MATH348 Advanced Engineering Mathematics

Main Page

>

Mathematical and Computer Sciences Course Wikis

These downloads require Adobe Acrobat Reader 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@gmail.com 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 Syllabus

MATH348.Spring2010.Syllabus Lecture Slides 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 need 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 Lecture Notes 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 Assignments The assignments for this course have reached a steady-state. Consequently, solutions are often available through students who have taken the course in the past. Since these resources might not be available to all students, I have drafted a set of solutions to these homework assignments which I make available through this site. These solutions were, more or less, finalized during the Spring of 2010 and represents the end of an evolution starting around 2006. Outside of the lecture itself, these homeworks and solutions represents some of the oldest parts of the course and many of the ancestors can be found on older ticc pages. In the past the homeworks tended to have a good deal of discussion providing context to a problem so that both the mechanics and concepts could be gleaned. However, after talking with some students and course reviews I decided to move the commentary to the solutions in favor of a more streamlined problem statement. It is unclear whether this latest incarnation is 'better' than the past but what is clear is that they won't be regressing unless someone else wants to revamp them. If you want to see the previous versions then visit the older ticc pages. If you find any typos in these solutions then I would appreciate you letting me know. They are pretty clean but they could always be `cleaner.' With that said, I must make emphasize the following point: Caveat Emptor : We will work from these problems and since solutions are readily available it is up to the individual user to make sure that they are LEARNING the material. If you buy into a program of procrastination followed by rapid and thoughtless recreation then you may find an inadequate product, which cannot be returned. MATH 348 : Advanced Engineering Mathematics - Assignments 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 I - 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 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) 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 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 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 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 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 wave-front Shockwave Slowmo NASA - Shock Wave Simulator Shockwave :)