in the homework and at the same time the more advanced students are still challenged by the deeper concepts present in many of the problems.  This is the goal of the homework assignments. 
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===Homework Assignments===
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The assignments for this course have reached a steady-state. Consequently, solutions are often available through students who have taken the course in the past. Since these resources might not be available to all students, I have drafted a set of solutions to these homework assignments which I make available through this site. These solutions were, more or less, finalized during the Spring of 2010 and represents the end of an evolution starting around 2006. Outside of the lecture itself, these homeworks and solutions represents some of the oldest parts of the course and many of the ancestors can be found on [[MATH-348 Advanced Engineering Mathematics - Archive | older ticc pages ]].
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In the past the homeworks tended to have a good deal of discussion providing context to a problem so that both the mechanics and concepts could be gleaned. However, after talking with some students and course reviews I decided to move the commentary to the solutions in favor of a more streamlined problem statement. It is unclear whether this latest incarnation is 'better' than the past but what is clear is that they won't be regressing unless someone else wants to revamp them. If you want to see the previous versions then visit the [[MATH-348 Advanced Engineering Mathematics - Archive | older ticc pages ]]. If you find any typos in these solutions then I would appreciate you letting me know. They are pretty clean but they could always be `cleaner.'
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With that said, I must make emphasize the following point:
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Homework is an essential part of any course. We will only have class/lecture roughly 48 hours in one semester. While this sounds like a lot it really isn't a ton. Here are some comparisons.
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      Caveat Emptor : We will work from these problems and since solutions are
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48 Hours is the same as:
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      readily available it is up to the individual user to make sure that they
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  1. One and one-fifth work weeks.
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      are LEARNING the material. If you buy into a program of procrastination
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  2. Four months of average daily facebooking (or so I've read)
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      followed by rapid and thoughtless re-creation then you may find yourself with an
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  3. Six weeks of average video gameplay.
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      inadequate product that cannot be returned.  
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  4. Seven days of average phone usage
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  5. Thirty-two days of average texting.
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  6. Two and one-half weeks of average driving.
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I guess the point I'm trying to make is that some of these things are what people do everyday and we do them b/c we deem them important. That's fine, but when deciding what you do everyday, remember that this course is about $1000-important to whomever is paying for it. A majority of student learning occurs outside of class, which is largely spent doing homework. The homeworks for this course are meant to guide/focus this time and your homework will primarily reflect the time and effort spent with them. I encourage you to work every day with the goal of spending six-hours outside of class per week on AEM material.
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{{PDF Table Item|filename=Math348HomeworkCover_S13.pdf | title=MATH348.HWCoverSheet}}
  
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*[[MATH-348 Advanced Engineering Mathematics - Textbook Usage |MATH 348 : Advanced Engineering Mathematics - Textbook Usage ]]
  
 
*[[MATH-348 Advanced Engineering Mathematics - Assignments |MATH 348 : Advanced Engineering Mathematics - Assignments ]]
 
*[[MATH-348 Advanced Engineering Mathematics - Assignments |MATH 348 : Advanced Engineering Mathematics - Assignments ]]
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*[[MATH-348 Advanced Engineering Mathematics - Supplemental  |MATH 348 : Advanced Engineering Mathematics - Supplemental Materials ]]
 
*[[MATH-348 Advanced Engineering Mathematics - Supplemental  |MATH 348 : Advanced Engineering Mathematics - Supplemental Materials ]]
 
*[[MATH-348 Advanced Engineering Mathematics - Archive |MATH 348 : Advanced Engineering Mathematics - Archive ]]
 
*[[MATH-348 Advanced Engineering Mathematics - Archive |MATH 348 : Advanced Engineering Mathematics - Archive ]]
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*[[MATH-348 AEM - SubWiki | MATH348 : AEM SubWiki]]

Latest revision as of 21:32, 15 November 2015

Main Page > Mathematical and Computer Sciences Course Wikis
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Contents

Course Information

MATH348: Advanced Engineering Mathematics - Introduction to partial differential equations, with applications to physical phenomena. Fourier series. Linear algebra, with emphasis on sets of simultaneous equations. Prerequisite: MATH 225 or equivalent.

Instructor Information

Textbook Information

I do not require a textbook for this course as the lecture notes should suffice. However, owning a post Calc/DiffEQ textbook may be useful. I provide some options below.

Kreyszig Abridged edition

The bookstore sells an abridged version of the Kreyszig text, which is now in its tenth edition -- all previous CSM abridged editions will be acceptable for this course. The abridged version contains the seven chapters and an appendix:

1. Chapter 5: Power Series Solutions to ODE and Frobenius method

2. Chapter 7: Systems of Linear Algebraic Equations

3. Chapter 8: Eigenvalues and Eigenvectors

4. Chapter 11: Fourier Series

5. Chapter 12: Introduction to Linear Partial Differential Equations

6. Chapter 20: Numerical Methods in Linear Algebra

7. Chapter 21: Numerical Methods in Differential Equations


While this will meet out needs, if you plan to continue in mathematics for a minor or area of special interest or seek an advanced degree in your field then you are advised to get the unabridged edition.

Texts on Fourier Analysis

The following are some texts that you may want to consider for study of Fourier "Analysis" (AKA Fourier methods.)


Texts on PDE

The following are some texts that you may want to consider for study of linear PDE.

Texts on Linear Algebra

The following are some texts that you may want to consider for study of linear algebra.

Continued use of your Differential Equations (MATH225) text

Your MATH225 differential equations text was chosen, partially, so that you could use it for topics in this course. The following will outline how the chapters in Differential Equations by Zill and Cullen matches up with AEM material.

  1. First task is to review some concepts in ODE. Specifically, we will need to remember/learn how to:
    • Constant Linear Problems: 4.3
    • Undetermined Coefficients: 4.4
    • Variation of Parameters: 4.6 - this was likely not covered in your course, we will cover it in a homework problem.
    • Mass-spring Problems: 5.1
    • Series Solutions to Linear Equations: 6.1
    • Bessel's Equation: 6.3.1
    • Boundary Value Problems and Sturm-Liouville Problems: 5.2 (example 2) and to some extend chapter 12-13 although this will come later with PDE, 11.4 (example 1)
  2. Fourier Series: 11.1-11.3
  3. Fourier integral/transforms: 14.3-14.4
  4. Linear Partial Differential Equations: Chapter 12 and Chapter 13
  5. Linear Algebra: Appendix II, we will actually need far more than this appendix will cover but it will be a good start.

Course Materials

The following outlines materials specific to this course. The materials, as indicated, have been developed over time and have achieved a steady-state. An archive of older ticc pages is available. The ticc websites pick up at Spring 2008 when I started presenting linear algebra first.

Syllabus

Lecture Pictures

This semester, Spring 2012, I will try to take pictures of the boards before I scrub them. One word of warning, these are not a substitute for lecture itself. The interactions and development are often important in understanding the material.

Spring 2012

1.11.2012, 1.13.2012, 1.16.2012, 1.18.2012,1.20.2012, 1.23.2012, 1.25.2012,1.27.2012, 1.30.2012, 2.6.2012, 2.8.2012, 2.10.2012, 2.13.2012, 2.15.2012, 2.17.2012. 2.22.2012, 2.24.2012, 2.27.2012,2.29.2012, 3.2.2012, 3.5.2012, 3.7.2012, 3.19.2012, 3.21.2012,3.23.2012, 3.26.2012, 3.28.2012, 4.2.2012, 4.4.2012, 4.7.2012, 4.9.2012, 4.11.2012, 4.13.2012, 4.16.2012, 4.20.2012, 4.23.2012, 4.25.2012, 4.27.2012, 4.30.2012, 5.2.2012

Fall 2012

8.22.2012, 8.24.2012, 8.27.2012, 8.29.2012,8.31.2012, 9.3.2012, 9.5.2012, 9.7.2012, 9.10.2012,9.12.2012, 9.14.2012, 9.17.2012, 9.19.2012, 9.21.2012, 9.24.2012, 9.26.2012, 9.28.2012, 10.1.2012, 10.3.2012, 10.5.2012, 10.8.2012, 10.10.2012, 10.12.2012, 10.19.2012, 10.22.2012, 10.24.2012, 10.29.2012, 10.31.2012, 11.2.2012, 11.5.2012, 11.7.2012, 11.9.2012, 11.12.2012, 11.14.2012, 11.16.2012, 11.19.2012, 11.26.2012, 11.30.2012, 12.3.2012, 11.5.2012

Spring 2013

1.9.2013, 1.11.2013, 1.14.2013, 1.16.2013, 1.18.2013, 1.21.2013, 1.23.2013, 1.25.2013, 1.28.2013, 1.30.2013, 2.1.2013, 2.4.2013, 2.6.2013, 2.8.2013, 2.11.2013, 2.13.2013, 2.15.2013, 2.20.2013, 2.22.2013, 2.25.2013, 2.27.2013, 3.1.2013, 3.4.2013, 3.6.2013, 3.8.2013, 3.18.2013, 3.20.2013, 3.25.2013 -- 4.3.2013: Acoustics and Waves on a Circle, 4.5.2013 -- 4.19.2013: Complex FS through FT, 4.22.2013

Useful Blog Posts

Here you will find posts on the math348.wordpress.com blog that typically get reposted semester after semester.

Lecture Slides and Notes

There are various lecture slides associated with the course. They were developed during the Spring of 2010 and are intended to deliver important bulk concepts while avoiding the desire to write down 'every little thing.' Specifically, the slides address:

1. Definitions that are not useful for me to write and students to rewrite during lecture.

2. Derivations that will never need to be reproduced but need to be communicated quickly because they lead to important consequences.

3. Derivations that will need to be reproduced and have been recorded for clarity.

Listed in each slide set are: 

   Associated Section/Pages from EK.AEM
   Associated Lecture Notes
   Associated Homework Assignments

There is a set of lecture notes associated with the course. They were developed during the Fall of 2008 through the Spring of 2009 and are intended to outline key-points, objectives and goals from the text in the order we cover them. Listed in each set are: 

   Associated Sections/Pages from EK.AEM
   Suggested Problems from EK.AEM
   Brief Outline of Lecture Talking Points
   Lecture Objectives
   Lecture Goals

Homework Assignments

Homework is an essential part of any course. We will only have class/lecture roughly 48 hours in one semester. While this sounds like a lot it really isn't a ton. Here are some comparisons. 

48 Hours is the same as:
 1. One and one-fifth work weeks.
 2. Four months of average daily facebooking (or so I've read)
 3. Six weeks of average video gameplay.
 4. Seven days of average phone usage
 5. Thirty-two days of average texting.
 6. Two and one-half weeks of average driving.

I guess the point I'm trying to make is that some of these things are what people do everyday and we do them b/c we deem them important. That's fine, but when deciding what you do everyday, remember that this course is about $1000-important to whomever is paying for it. A majority of student learning occurs outside of class, which is largely spent doing homework. The homeworks for this course are meant to guide/focus this time and your homework will primarily reflect the time and effort spent with them. I encourage you to work every day with the goal of spending six-hours outside of class per week on AEM material.


MATH348.HWCoverSheet

Exams

Previous exams going back through Fall2008 and review sheets are available for studying via the following link.


Student Feedback

MATH348.PostVSSurvey.Fall2011

Supplemental Materials
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