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
Instructor : Scott Strong
Office : 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 : 11:00am11:50am  Location: Coolbaugh Hall 131
C : 1:00pm1:50pm  Location: Green Center 211
D : 2:00pm2:50pm  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 15th19th : Spring Break
April 8th10th : EDays
May 3th7th : Dead Week
May 7th : Dead Day
Office Hours
Fixed Office Hours :
MWF : 12:00pm12:50pm
Monday : 3:00pm5:00pm
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 unavailable.
Textbook Information
Textbook : Advanced Engineering Mathematics  Erwin Kreyszig, ISBN 9780471488859
9th Edition Amazon : Advanced Engineering Mathematics  Erwin Kreyszig, ISBN 9780471488859
8th Edition Amazon (Used) : Advanced Engineering Mathematics  Erwin Kreyszig, ISBN 9780471488859
Course Materials
These downloads require Adobe Acrobat Reader
MATH348.Spring2010.Syllabus

MATH348.Spring2010.Syllabus
Lecture Slides

00.LS.Introduction

00.LS.Introduction

00.LS.Introduction

00.LS.Introduction

00.LS.Introduction

01.LS.Classical Vector Spaces

02.LS.Geometry in R^n

03.LS.KinematicsAndDynamics

03.LS.KinematicsAndDynamics  Those Evil Natured Robots
Linear Algebra and its Applicationsby Peter D. Lax

04.LS.Abstract Vector Spaces

05.LS.Fourier Series to Fourier Integral to Fourier Transform  Update 4/5/2010

06.LS.1D Heat EquationSeparation of Variables

07.LS.The Acoustic Approximation and Wave Equations
Lecture Notes

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00.LN.Overview And Outline

01.LN.LinearDefinitions : Updated 1.27.2010. Footnotes have been added referencing locations in the text where these definitions can be found.

02.LN.Introduction To Linear Equations

03.LN.Solving Linear Systems

04.LN.Square Systems  Determinants and Matrix Inversion

05.LN.Introduction to Linear Vector Spaces

06.LN.Chapter 7  Wrap Up

07.LN.Eigenproblems

08.LN.Diagonalization

09.LN.Introduction to Fourier Series : Review of Periodic and Symmetric Functions

10.LN.Complex Fourier Series

11.LN.Fourier Integral to Fourier Transform

12.LN.Fourier Transform

13.LN.IntroToPDE

14.LN.HeatEquation

15.LN.WaveEquation
Assignments

Homework0  Due Jan. 18th by 5:00pm

Homework0  Solutions

Homework1  Due Feb. 3rd by 5:00pm  Note: Updated 1/19/2010, fixed a typo in problem 2 matrix 2, a_{22} = 3

Homework1  Solutions
Graphics for Homework 1
Geometry of Problem 2 System 1
Geometry of Problem 2 System 2
Geometry of Problem 2 System 3
Geometry of Problem 2 System 4
Geometry of Problem 2 System 5
Interpolated Parabolas of Problem 4 Set 1
Interpolated Parabolas of Problem 4 Set 2
Geometry of Least Squares Problem of Problem 4 Set 2
Interpolated Parabolas of Problem 4 Set 3
Fourier Transform

Homework2  Due Feb. 12th by 5:00pm : 1) Header Box Updated 2) Problem 4.2 \lambda = n^2

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.
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

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. :)

Homework3  Solutions

Homework4  Due: March 12th

Homework4  Solutions

Homework5  Due: March 31st

Homework5  Solutions

Homework6  Due: April 12th

Homework6  Solutions

Homework7  Due April 28  Last edits (minor) at 4:31pm.

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.

Homework8  Due May 3

Homework8  Solutions
Exams
Exam I
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:

Exam 1  Review Sheet
The following exams with solutions are posted for your review.

Exam 1  Fall2008

Exam 1  Fall2008 Solutions

Exam I  Spring2009

Exam I  Spring2009 Solutions

Exam I  Summer2009

Exam I  Summer2009 Solutions

Exam I  Fall2009

Exam I  Fall2009 Solutions
Exam I  Statistics
Mean = 37.15 (74,31%)
Median = 38 (76%)
Mode = 47 (94%)
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 %

Exam I  Spring2010

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:

Exam 2  Review Sheet
The following are the results of Q+A's from previous semesters:

Exam 2  Spring2009 Q + A

Exam 2  Fall2008 Q + A
The following exams with solutions are posted for your review.

Exam II  Spring2009 See Soln for problem 3 graph.

Exam II  Spring2009 Solutions

Exam 2  Fall2008

Exam 2  Fall2008 Solutions

Exam II  Summer2009

Exam II  Summer2009 Solutions

Exam II  Fall2009

Exam II  Fall2009 Solutions  Graphs Included
Exam II  Statistics
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 %

Exam II  Spring2010

Exam I  Spring2010 Solutions
Final Exam
The final exam will be held Saturday May 8th from 7:00pm9:00pm. 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.
There will be no notecards or calculators. The exam will have ten required questions and contain material outlined in the following review:

Final Exam  Review Sheet
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.

OLD PDE EXAM  See Soln for the graph in problem 1

OLD PDE EXAM  SOLN
Other Materials
Linear Algebra
Three Planes in Space

Three Planes in Space  Four Different Ways

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 nonhomogeneous problem.
Animation : Ax=0 with oomany solutions that form a line in space.
Animation : Ax=b with oomany solutions that form a line in space.
Animation : Ax=b with a single solution
Animation : Ax=b with no solutions
Linear Algebra Software
Linear Algebra Toolkit
Fourier Methods
Review of Functions

Special Angles and the Unit Circle

A61.TrigIdentities
Odd and Even Functions (Wikipedia) : (see Also 09.LN)
Periodic Functions (Wikipedia) : (See Also 09.LN)
Fourier Series

FS for f(x}=x, x \in (\pi,\pi)

FS for f(x}=Exp(Abs(x)), x \in (\pi,\pi)
Fourier Series  Wikipedia
Gibbs Phenomenon  Wikipedia
Fourier Transform
Fourier Transform  Wikipedia
Wikipedia  Sinc Function
Mathworld  Sinc Function
Wikipedia  NyquistShannon Sampling Theorem
Mathworld  Convolution (Animation)
Convolution and Diffraction (Animations)
Convolution and Diffraction (Animations)
Wikipedia  Convolution (Animation)
Green's Function  Wikipedia

Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125}
Partial Differential Equations
Ordinary Differential Equations

Review of Ordinary Differential Equations (DRAFT  11/16/09)
Millennium Bridge  Wikipedia
You Tube Video  Millennium Bridge Resonance
Heat Equation
Heat Movie 1  abs(x)
Heat Movie 2  parabola
Heat Movie 3  Double V
Heat Movie 4  Forced Heat Equation with B.C. u(0,t)=u(L,t)=0
Heat Movie 5  Forced Heat Equation with B.C. u_{x}(0,t)=u_{x}(L,t)=0
Wave Equation
1D Wave Equation
Wave on a 1D Sting with Fixed Endpoints
Wave on a 1D Sting with Fixed Endpoints  Animated with first 5 Fourier Modes (Fundamental Mode in Red)
Wave on a 1D Sting with FLAT Endpoints from HW10
Wave on a 1D Sting with FLAT Endpoints from HW10  Animated with first 5 Fourier Modes (Fundamental Mode in Red)
Traveling Wave :u_{0}(x) = − tanh(x): Red = Right Traveling, Blue=Left Traveling, Black = Superposition
2D Wave Equation Rectangular and Polar
Rectangular Membrane Movie 1 Text Example pg577
Rectangular Membrane 2 Text Example pg577
Applet  Pretty Cool
Rectangular Membrane Modes
Animations of Rectangular Membrane Modes  Pretty Good
Animations done by Dr. Russell  All sorts of stuff!
The WellTempered Timpani By Richard K. Jones
Vibrating Membrane1  12.9.1 Example
Vibrating Membrane2  12.9.1 Example
Vibrating Membrane3  12.9.1 Example
Vibrating Membrane4  12.9.1 Example
Nonlinear Wave Phenomenon
Wikipedia Article on Shock Waves
Animation of Shock Wave Formation in Pressure Field
Shock Wave (Plane)  You Tube 1
Shock Wave (Plane)  You Tube 2
Shock Wave (Explosion)  You Tube 3
Shock Wave (Explosion)  You Tube 4 : Ignore The the cartoon bubble
Shock Wave (Simulation)  You Tube 5 : Notice the distortion of the expanding wavefront
Shockwave Slowmo
NASA  Shock Wave Simulator
Shockwave :)

