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ME 6443: Variational Methods in Engineering
Offered Every Fall
| Credit Hours: |
3-0-3 |
| Prerequisites: |
Graduate standing in engineering or related discipline |
| Catalog Description: |
Calculus of variations, Hamilton's principle and Lagrange's equations, Sturm-Liouville problems, approximation techniques. |
| Textbooks: |
Robert Weinstock, Calculus of Variations, Dover Publications, 1980.
Francis Hilderbrand, Methods of Applied Mathematics, 2nd Edition, Dover, 1992. |
| Instructors: |
Aldo Ferri, Jerry Ginsberg, John Papastavridis |
| Topics: |
- Introduction, review of min/max of functions, algebraic equality and inequality constraints; Lagrange multipliers
- Basics of the calculus of variations
- Isoperimetric constraints; finite and differential constraints
- Hamilton's principle and Lagrange's equations
- Sturm-Liouville problems
- Functions of two variables or more variables; vibration of strings, rods, beams; static and dynamic deformation of membranes and plates
- Approximation techniques; Ritz methods such as the Bubnov-Galerkin and Petrov-Galerkin techniques; method of weighted residuals; finite-element analysis
- Optimal control theory; quadratic cost functions; two-point boundary-value problems; Riccati equation; optimal state-feedback.
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| Grading Scheme (%): |
Homework |
10 |
Midterm |
40 |
Final |
50 |
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