Revision as of 15:44, 22 March 2010

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
   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 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

These downloads require Adobe Acrobat Reader MATH348.Spring2010.Syllabus Lecture Slides 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 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 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 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 29th Homework5 - 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 Other Materials Linear Algebra Three Planes in Space 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. Animation : Ax=0 with oo-many solutions that form a line in space. Animation : Ax=b with oo-many 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 - Nyquist-Shannon 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)