# 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 : 11:00am-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


## 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 unavailable.

## Textbook Information

    Textbook : Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9
9th Edition Amazon : Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9
8th Edition Amazon (Used) : Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9


# Course Materials

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
04.LS.Abstract Vector Spaces
05.LS.Fourier Series to Fourier Integral to Fourier Transform - Update 4/5/2010
06.LS.1D Heat Equation-Separation of Variables
07.LS.The Acoustic Approximation and Wave Equations

## Lecture Notes

??
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 7:00pm-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.

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 non-homogeneous problem.


## Fourier Methods

### Review of Functions

Special Angles and the Unit Circle
A61.TrigIdentities

### Fourier Series

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

### Fourier Transform

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)