# 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 Information## Textbook InformationI do not require a textbook for this course as the lecture notes should suffice. However, owning a post Calc/DiffEQ textbook may be useful. I provide some options below. ## Kreyszig Abridged editionThe bookstore sells an abridged version of the Kreyszig text, which is now in its tenth edition -- all previous CSM abridged editions will be acceptable for this course. The abridged version contains the seven chapters and an appendix: 1. Chapter 5: Power Series Solutions to ODE and Frobenius method 2. Chapter 7: Systems of Linear Algebraic Equations 3. Chapter 8: Eigenvalues and Eigenvectors 4. Chapter 11: Fourier Series 5. Chapter 12: Introduction to Linear Partial Differential Equations 6. Chapter 20: Numerical Methods in Linear Algebra 7. Chapter 21: Numerical Methods in Differential Equations
- Schaums Outline Series - Advanced Mathematics for Engineers and Scientists. There is a lot of overlap between this book and what we will cover.
## Texts on Fourier AnalysisThe following are some texts that you may want to consider for study of Fourier "Analysis" (AKA Fourier methods.) - Fourier Series by Tolstov and published by Dover
- Schaum's Outline of Fourier Analysis with Applications to Boundary Value Problems
- Schaum's Outline of Signals and Systems, Second Edition
- Schaums Outline of Digital Signal Processing, 2nd Edition (Schaum's Outline Series)
## Texts on PDEThe following are some texts that you may want to consider for study of linear PDE. - PDE for Scientists and Engineers Dover Text
- Schaum's Outline of Partial Differential Equations (Schaum's Outline Series)
- Applied PDE by Richard Haberman This is the text used for MATH455-PDE, if you are considering a minor then you will be able to use it twice.
## Texts on Linear AlgebraThe following are some texts that you may want to consider for study of linear algebra. - Linear Algebra by David C. Lay This text used for MATH332-Linear Algebra, if you are considering a minor then you will be able to use it twice.
- Schaum's Outline of Linear Algebra Fourth Edition
- Matrices and Linear Algebra (Dover Books on Mathematics)
- Linear Algebra (Dover Books on Mathematics - Mature)
## Continued use of your Differential Equations (MATH225) textYour MATH225 differential equations text was chosen, partially, so that you could use it for topics in this course. The following will outline how the chapters in Differential Equations by Zill and Cullen matches up with AEM material. - First task is to review some concepts in ODE. Specifically, we will need to remember/learn how to:
- Constant Linear Problems: 4.3
- Undetermined Coefficients: 4.4
- Variation of Parameters: 4.6 - this was likely not covered in your course, we will cover it in a homework problem.
- Mass-spring Problems: 5.1
- Series Solutions to Linear Equations: 6.1
- Bessel's Equation: 6.3.1
- Boundary Value Problems and Sturm-Liouville Problems: 5.2 (example 2) and to some extend chapter 12-13 although this will come later with PDE, 11.4 (example 1)
- Fourier Series: 11.1-11.3
- Fourier integral/transforms: 14.3-14.4
- Linear Partial Differential Equations: Chapter 12 and Chapter 13
- Linear Algebra: Appendix II, we will actually need far more than this appendix will cover but it will be a good start.
## Course MaterialsThe following outlines materials specific to this course. The materials, as indicated, have been developed over time and have achieved a steady-state. An archive of older ticc pages is available. The ticc websites pick up at Spring 2008 when I started presenting linear algebra first. ## Syllabus## Lecture PicturesThis semester, Spring 2012, I will try to take pictures of the boards before I scrub them. One word of warning, these are not a substitute for lecture itself. The interactions and development are often important in understanding the material. ## Spring 20121.11.2012, 1.13.2012, 1.16.2012, 1.18.2012,1.20.2012, 1.23.2012, 1.25.2012,1.27.2012, 1.30.2012, 2.6.2012, 2.8.2012, 2.10.2012, 2.13.2012, 2.15.2012, 2.17.2012. 2.22.2012, 2.24.2012, 2.27.2012,2.29.2012, 3.2.2012, 3.5.2012, 3.7.2012, 3.19.2012, 3.21.2012,3.23.2012, 3.26.2012, 3.28.2012, 4.2.2012, 4.4.2012, 4.7.2012, 4.9.2012, 4.11.2012, 4.13.2012, 4.16.2012, 4.20.2012, 4.23.2012, 4.25.2012, 4.27.2012, 4.30.2012, 5.2.2012 ## Fall 20128.22.2012, 8.24.2012, 8.27.2012, 8.29.2012,8.31.2012, 9.3.2012, 9.5.2012, 9.7.2012, 9.10.2012,9.12.2012, 9.14.2012, 9.17.2012, 9.19.2012, 9.21.2012, 9.24.2012, 9.26.2012, 9.28.2012, 10.1.2012, 10.3.2012, 10.5.2012, 10.8.2012, 10.10.2012, 10.12.2012, 10.19.2012, 10.22.2012, 10.24.2012, 10.29.2012, 10.31.2012, 11.2.2012, 11.5.2012, 11.7.2012, 11.9.2012, 11.12.2012, 11.14.2012, 11.16.2012, 11.19.2012, 11.26.2012, 11.30.2012, 12.3.2012, 11.5.2012 ## Spring 20131.9.2013, 1.11.2013, 1.14.2013, 1.16.2013, 1.18.2013, 1.21.2013, 1.23.2013, 1.25.2013, 1.28.2013, 1.30.2013, 2.1.2013, 2.4.2013, 2.6.2013, 2.8.2013, 2.11.2013, 2.13.2013, 2.15.2013, 2.20.2013, 2.22.2013, 2.25.2013, 2.27.2013, 3.1.2013, 3.4.2013, 3.6.2013, 3.8.2013, 3.18.2013, 3.20.2013, 3.25.2013 -- 4.3.2013: Acoustics and Waves on a Circle, 4.5.2013 -- 4.19.2013: Complex FS through FT, 4.22.2013 ## Useful Blog PostsHere you will find posts on the math348.wordpress.com blog that typically get reposted semester after semester. - Post about spectrograms and the b-side to the Windowlicker single by Aphex Twin.
## Lecture Slides and NotesThere 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 desire 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 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 ## Homework AssignmentsHomework is an essential part of any course. We will only have class/lecture roughly 48 hours in one semester. While this sounds like a lot it really isn't a ton. Here are some comparisons. 48 Hours is the same as: 1. One and one-fifth work weeks. 2. Four months of average daily facebooking (or so I've read) 3. Six weeks of average video gameplay. 4. Seven days of average phone usage 5. Thirty-two days of average texting. 6. Two and one-half weeks of average driving. I guess the point I'm trying to make is that some of these things are what people do everyday and we do them b/c we deem them important. That's fine, but when deciding what you do everyday, remember that this course is about $1000-important to whomever is paying for it. A majority of student learning occurs outside of class, which is largely spent doing homework. The homeworks for this course are meant to guide/focus this time and your homework will primarily reflect the time and effort spent with them. I encourage you to work every day with the goal of spending six-hours outside of class per week on AEM material.
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## ExamsPrevious exams going back through Fall2008 and review sheets are available for studying via the following link.
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