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Mathematical Methods for Engineers (10.539/24.539)
Detailed Course Syllabus

The tables below represent a working course syllabus that lists the primary subjects to be treated and the associated homework assignment that covers the material on a particular topic. Generally, it represents a rough road map for the entire course, and it directly follows your Math Methods Lecture Notes (indicated chapters refer to the Lecture Notes). This syllabus is tentative and it will be modified as required to meet the needs of this particular class. There will be roughly nine homework sets and two or three projects, which averages to about one assignment per week (times allocated may be adjusted slightly to account for the difficulty or length of the particular assignment). The specific problems for each assignment will be given in class and posted on the web as they become available, and the due dates for the assignments will be announced in class.

Solution of ODEs
HW Assignment
1 - 3
Review of Introductory Differential Equations and Linear Algebra
HW #1
General Solution to IVPs (analytical and numerical solution to 1st order systems)
HW #2
Project #1 -- Some Typical IVPs
General Solution to BVPs (numerical solution via the Shooting and FD methods)
HW #3
Numerical Solution of Algebraic Equations
Project #2 -- Some Typical BVPs
Appendix I
Introduction to COMSOL Multiphysics (with focus on solution of ODEs)
HW #4

Advanced Analysis Techniques
HW Assignment
Power Series Solution Method
HW #5
Special Functions and Orthogonality
HW #6
Sturm-Liouville Theory and Generalized Fourier Series

Solution of PDEs
HW Assignment
Analytical Solution of PDEs (Separation of Variables and Integral Transform Methods)
HW #7
Numerical Solution of PDEs via the FD Method
HW #8
Appendix I
Introduction to COMSOL Multiphysics (with focus on solution of PDEs)
HW #9
Project #3 -- Some Typical PDEs

Last updated by Prof. John R. White (Sept. 2007)

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