MATH-348 Advanced Engineering Mathematics - Spring 2009

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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

Instructor : Scott Strong

Office : Chauvenet Hall 278

Office Phone : 303.384.2446

email : math348.spring2009@gmail.com

Course Calander

Classes Begin : January 7th, 2009

Meeting Days : Monday, Wednesday, Friday

Course Sections :

    Section B,  12:00pm-12:50pm, Alderson Hall 330
    Section C, 1:00pm-1:50pm, Green Center 211
    Section D, 2:00pm-2:50pm, Green Center 211

Class Holidays :

    February 16th, 2009 - Presidents Day
    March 9th-13th, 2009 - Spring Break
    April 2nd-4th, 2009 - E-Days

Classes End : April 30th, 2009

Important Dates :

   January  22nd - Last Day to Withdrawal  (Without a W)
   March 24th - Last Day to Withdrawal 

Office Hours

Fixed Office Hours :

 M : 3-4pm
 W : 11-12pm
 F : 11-12pm 

If you cannot meet during the previous office hours then please contact me to schedule another meeting time.

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

These downloads require Adobe Acrobat Reader Course Documents Handouts A61.TrigIdentities Special Angles and the Unit Circle FS for f(x}=x, x \in (-\pi,\pi) FS for f(x}=Exp(Abs(x)), x \in (-\pi,\pi) 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) Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125} 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 on a 1-D Sting with Fixed Endpoints Wave on a 1-D Sting with Fixed Endpoints - Animated with first 5 Fourier Modes (Fundamental Mode in Red) Wave on a 1-D Sting with FLAT Endpoints from HW10 Wave on a 1-D Sting with FLAT Endpoints from HW10 - Animated with first 5 Fourier Modes (Fundamental Mode in Red) Traveling Wave :u0(x) = − tanh(x): Red = Right Traveling, Blue=Left Traveling, Black = Superposition 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 Well-Tempered 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 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 wave-front NASA - Shock Wave Simulator Shockwave :) Millennium Bridge - Wikipedia You Tube Video - Millennium Bridge Resonance Lecture Slides Lecture 1 Lecture 2 Lecture 3-4 Lecture 5 Lecture 6'ish Lecture Six Lecture Seven Lecture Eight Lecture Nine Lecture Ten Lecture Eleven Lecture Twelve Lecture Thirteen Lecture Fourteen Lecture Fifteen Syllabus MATH348.Spring2009.Syllabus Exams Exam I will be held on February 13th in class there will be no class the following Wednesday. There will be no notecards or calculators. The exam will be five questions and contain material outlined in the following review: Exam 1 - Review Sheet Exam 1 - Fall2008 Exam 1 - Fall2008 Solutions Exam I - Statistics Average = 39.69 = 79.38% Median = 41 = 82% A's = 27, B's = 31 , C's = 17 , D's = 16, F's =9, Total Number of Exams = 100 Exam I - Spring2009 Exam I - Spring2009 Solutions Exam II will be held on April 1st in class there will be no class the following Monday. There will be no notecards or calculators. The exam will be five questions and contain material outlined in the following review: Exam 2 - Review Sheet Exam 2 - Spring2009 Q + A Exam 2 - Fall2008 Exam 2 - Fall2008 Solutions Exam 2 - Fall2008 Q + A Exam II - Statistics Average = 37.14 = 74.29% Median = 37 = 74%, A's = 9, B's = 25 , C's = 31 , D's = 23, F's =9, Total Number of Exams = 97 Exam II - Spring2009 See Soln for problem 3 graph. Exam II - Spring2009 Solutions The final exam will be held on May 4th from 10:15am-12:15am. The classes will be split across rooms. Please go to the room assigned to the class you are enrolled in. There will be no notecards or calculators. The exam will be cumulative with an emphasis on PDE. MATH348B-BE241 Proctor: Ecklund MATH348C-BB201 Proctor: Bridgman MATH348D-BB204A Proctor: Strong Since, it is likely I won't see most of you at the exam -- Have a good summer and it was nice having class with you. :) I will not be posting a practice exam, since it is policy to not disseminate final exams. I do have an old PDE only exam and I will post it below. Final Exam - Review Sheet OLD PDE EXAM - See Soln for the graph in problem 1 OLD PDE EXAM - SOLN Assignments MATH348.Spring2009.Homework1 MATH348.Spring2009.Homework1.Solutions MATH348.Spring2009.Homework2 MATH348.Spring2009.Homework2Solutions Picture of a Parallelepiped : [1] MATH348.Spring2009.Homework3 MATH348.Spring2009.Homework3Solutions MATH348.Spring2009.Homework4 MATH348.Spring2009.Homework4Solutions MATH348.Spring2009.Homework5 MATH348.Spring2009.Homework5Solutions MATH348.Spring2009.Homework6 NOTE : For the graphs you may want to consider using the eigenmath program posted below. Eigenmath Script for Example1 Results Feel free to post better scripts. I'm sure that this program could find the coefficients from their integral definitions. NOTE : A typo has been corrected. You should assume that E=\omega = 1 and L = \pi. NOTE : Thanks to David Melton for Another Graphing Utility - Graphs Truncated FS MATH348.Spring2009.Homework6Solutions MATH348.Spring2009.Homework7 MATH348.Spring2009.Homework7Solutions MATH348.Spring2009.Homework8 MATH348.Spring2009.Homework8Solutions MATH348.Spring2009.Homework9 MATH348.Spring2009.Homework9Solutions MATH348.Spring2009.Homework10 MATH348.Spring2009.Homework10Solutions

Course Links

Graphing Utilities

   Free Mathematica Like Program for Windows and Mac
   Eigenmath Manual