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Mathematical Methods in Engineering I
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| Organization: | University of Notre Dame |
| Department: | Department of Chemical Engineering |
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College
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Development of a comprehensive, but introductory, understanding of linear analysis as applied to algebraic and differential systems. This is done by applying the general solution methods, inverse operators and spectral expansions, to a variety of problems chosen for either their physical or mathematical interest.
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* Mathematical Methods in Chemical Engineering by Varma and Morbidelli Oxford (1997) * Principles and Techniques of Applied Mathematics by Friedman Dover (1990) * Foundations of Applied Mathematics by Greenberg Prentice-Hall (1978) |
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This is an applied math course that is intended to serve the dual role of being the only graduate mathematics class for many chemical engineers (suggesting a need for breadth) but just the first of many others (suggesting a need for some depth) It is application motivated and problem based. Proofs are done only when they give special insight.
Topics include a comprehensive introduction to linear algebra, a selected treatment of ordinary differential equations as they apply to important problems in engineering and science and a brief introduction to partial differential equations that arise in science and engineering. Every attempt is made to unify the linear operator concept throughout the topics of this course.
Topics:
Linear algebra: - Basic linear algebra
- Applications of linear algebra
- Linear spaces and linear operators
- Algebraic eigenvalue problems
Linear ordinary differential equations: - Initial value problems
- Boundary value problems
- Differential eigenvalue problems
Partial Differential Equations: - Order and classifications
- Separation of variables
- Similarity solutions
- Finite Fourier Transform
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http://www.nd.edu/~mjm/cheg542.html
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