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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

MATH 348 : Advanced Engineering Mathematics - Textbook Usage

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.

Schaums Outline Series - Advanced Mathematics for Engineers and Scientists. There is a lot of overlap between this book and what we will cover.

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.

PDE for Scientists and Engineers Dover Text
Schaum's Outline of Partial Differential Equations (Schaum's Outline Series)
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.

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.
Schaum's Outline of Linear Algebra Fourth Edition
Matrices and Linear Algebra (Dover Books on Mathematics)
Linear Algebra (Dover Books on Mathematics - Mature)

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.

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)

Fourier Series: 11.1-11.3
Fourier integral/transforms: 14.3-14.4
Linear Partial Differential Equations: Chapter 12 and Chapter 13
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.

Useful Blog Posts

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

Post about spectrograms and the b-side to the Windowlicker single by Aphex Twin.

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

MATH 348 : Advanced Engineering Mathematics - Lecture Slides

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

MATH 348 : Advanced Engineering Mathematics - Lecture Notes

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

MATH 348 : Advanced Engineering Mathematics - Textbook Usage

MATH 348 : Advanced Engineering Mathematics - Assignments

Exams

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

MATH 348 : Advanced Engineering Mathematics - Exams

Student Feedback

MATH348.PostVSSurvey.Fall2011

MATH348 Advanced Engineering Mathematics

Latest revision as of 21:32, 15 November 2015

Contents

Course Information

Instructor Information

Textbook Information

Kreyszig Abridged edition

Texts on Fourier Analysis

Texts on PDE

Texts on Linear Algebra

Continued use of your Differential Equations (MATH225) text

Course Materials

Syllabus

Lecture Pictures

Spring 2012

Fall 2012

Spring 2013

Useful Blog Posts

Lecture Slides and Notes

Homework Assignments

Exams

Student Feedback

Supplemental Materials

Personal tools

Namespaces

Variants

Views

Actions

Search

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@@ Line 2: / Line 2: @@
 {{Hierarchy Item|link=Mathematics_Course_Wikis|title=Mathematical and Computer Sciences Course Wikis}}
 {{End Hierarchy}}
+{{Start PDF Table}}
 =Course Information=
@@ Line 7: / Line 10: @@
 ==Instructor Information ==
-Instructor : [http://www.mines.edu/~sstrong Scott Strong]
-Office : [http://www.mines.edu/csm_maps/buildings/ChauvenetHall/ Chauvenet Hall 266]
-Office Phone : 303.384.2446
-email : math348.spring2010@gmail.com
-==Course Calendar ==
-Classes Begin : January 13th, 2010
-Lecture Days : Monday, Wednesday, Friday
-Course Sections :
-   B : 11:00am-11:50am - Location: Coolbaugh Hall 131
-   C : 1:00pm-1:50pm - Location: Green Center 211
-   D : 2:00pm-2:50pm - Location: Alderson Hall 430
-Last Day to Drop Without a W : January 28th
-Last Day to Withdraw : March 30th
-Classes End : May 14th, 2010
-Important Dates :
-    February 14th : No Classes
-    March 15th-19th : Spring Break
-    April 8th-10th : E-Days
-    May 3th-7th : Dead Week
-    May 7th : Dead Day
-==Office Hours ==
-Fixed Office Hours :
-  MWF : 12:00pm-12:50pm
-  Monday : 3:00pm-5:00pm
-If you cannot meet during the previous office hours then please contact me to schedule another meeting time. Please see this google calender to see the times I am [http://www.google.com/calendar/embed?src=c0968scnfp1f6h13s1rfd7sess%40group.calendar.google.com&ctz=America/Denver unavailable.]
 ==Textbook Information==
-     Textbook : [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471488852.html Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9]
-th 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]
-th 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]
-=Course Materials=
+*[[MATH-348 Advanced Engineering Mathematics - Textbook Usage |MATH 348 : Advanced Engineering Mathematics - Textbook Usage ]]
-{{Start PDF Table}}
-{{PDF Table Item|filename=Math348_syllabus.spring2010.pdf | title=MATH348.Spring2010.Syllabus}}
+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.
-==Lecture Slides==
-{{PDF Table Item|filename=Math348_LS.00.pdf | title=00.LS.Introduction }}
-{{PDF Table Item|filename=Math348_LS.01.pdf | title=01.LS.Classical Vector Spaces}}
-{{PDF Table Item|filename=Math348_LS.02.pdf | title=02.LS.Geometry in R^n}}
-{{PDF Table Item|filename=Math348_LS.03.pdf | title=03.LS.KinematicsAndDynamics}}
-{{PDF Table Item|filename=TextMaterial.LS.03.pdf | title=03.LS.KinematicsAndDynamics - Those Evil Natured Robots}}
-[http://books.google.com/books?id=e7FJM6aqZD8C&printsec=frontcover&dq=Lax+Linear+Algebra&source=bl&ots=XvDVMZpQmz&sig=Pfq6ufaSBs4dw7EXXRcM9ALgw80&hl=en&ei=bLaNS7TqEoWMtAOS64TRCA&sa=X&oi=book_result&ct=result&resnum=3&ved=0CBgQ6AEwAg#v=onepage&q=&f=false  Linear Algebra and its Applications][http://en.wikipedia.org/wiki/Peter_Lax by Peter D. Lax]
-{{PDF Table Item|filename=Math348_LS.04.pdf | title=04.LS.Abstract Vector Spaces}}
+===Kreyszig Abridged edition===
-{{PDF Table Item|filename=Math348_LS.05.edit.pdf | title=05.LS.Fourier Series to Fourier Integral to Fourier Transform - Update 4/5/2010}}
-{{PDF Table Item|filename=Math348_LS.06.pdf | title=06.LS.1D Heat Equation-Separation of Variables}}
-{{PDF Table Item|filename=Math348_LS.07.pdf | title=07.LS.The Acoustic Approximation and wave equations in 1D}}
-==Lecture Notes==
+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:
-{{PDF Table Item|filename=Math348_LN.00.pdf | title=00.LN.Overview And Outline}}
-{{PDF Table Item|filename=Math348_LN.01.update.pdf | title=01.LN.LinearDefinitions : Updated 1.27.2010. Footnotes have been added referencing locations in the text where these definitions can be found. }}
-{{PDF Table Item|filename=Math348_LN.02.pdf | title=02.LN.Introduction To Linear Equations}}
-{{PDF Table Item|filename=Math348_LN.03.pdf | title=03.LN.Solving Linear Systems}}
-{{PDF Table Item|filename=Math348_LN.04.pdf | title=04.LN.Square Systems - Determinants and Matrix Inversion}}
-{{PDF Table Item|filename=Math348_LN.05.pdf | title=05.LN.Introduction to Linear Vector Spaces}}
-{{PDF Table Item|filename=Math348_LN.06.pdf | title=06.LN.Chapter 7 - Wrap Up}}
-{{PDF Table Item|filename=Math348_LN.07.pdf | title=07.LN.Eigenproblems}}
-{{PDF Table Item|filename=Math348_LN.08.pdf | title=08.LN.Diagonalization}}
-{{PDF Table Item|filename=Math348_LN.09.pdf | title=09.LN.Introduction to Fourier Series : Review of Periodic and Symmetric Functions }}
-{{PDF Table Item|filename=Math348_LN.10.pdf | title=10.LN.Complex Fourier Series }}
-{{PDF Table Item|filename=Math348_LN.11.pdf | title=11.LN.Fourier Integral to Fourier Transform }}
-{{PDF Table Item|filename=Math348_LN.12.pdf | title=12.LN.Fourier Transform }}
-{{PDF Table Item|filename=Math348_LN.13e.pdf | title=13.LN.IntroToPDE }}
-{{PDF Table Item|filename=Math348_LN.14.pdf | title=14.LN.HeatEquation }}
-{{PDF Table Item|filename=Math348_LN.15.pdf | title=15.LN.WaveEquation }}
-==Assignments==
+. Chapter 5: Power Series Solutions to ODE and [http://en.wikipedia.org/wiki/Frobenius_method Frobenius method]
-{{PDF Table Item|filename=Math348_HW.00.pdf | title=Homework0 - Due Jan. 18th by 5:00pm}}
-{{PDF Table Item|filename=Math348_HW.00.Soln.pdf | title=Homework0 - Solutions}}
-{{PDF Table Item|filename=Math348_HW.01.edit1.pdf | title=Homework1 - Due Feb. 3rd by 5:00pm - Note: Updated 1/19/2010, fixed a typo in problem 2 matrix 2, a_{22} = -3 }}
-{{PDF Table Item|filename=Math348_HW.01.Soln.pdf | title=Homework1 - Solutions }}
-      Graphics for Homework 1
+. Chapter 7: [http://en.wikipedia.org/wiki/Linear_algebra Systems of Linear Algebraic Equations]
-      [http://ticc.mines.edu/csm/wiki/images/9/97/Math348_HW.1.2.1.Plot.pdf Geometry of Problem 2 System 1]
-      [http://ticc.mines.edu/csm/wiki/images/0/03/Math348_HW.1.2.2.Plot.pdf Geometry of Problem 2 System 2]
-      [http://ticc.mines.edu/csm/wiki/images/c/cc/Math348_HW.1.2.3.Plot.pdf Geometry of Problem 2 System 3]
-      [http://ticc.mines.edu/csm/wiki/images/c/cc/Math348_HW.1.2.4.Plot.pdf Geometry of Problem 2 System 4]
-      [http://ticc.mines.edu/csm/wiki/images/1/1d/Math348_HW.1.2.5.Plot.pdf Geometry of Problem 2 System 5]
-      [http://ticc.mines.edu/csm/wiki/images/c/ca/Math348_HW.1.4.2.1.Plot.pdf Interpolated Parabolas of Problem 4  Set 1]
-      [http://ticc.mines.edu/csm/wiki/images/a/a7/Math348_HW.1.4.2.2.Plot.pdf Interpolated Parabolas of Problem 4  Set 2]
-      [http://ticc.mines.edu/csm/wiki/images/a/a4/Math348_HW.1.4.2.2.lsp.Plot.pdf Geometry of Least Squares Problem of Problem 4  Set 2]
-      [http://ticc.mines.edu/csm/wiki/images/8/86/Math348_HW.1.4.2.3.Plot.pdf Interpolated Parabolas of Problem 4  Set 3]
-Fourier Transform
-{{PDF Table Item|filename=Math348_HW.02.edit2.pdf | title=Homework2 - Due Feb. 12th by 5:00pm : 1) Header Box Updated 2) Problem 4.2 \lambda = n^2}}
-{{PDF Table Item|filename=Math348_HW.02..edit2.Soln.pdf | title=Homework2 - Solutions : Update - There were a couple of typos, nothing major, corrected. 2/8/2010 : Updated again - One of the typos I corrected last time was not a typo at all (1.4). I have put it back in its place.}}
+. Chapter 8: [http://en.wikipedia.org/wiki/Eigenvalue,_eigenvector_and_eigenspace Eigenvalues and Eigenvectors]
+. Chapter 11: [http://en.wikipedia.org/wiki/Fourier_series Fourier Series]
-Homework 3 - Note : I have just noticed a pesky typo. Equation (2) from the assignment, (26) from the solutions, should read l_1 u(a) + k_1 u'(a) =  0 and NOT l_1 u(a) + k_1 u'(b) =  0
+. Chapter 12: Introduction to Linear [http://en.wikipedia.org/wiki/Partial_differential_equation Partial Differential Equations]
-{{PDF Table Item|filename=Math348_HW.edit4.03.pdf | title=Homework3 - Due Feb. 22th by 5:00pm : Update - There were multiple things going on here. Once I updated the assignment with an old copy that was missing problems.... Ugh, it's all fixed up now. :)}}
-{{PDF Table Item|filename=Math348_HW.03.edit1.Soln.pdf | title=Homework3 - Solutions}}
-{{PDF Table Item|filename=Math348_HW.04.pdf | title=Homework4 - Due: March 12th }}
-{{PDF Table Item|filename=Math348_HW.04.Soln.pdf | title=Homework4 - Solutions}}
-{{PDF Table Item|filename=Math348_HW.05.e2.pdf | title=Homework5 - Due: March 31st }}
-{{PDF Table Item|filename=Math348_HW.05.Soln.pdf | title=Homework5 - Solutions}}
-{{PDF Table Item|filename=Math348_HW.06.pdf | title=Homework6 - Due: April 12th }}
-{{PDF Table Item|filename=Math348_HW.06.soln.pdf | title=Homework6 - Solutions }}
-{{PDF Table Item|filename=Math348_HW.07e3.pdf | title=Homework7 - Due April 28 - Last edits (minor) at 4:31pm. }}
-{{PDF Table Item|filename=Math348_HW.07e2.soln.pdf | title=Homework7 - Solutions - Last edits (minor) at 4:31pm  : Note at a step in problem 1.1 I use quantities like I1 and I2. By these I mean l1 and l2. }}
-{{PDF Table Item|filename=Math348_HW.08.pdf | title=Homework8 - Due May 3 }}
-{{PDF Table Item|filename=Math348_HW.08.soln.pdf | title=Homework8 - Solutions }}
-==Exams==
+. Chapter 20:  [http://en.wikipedia.org/wiki/Numerical_linear_algebra  Numerical Methods in Linear Algebra]
-===Exam I===
+. Chapter 21: [http://en.wikipedia.org/wiki/Category%3ANumerical_differential_equations Numerical Methods in Differential Equations]
-Exam I will be held on March 1st in class. There will be no notecards or calculators. The exam will have five required questions and contain material outlined in the following review:
-{{PDF Table Item|filename=Math348_E1Review.pdf|title=Exam 1 - Review Sheet}}
-The following exams with solutions are posted for your review.
+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.
-{{PDF Table Item|filename=Math348_e1.fall2008.pdf|title=Exam 1 - Fall2008 }}
+*[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.
-{{PDF Table Item|filename=Math348_e1Soln.fall2008.pdf|title=Exam 1 - Fall2008 Solutions}}
-{{PDF Table Item|filename=Math348_e1.spring2009.pdf|title=Exam I - Spring2009 }}
-{{PDF Table Item|filename=Math348_e1Soln.spring2009.pdf|title=Exam I - Spring2009 Solutions}}
-{{PDF Table Item|filename=Math348_e1.summer2009.pdf|title=Exam I - Summer2009 }}
-{{PDF Table Item|filename=Math348_e1Soln.summer2009.pdf|title=Exam I - Summer2009 Solutions}}
-{{PDF Table Item|filename=Math348_e1.fall2009.pdf|title=Exam I - Fall2009 }}
-{{PDF Table Item|filename=Math348_e1Soln.Fall2009.pdf|title=Exam I - Fall2009 Solutions}}
+===Texts on Fourier Analysis===
+The following are some texts that you may want to consider for study of Fourier "Analysis" (AKA Fourier methods.)
-     Exam I -  Statistics
+*[http://www.amazon.com/Fourier-Dover-Mathematics-Georgi-Tolstov/dp/0486633179/ref=pd_sim_b_3 Fourier Series by Tolstov and published by Dover]
-     Mean = 37.15 (74,31%)
+*[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]
-     Median = 38 (76%)
+*[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]
-     Mode = 47 (94%)
+*[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)]
-     A's = 34, B's = 17, C's = 24, D's = 18, F's = 25, Total Number of Exams  = 118
-     A's = 29%, B's = 14%, C's = 20%, D's = 15%, F's = 21 %
-{{PDF Table Item|filename=Math348_e1.spring2010.pdf|title=Exam I - Spring2010 }}
-{{PDF Table Item|filename=Math348_e1Soln.spring2010.edit.pdf|title=Exam I - Spring2010 Solutions}}
-===Exam II===
-Exam II will be held on April 16th in class. There will be no notecards or calculators. The exam will have five required questions and contain material outlined in the following review:
-{{PDF Table Item|filename=Math348_e2review.pdf|title=Exam 2 - Review Sheet}}
+===Texts on PDE===
+The following are some texts that you may want to consider for study of linear PDE.
-The following are the results of Q+A's from previous semesters:
+*[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]
+*[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) ]
+*[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.
-{{PDF Table Item|filename=Math348_e2QA.Spring2009.pdf|title=Exam 2 - Spring2009 Q + A}}
+*[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.
-{{PDF Table Item|filename=Math348_e2QA.fall2008.pdf|title=Exam 2 - Fall2008 Q + A}}
+*[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]
+*[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)]
+*[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)]
-The following exams with solutions are posted for your review.
+===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.
-{{PDF Table Item|filename=Math348_e2.spring2009.pdf|title=Exam II - Spring2009 }} See Soln for problem 3 graph.
+<ol>
-{{PDF Table Item|filename=Math348_e2Soln.spring2009.pdf|title=Exam II - Spring2009 Solutions}}
+ <li> First task is to review some concepts in ODE. Specifically, we will need to remember/learn how to: </li>
-{{PDF Table Item|filename=Math348_e2.fall2008.pdf|title=Exam 2 - Fall2008 }}
+  <ul>
-{{PDF Table Item|filename=Math348_e2Soln.fall2008.pdf|title=Exam 2 - Fall2008 Solutions}}
+  <li>Constant Linear Problems: 4.3</li>
-{{PDF Table Item|filename=Math348_e2.summer2009.pdf|title=Exam II - Summer2009 }}
+  <li> Undetermined Coefficients: 4.4 </li>
-{{PDF Table Item|filename=Math348_e2Soln.summer2009.pdf|title=Exam II - Summer2009 Solutions}}
+  <li> Variation of Parameters: 4.6 - this was likely not covered in your course, we will cover it in a homework problem.</li>
-{{PDF Table Item|filename=Math348_e2.fall2009.pdf|title=Exam II - Fall2009 }}
+  <li> Mass-spring Problems: 5.1 </li>
-{{PDF Table Item|filename=Math348_e2Soln.Fall2009.pdf|title=Exam I - Fall2009 Solutions - Graphs Included}}
+  <li> Series Solutions to Linear Equations: 6.1 </li>
+  <li> Bessel's Equation: 6.3.1 </li>
+  <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>
+ <li> Fourier Series: 11.1-11.3 </li>
+ <li> Fourier integral/transforms: 14.3-14.4</li>
+ <li> Linear Partial Differential Equations: Chapter 12 and Chapter 13 </li>
+ <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>
+=Course Materials=
-     Exam II -  Statistics
+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.
-     Mean = 36.5 (72.5%)
-     Median = 37.5 (75%)
-     A's = 9, B's = 32, C's = 38, D's = 19, F's = 16, Total Number of Exams  = 114
-     A's = 8%, B's = 28%, C's = 33%, D's = 17%, F's = 14 %
-{{PDF Table Item|filename=Math348_e2.spring2010.pdf|title=Exam II - Spring2010 }}
+==Syllabus==
-{{PDF Table Item|filename=Math348_e2Soln.Spring2010.pdf|title=Exam I - Spring2010 Solutions}}
-===Final Exam===
+==Lecture Pictures==
-The final exam will be held Saturday May 8th from 7:00pm-9:00pm. The classes will be testing in the following rooms:
-    Class    : Meeting Time    : Testing Room   : Proctor
-    MATH348B : 11:00am Section : Petroleum Hall : Jennifer Strong
-    MATH348C : 1:00pm Section  : CT 102         : Scott Strong
-    MATH348D : 2:00pm Section  : CO209          : Doug Poole
-Since we will be in different rooms it is very important that you go to the room associated with your section.
+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===
+[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],
+[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],
+[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],
+[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]
-There will be no notecards or calculators. The exam will have ten required questions and contain material outlined in the following review:
+===Fall 2012===
-{{PDF Table Item|filename=Math348_fereview.pdf|title=Final Exam - Review Sheet}}
+[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],
+[https://picasaweb.google.com/104969599060487036456/September212012?authuser=0&feat=directlink 9.21.2012],
+[https://picasaweb.google.com/104969599060487036456/September242012?authuser=0&feat=directlink 9.24.2012],
+[https://picasaweb.google.com/104969599060487036456/September262012?authuser=0&feat=directlink 9.26.2012],
+[https://picasaweb.google.com/104969599060487036456/September282012?authuser=0&feat=directlink 9.28.2012],
+[https://picasaweb.google.com/104969599060487036456/October12012?authuser=0&feat=directlink 10.1.2012],
+[https://picasaweb.google.com/104969599060487036456/October32012?authuser=0&feat=directlink 10.3.2012],
+[https://picasaweb.google.com/104969599060487036456/October52012?authuser=0&feat=directlink 10.5.2012],
+[https://picasaweb.google.com/104969599060487036456/October82012?authuser=0&feat=directlink 10.8.2012],
+[https://picasaweb.google.com/104969599060487036456/October102012?authuser=0&feat=directlink 10.10.2012],
+[https://picasaweb.google.com/104969599060487036456/October122012?authuser=0&feat=directlink 10.12.2012],
+[https://picasaweb.google.com/104969599060487036456/October192012?authuser=0&feat=directlink 10.19.2012],
+[https://picasaweb.google.com/104969599060487036456/October222012?authuser=0&feat=directlink 10.22.2012],
+[https://picasaweb.google.com/104969599060487036456/October242012?authuser=0&feat=directlink 10.24.2012],
+[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],
+[https://picasaweb.google.com/104969599060487036456/November22012?authuser=0&feat=directlink 11.2.2012],
+[https://picasaweb.google.com/104969599060487036456/November52012?authuser=0&feat=directlink 11.5.2012],
+[https://picasaweb.google.com/104969599060487036456/November72012?authuser=0&feat=directlink 11.7.2012],
+[https://picasaweb.google.com/104969599060487036456/November92012?authuser=0&feat=directlink 11.9.2012],
+[https://picasaweb.google.com/104969599060487036456/November122012?authuser=0&authkey=Gv1sRgCIWXycSF0ZWpRw&feat=directlink 11.12.2012],
+[https://picasaweb.google.com/104969599060487036456/November142012?authuser=0&feat=directlink 11.14.2012],
+[https://picasaweb.google.com/104969599060487036456/November162012?authuser=0&feat=directlink 11.16.2012],
+[https://picasaweb.google.com/104969599060487036456/November192012?authuser=0&feat=directlink 11.19.2012],
+[https://picasaweb.google.com/104969599060487036456/Novebmer262012?authuser=0&feat=directlink 11.26.2012],
+[https://picasaweb.google.com/104969599060487036456/November302012?authuser=0&feat=directlink 11.30.2012],
+[https://picasaweb.google.com/104969599060487036456/December32012?authuser=0&feat=directlink 12.3.2012],
+[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],
+[https://picasaweb.google.com/104969599060487036456/January162013?authuser=0&feat=directlink 1.16.2013],
+[https://picasaweb.google.com/104969599060487036456/January182013?authuser=0&feat=directlink 1.18.2013],
+[https://picasaweb.google.com/104969599060487036456/January212013?authuser=0&feat=directlink 1.21.2013],
+[https://picasaweb.google.com/104969599060487036456/January232013?authuser=0&feat=directlink 1.23.2013],
+[https://picasaweb.google.com/104969599060487036456/January252013?authuser=0&feat=directlink 1.25.2013],
+[https://picasaweb.google.com/104969599060487036456/January282013?authuser=0&feat=directlink 1.28.2013],
+[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]
-The following is an old 50 minute PDE exam, which should give you some idea of the content and structure of the PDE portion of the exam.
+*[[MATH-348 Advanced Engineering Mathematics - Lecture Pictures |MATH 348 : Advanced Engineering Mathematics - Lecture Pictures: Archive ]]
-{{PDF Table Item|filename=Math348_ePDE.old.pdf|title=OLD PDE EXAM - See Soln for the graph in problem 1}}
+==Useful Blog Posts==
-{{PDF Table Item|filename=Math348_ePDESOLN.old.pdf|title=OLD PDE EXAM - SOLN}}
-=Other Materials=
+Here you will find posts on the [http://math348.wordpress.com math348.wordpress.com blog] that typically get reposted semester after semester.
-==Linear Algebra==
-===Three Planes in Space===
-{{PDF Table Item|filename=Math348_planes.summer2009.pdf | title=Three Planes in Space - Four Different Ways}}
-  '''Legend for the Animations'''
-    Red = First Plane Equation
-    Orange = Second Plane Equation
-    Yellow = Third Plane Equation
-    Green = Column Space of A (AKA the set of all linear combination of the pivot columns of A)
-    Blue = Right Hand Side for non-homogeneous problem.
-[http://www.mines.edu/~sstrong/Media/LA_geometry/nonUnique.avi Animation : Ax=0 with oo-many solutions that form a line in space.]
-[http://www.mines.edu/~sstrong/Media/LA_geometry/nonUnique2.avi Animation : Ax=b with oo-many solutions that form a line in space.]
+*[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://www.mines.edu/~sstrong/Media/LA_geometry/Unique.avi Animation : Ax=b with a single solution]
+==Lecture Slides and Notes==
-[http://www.mines.edu/~sstrong/Media/LA_geometry/nonExist.avi Animation : Ax=b with no solutions]
+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:
-===Linear Algebra Software===
+. Definitions that are not useful for me to write and students to rewrite during lecture.
-[http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi Linear Algebra Toolkit]
-==Fourier Methods==
+. Derivations that will never need to be reproduced but need to be communicated quickly because they lead to important consequences.
-===Review of Functions===
+. Derivations that will need to be reproduced and have been recorded for clarity.
-{{PDF Table Item|filename=Unit_Circle.pd‎f|title=Special Angles and the Unit Circle}}
-{{PDF Table Item|filename=A61-TrigFormula.pdf|title=A61.TrigIdentities}}
-[http://en.wikipedia.org/wiki/Even_and_odd_functions  Odd and Even Functions (Wikipedia) : (see Also 09.LN)]
-[http://en.wikipedia.org/wiki/Periodic_function Periodic Functions (Wikipedia) : (See Also 09.LN)]
+Listed in each slide set are:
-===Fourier Series===
+    Associated Section/Pages from EK.AEM
+    Associated Lecture Notes
+    Associated Homework Assignments
-{{PDF Table Item|filename=Example11.1.1.pdf|title=FS for f(x}=x, x \in (-\pi,\pi)}}
+*[[MATH-348 Advanced Engineering Mathematics - Lecture Slides |MATH 348 : Advanced Engineering Mathematics - Lecture Slides ]]
-{{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===
+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://en.wikipedia.org/wiki/Fourier_transform Fourier Transform - Wikipedia]
+    Associated Sections/Pages from EK.AEM
-[http://en.wikipedia.org/wiki/Sinc_function Wikipedia - Sinc Function]
+    Suggested Problems from EK.AEM
-[http://mathworld.wolfram.com/SincFunction.html Mathworld - Sinc Function]
+    Brief Outline of Lecture Talking Points
-[http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem Wikipedia - Nyquist-Shannon Sampling Theorem]
+    Lecture Objectives
+    Lecture Goals
-[http://mathworld.wolfram.com/Convolution.html Mathworld - Convolution (Animation)]
+*[[MATH-348 Advanced Engineering Mathematics - Lecture Notes |MATH 348 : Advanced Engineering Mathematics - Lecture Notes ]]
-[http://cnx.org/content/m13106/latest/  Convolution and Diffraction (Animations)]
+==Homework Assignments==
-[http://cnx.org/content/m13106/latest/  Convolution and Diffraction (Animations)]
+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.
+Hours is the same as:
+. One and one-fifth work weeks.
+. Four months of average daily facebooking (or so I've read)
+. Six weeks of average video gameplay.
+. Seven days of average phone usage
+. Thirty-two days of average texting.
+. 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://commons.wikimedia.org/wiki/File:Convolution_Animation_(Boxcar_and_Ramp).gif Wikipedia - Convolution (Animation)]
+*[[MATH-348 Advanced Engineering Mathematics - Textbook Usage |MATH 348 : Advanced Engineering Mathematics - Textbook Usage ]]
-[http://en.wikipedia.org/wiki/Green's_function Green's Function - Wikipedia]
+*[[MATH-348 Advanced Engineering Mathematics - Assignments |MATH 348 : Advanced Engineering Mathematics - Assignments ]]
-{{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==
+==Exams==
-===Ordinary Differential Equations===
-{{PDF Table Item|filename=Math348_ODEReview.fall2009.pdf|title= Review of Ordinary Differential Equations (DRAFT - 11/16/09)}}
-[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]
+Previous exams going back through Fall2008 and review sheets are available for studying via the following link.
-===Heat Equation===
-[http://www.mines.edu/~sstrong/AEM_Materials/V.mp4 Heat Movie 1 - abs(x)]
-[http://www.mines.edu/~sstrong/AEM_Materials/parabola.mp4 Heat Movie 2 - parabola]
-[http://www.mines.edu/~sstrong/AEM_Materials/doubleV.mp4 Heat Movie 3 - Double V]
-[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 ]
-[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 ]
-===Wave Equation===
-====1D Wave Equation====
-[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)]
-[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)]
-[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]
+*[[MATH-348 Advanced Engineering Mathematics - Exams |MATH 348 : Advanced Engineering Mathematics - Exams ]]
-[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]]