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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email : math348@gmail.com
 
  
 
==Textbook Information==
 
==Textbook Information==
  
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    Textbook : [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471488852.html Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9]
 
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    9th Edition Amazon : [http://www.amazon.com/Advanced-Engineering-Mathematics-Textbook-Solutions/dp/0470084847/ref=sr_1_4?ie=UTF8&s=books&qid=1231462860&sr=1-4 Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9]
 
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    8th Edition Amazon (Used) : [http://www.amazon.com/gp/offer-listing/0471154962/ref=dp_olp_1 Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9]
 
  
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=Course Materials=
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*[[MATH-348 Advanced Engineering Mathematics - Textbook Usage |MATH 348 : Advanced Engineering Mathematics - Textbook Usage ]]
  
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==Syllabus==
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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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{{PDF Table Item|filename=Math348_syllabus.spring2010.pdf | title=MATH348.Spring2010.Syllabus}}
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==Lecture Slides==
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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 need to write down 'every little thing.' Specifically, the slides address:
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===Kreyszig Abridged edition===
  
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1. Definitions that are not useful for me to write and students to rewrite during lecture.
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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:
  
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2. Derivations that will never need to be reproduced but need to be communicated quickly because they lead to important consequences.
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1. Chapter 5: Power Series Solutions to ODE and [http://en.wikipedia.org/wiki/Frobenius_method Frobenius method]
  
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3. Derivations that will need to be reproduced and have been recorded for clarity.  
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2. Chapter 7: [http://en.wikipedia.org/wiki/Linear_algebra Systems of Linear Algebraic Equations]
  
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Listed in each slide set are:
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3. Chapter 8: [http://en.wikipedia.org/wiki/Eigenvalue,_eigenvector_and_eigenspace Eigenvalues and Eigenvectors]
  
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    Associated Section/Pages from EK.AEM
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4. Chapter 11: [http://en.wikipedia.org/wiki/Fourier_series Fourier Series]
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    Associated Lecture Notes
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    Associated Homework Assignments
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*[[MATH-348 Advanced Engineering Mathematics - Lecture Slides |MATH 348 : Advanced Engineering Mathematics - Lecture Slides ]]
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5. Chapter 12: Introduction to Linear [http://en.wikipedia.org/wiki/Partial_differential_equation Partial Differential Equations]
  
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==Lecture Notes==
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6. Chapter 20:  [http://en.wikipedia.org/wiki/Numerical_linear_algebra  Numerical Methods in Linear Algebra]
  
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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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7. Chapter 21: [http://en.wikipedia.org/wiki/Category%3ANumerical_differential_equations Numerical Methods in Differential Equations]
  
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    Associated Sections/Pages from EK.AEM
 
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    Suggested Problems from EK.AEM
 
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    Brief Outline of Lecture Talking Points
 
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    Lecture Objectives
 
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    Lecture Goals 
 
  
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*[[MATH-348 Advanced Engineering Mathematics - Lecture Notes |MATH 348 : Advanced Engineering Mathematics - Lecture Notes ]]
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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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==Assignments==
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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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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 older ticc pages.
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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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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 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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*[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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With that said, I must make emphasize the following point:
 
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      Caveat Emptor : We will work from these problems and since solutions are
 
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      readily available it is up to the individual user to make sure that they
 
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      are LEARNING the material. If you buy into a program of procrastination
 
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      followed by rapid and thoughtless recreation then you may find an
 
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      inadequate product, which cannot be returned.
 
  
  
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*[[MATH-348 Advanced Engineering Mathematics - Assignments |MATH 348 : Advanced Engineering Mathematics - Assignments ]]
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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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==Exams==
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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.
 +
===Texts on Linear Algebra===
 +
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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*[[MATH-348 Advanced Engineering Mathematics - Exams |MATH 348 : Advanced Engineering Mathematics - Exams ]]
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===Continued use of your Differential Equations (MATH225) text===
 +
[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>
 +
  </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>
 +
</ol>
  
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=Other Materials=
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=Course Materials=
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==Linear Algebra==
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===Three Planes in Space===
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{{PDF Table Item|filename=Math348_planes.summer2009.pdf | title=Three Planes in Space - Four Different Ways}}
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  '''Legend for the Animations'''
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    Red = First Plane Equation
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    Orange = Second Plane Equation
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    Yellow = Third Plane Equation
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    Green = Column Space of A (AKA the set of all linear combination of the pivot columns of A)
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    Blue = Right Hand Side for non-homogeneous problem.
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[http://www.mines.edu/~sstrong/Media/LA_geometry/nonUnique.avi Animation : Ax=0 with oo-many solutions that form a line in space.]
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[http://www.mines.edu/~sstrong/Media/LA_geometry/nonUnique2.avi Animation : Ax=b with oo-many solutions that form a line in space.]
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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. 
  
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[http://www.mines.edu/~sstrong/Media/LA_geometry/Unique.avi Animation : Ax=b with a single solution]
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==Syllabus==
  
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[http://www.mines.edu/~sstrong/Media/LA_geometry/nonExist.avi Animation : Ax=b with no solutions]
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==Lecture Pictures==
  
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===Linear Algebra Software===
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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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[http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi Linear Algebra Toolkit]
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===Spring 2012===
 +
[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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==Fourier Methods==
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===Fall 2012===
  
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===Review of Functions===
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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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{{PDF Table Item|filename=Unit_Circle.pd‎f|title=Special Angles and the Unit Circle}}
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[https://picasaweb.google.com/104969599060487036456/September212012?authuser=0&feat=directlink 9.21.2012],
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{{PDF Table Item|filename=A61-TrigFormula.pdf|title=A61.TrigIdentities}}
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[https://picasaweb.google.com/104969599060487036456/September242012?authuser=0&feat=directlink 9.24.2012],
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[http://en.wikipedia.org/wiki/Even_and_odd_functions Odd and Even Functions (Wikipedia) : (see Also 09.LN)]
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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],
 +
[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]
 +
   
 +
===Spring 2013===
 +
[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],
 +
[https://picasaweb.google.com/104969599060487036456/February12013?authuser=0&feat=directlink 2.1.2013],
 +
[https://picasaweb.google.com/104969599060487036456/February42013?authuser=0&feat=directlink 2.4.2013],
 +
[https://picasaweb.google.com/104969599060487036456/February62013?authuser=0&feat=directlink 2.6.2013],
 +
[https://picasaweb.google.com/104969599060487036456/February82013?authuser=0&feat=directlink 2.8.2013],
 +
[https://picasaweb.google.com/104969599060487036456/Feb112013?authuser=0&feat=directlink 2.11.2013],
 +
[https://picasaweb.google.com/104969599060487036456/Feb132013?authuser=0&feat=directlink 2.13.2013],
 +
[https://picasaweb.google.com/104969599060487036456/February152013?authuser=0&feat=directlink 2.15.2013],
 +
[https://picasaweb.google.com/104969599060487036456/February202013?authuser=0&feat=directlink 2.20.2013],
 +
[https://picasaweb.google.com/104969599060487036456/February222013?authuser=0&feat=directlink 2.22.2013],
 +
[https://picasaweb.google.com/104969599060487036456/Feb252013?authuser=0&feat=directlink 2.25.2013],
 +
[https://picasaweb.google.com/104969599060487036456/Feb272013?authuser=0&feat=directlink 2.27.2013],
 +
[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],
 +
[https://picasaweb.google.com/104969599060487036456/March62013?authuser=0&feat=directlink 3.6.2013],
 +
[https://picasaweb.google.com/104969599060487036456/March82013?authuser=0&feat=directlink 3.8.2013],
 +
[https://picasaweb.google.com/104969599060487036456/March182013?authuser=0&feat=directlink 3.18.2013],
 +
[https://picasaweb.google.com/104969599060487036456/March202013?authuser=0&feat=directlink 3.20.2013],
 +
[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],
 +
[https://picasaweb.google.com/104969599060487036456/April222013?authuser=0&feat=directlink 4.22.2013]
  
−
[http://en.wikipedia.org/wiki/Periodic_function Periodic Functions (Wikipedia) : (See Also 09.LN)]
+
*[[MATH-348 Advanced Engineering Mathematics - Lecture Pictures |MATH 348 : Advanced Engineering Mathematics - Lecture Pictures: Archive ]]
  
−
===Fourier Series===
+
==Useful Blog Posts==
  
−
{{PDF Table Item|filename=Example11.1.1.pdf|title=FS for f(x}=x, x \in (-\pi,\pi)}}
+
Here you will find posts on the [http://math348.wordpress.com math348.wordpress.com blog] that typically get reposted semester after semester.
−
{{PDF Table Item|filename=Example11.1.2.pdf|title=FS for f(x}=Exp(Abs(x)), x \in (-\pi,\pi)}}
+
−
[http://en.wikipedia.org/wiki/Fourier_series Fourier Series - Wikipedia]
+
−
[http://en.wikipedia.org/wiki/Gibbs_phenomenon  Gibbs Phenomenon - Wikipedia]
+
  
−
===Fourier Transform===
+
*[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].
  
−
[http://en.wikipedia.org/wiki/Fourier_transform Fourier Transform - Wikipedia]
+
==Lecture Slides and Notes==
−
[http://en.wikipedia.org/wiki/Sinc_function Wikipedia - Sinc Function]
+
−
[http://mathworld.wolfram.com/SincFunction.html Mathworld - Sinc Function]
+
−
[http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem Wikipedia - Nyquist-Shannon Sampling Theorem]
+
  
−
[http://mathworld.wolfram.com/Convolution.html Mathworld - Convolution (Animation)]
+
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:
  
−
[http://cnx.org/content/m13106/latest/  Convolution and Diffraction (Animations)]
+
1. Definitions that are not useful for me to write and students to rewrite during lecture.
  
−
[http://cnx.org/content/m13106/latest/  Convolution and Diffraction (Animations)]
+
2. Derivations that will never need to be reproduced but need to be communicated quickly because they lead to important consequences.
  
−
[http://commons.wikimedia.org/wiki/File:Convolution_Animation_(Boxcar_and_Ramp).gif Wikipedia - Convolution (Animation)]
+
3. Derivations that will need to be reproduced and have been recorded for clarity.  
  
−
[http://en.wikipedia.org/wiki/Green's_function Green's Function - Wikipedia]
+
Listed in each slide set are:
−
{{PDF Table Item|filename=FreqResponseHO.pdf|title= Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125} }}
+
  
−
==Partial Differential Equations==
+
    Associated Section/Pages from EK.AEM
−
===Ordinary Differential Equations===
+
    Associated Lecture Notes
−
{{PDF Table Item|filename=Math348_ODEReview.fall2009.pdf|title= Review of Ordinary Differential Equations (DRAFT - 11/16/09)}}
+
    Associated Homework Assignments
−
[http://en.wikipedia.org/wiki/Millennium_Bridge_(London) Millennium Bridge - Wikipedia]
+
  
−
[http://www.youtube.com/watch?v=eAXVa__XWZ8 You Tube Video - Millennium Bridge Resonance]
+
*[[MATH-348 Advanced Engineering Mathematics - Lecture Slides |MATH 348 : Advanced Engineering Mathematics - Lecture Slides ]]
  
−
===Heat Equation===
+
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:
  
−
[http://www.mines.edu/~sstrong/AEM_Materials/V.mp4 Heat Movie 1 - abs(x)]
+
    Associated Sections/Pages from EK.AEM
 +
    Suggested Problems from EK.AEM
 +
    Brief Outline of Lecture Talking Points
 +
    Lecture Objectives
 +
    Lecture Goals 
  
−
[http://www.mines.edu/~sstrong/AEM_Materials/parabola.mp4 Heat Movie 2 - parabola]
+
*[[MATH-348 Advanced Engineering Mathematics - Lecture Notes |MATH 348 : Advanced Engineering Mathematics - Lecture Notes ]]
  
−
[http://www.mines.edu/~sstrong/AEM_Materials/doubleV.mp4 Heat Movie 3 - Double V]
+
==Homework Assignments==
  
−
[http://www.mines.edu/~sstrong/AEM_Materials/Heat_Dirch_Force.avi Heat Movie 4 - Forced Heat Equation with B.C. u(0,t)=u(L,t)=0 ]
+
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.
 +
 
 +
{{PDF Table Item|filename=Math348HomeworkCover_S13.pdf | title=MATH348.HWCoverSheet}}
  
−
[http://www.mines.edu/~sstrong/AEM_Materials/Heat_Neumman_Forcing.avi Heat Movie 5 - Forced Heat Equation with B.C. u_{x}(0,t)=u_{x}(L,t)=0 ]
+
*[[MATH-348 Advanced Engineering Mathematics - Textbook Usage |MATH 348 : Advanced Engineering Mathematics - Textbook Usage ]]
  
−
===Wave Equation===
+
*[[MATH-348 Advanced Engineering Mathematics - Assignments |MATH 348 : Advanced Engineering Mathematics - Assignments ]]
  
−
====1D Wave Equation====
+
==Exams==
−
[http://www.mines.edu/~sstrong/AEM_Materials/Wave_Dirch_Triangle1.divx.ff.avi  Wave on a 1-D Sting with Fixed Endpoints]
+
  
−
[http://www.mines.edu/~sstrong/AEM_Materials/Wave_Dirch_Triangle2.divx.ff.avi  Wave on a 1-D Sting with Fixed Endpoints - Animated with first 5 Fourier Modes (Fundamental Mode in Red)]
+
Previous exams going back through Fall2008 and review sheets are available for studying via the following link.
  
−
[http://www.mines.edu/~sstrong/AEM_Materials/Wave_Neumman_Triangle2.divx.ff.avi  Wave on a 1-D Sting with FLAT Endpoints from HW10]
 
  
−
[http://www.mines.edu/~sstrong/AEM_Materials/Wave_Neumman_Triangle1.divx.ff.avi  Wave on a 1-D Sting with FLAT Endpoints from HW10 - Animated with first 5 Fourier Modes (Fundamental Mode in Red)]
+
*[[MATH-348 Advanced Engineering Mathematics - Exams |MATH 348 : Advanced Engineering Mathematics - Exams ]]
−
 
+
−
[http://www.mines.edu/~sstrong/AEM_Materials/Traveling%20Waves.divx.ff.avi  Traveling Wave :<math>u_{0}(x) = -\tanh(x)</math>: Red = Right Traveling, Blue=Left Traveling, Black = Superposition]
+
−
 
+
−
====2D Wave Equation Rectangular and Polar====
+
−
 
+
−
[http://www.mines.edu/~sstrong/AEM_Materials/2DWave_Rec_BookEx1a.avi Rectangular Membrane Movie 1 -Text Example pg577]
+
−
 
+
−
[http://www.mines.edu/~sstrong/AEM_Materials/2DWave_Rec_BookEx1b.avi Rectangular Membrane 2 -Text Example pg577]
+
−
 
+
−
[http://www.falstad.com/membrane/ Applet - Pretty Cool]
+
−
 
+
−
[http://hyperphysics.phy-astr.gsu.edu/Hbase/music/recmem.html Rectangular Membrane Modes]
+
−
 
+
−
[http://www.kettering.edu/~drussell/Demos/MembraneSquare/Square.html Animations of Rectangular Membrane Modes - Pretty Good]
+
−
 
+
−
[http://www.kettering.edu/~drussell/demos.html Animations done by Dr. Russell - All sorts of stuff! ]
+
−
 
+
−
 
+
−
[http://music.nebrwesleyan.edu/wtt/index.html The Well-Tempered Timpani By Richard K. Jones]
+
−
 
+
−
[http://www.mines.edu/~sstrong/AEM_Materials/Membrane1.mp4 Vibrating Membrane1 - 12.9.1 Example]
+
−
 
+
−
[http://www.mines.edu/~sstrong/AEM_Materials/membrane2.mp4 Vibrating Membrane2 - 12.9.1 Example]
+
−
 
+
−
[http://www.mines.edu/~sstrong/AEM_Materials/Mambrane3.mp4 Vibrating Membrane3 - 12.9.1 Example]
+
−
 
+
−
[http://www.mines.edu/~sstrong/AEM_Materials/Mambrane4.mp4 Vibrating Membrane4 - 12.9.1 Example]
+
−
 
+
−
 
+
−
 
+
−
====Nonlinear Wave Phenomenon====
+
−
 
+
−
[http://en.wikipedia.org/wiki/Shock_wave  Wikipedia Article on Shock Waves]
+
−
 
+
−
[http://physics-animations.com/Physics/English/swa_txt.htm  Animation of Shock Wave Formation in Pressure Field]
+
−
 
+
−
[http://www.youtube.com/watch?v=jZ3Hhdr8EjI&feature=PlayList&p=2AE42B05690BA5AD&playnext=1&playnext_from=PL&index=2  Shock Wave (Plane) - You Tube 1]
+
−
 
+
−
[http://www.youtube.com/watch?v=QX04ySm4TTk&feature=PlayList&p=2AE42B05690BA5AD&index=3&playnext=2&playnext_from=PL Shock Wave (Plane) - You Tube 2]
+
−
 
+
−
[http://www.youtube.com/watch?v=9r_2l5_FviU Shock Wave (Explosion) - You Tube 3]
+
−
+
−
[http://www.youtube.com/watch?v=GvVQEl_q2ZM Shock Wave (Explosion) - You Tube 4 : Ignore The the cartoon bubble]
+
−
 
+
−
[http://www.youtube.com/watch?v=pz7lcHN7GxQ Shock Wave (Simulation) - You Tube 5 : Notice the distortion of the expanding wave-front]
+
  
−
[http://www.break.com/index/explosion-shock-waves-in-slow-motion.html Shockwave Slowmo]
+
==Student Feedback==
 +
{{PDF Table Item|filename=PostVSSurvey.F11.pdf | title=MATH348.PostVSSurvey.Fall2011}}
  
−
[http://exploration.grc.nasa.gov/education/rocket/shock.html NASA - Shock Wave Simulator]
+
=Supplemental Materials=
  
−
[http://www.tfarchive.com/cartoons/wallpapers/shockwave17.jpg Shockwave :)]
+
*[[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 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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