MATH348 Advanced Engineering Mathematics
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Course InformationMATH348: 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 InformationInstructor : Scott Strong Office : Chauvenet Hall 266 Office Phone : 303.384.2446 email : math348@gmail.com Textbook InformationTextbook : 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 MaterialsSyllabusMATH348.Spring2010.Syllabus
| Lecture SlidesThere 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 Lecture NotesThere 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 AssignmentsThe 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.
Exams
Other MaterialsLinear AlgebraThree Planes in SpaceThree 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 SoftwareFourier MethodsReview of FunctionsSpecial Angles and the Unit Circle
| A61.TrigIdentities
| Odd and Even Functions (Wikipedia) : (see Also 09.LN) Periodic Functions (Wikipedia) : (See Also 09.LN) Fourier SeriesFS 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 TransformFourier Transform - Wikipedia Wikipedia - Sinc Function Mathworld - Sinc Function Wikipedia - Nyquist-Shannon Sampling Theorem Mathworld - Convolution (Animation) Convolution and Diffraction (Animations) Convolution and Diffraction (Animations) Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125}
| Partial Differential EquationsOrdinary Differential EquationsReview of Ordinary Differential Equations (DRAFT - 11/16/09)
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You Tube Video - Millennium Bridge Resonance Heat EquationHeat 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 Equation1D Wave EquationWave on a 1-D Sting with Fixed Endpoints Wave on a 1-D Sting with FLAT Endpoints from HW10 Traveling Wave :u0(x) = − tanh(x): Red = Right Traveling, Blue=Left Traveling, Black = Superposition 2D Wave Equation Rectangular and PolarRectangular Membrane Movie 1 -Text Example pg577 Rectangular Membrane 2 -Text Example pg577 Animations of Rectangular Membrane Modes - Pretty Good Animations done by Dr. Russell - All sorts of stuff!
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 PhenomenonWikipedia 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 |