TAM 542
TAM 542 - Mathematical Methods II
Spring 2024
| Title | Rubric | Section | CRN | Type | Hours | Times | Days | Location | Instructor |
|---|---|---|---|---|---|---|---|---|---|
| Mathematical Methods II | TAM542 | E | 36402 | LCD | 4 | 1600 - 1750 | M W | 2200 Sidney Lu Mech Engr Bldg | Moshe Matalon Tixian Wang |
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Official Description
Detailed Course Description
Continuation of TAM 541. Modeling, inequalities, elements of functional analysis; partial differential equations, existence and uniqueness, second-order equations; hyperbolic conservation laws; numerical methods, eigenfunction expansions, integral transforms, and fundamental solutions; engineering applications drawn from mechanics. Prerequisite: TAM 541. 4 graduate hours.
Textbook:
Applied Partial Differential Equations, Richard Haberman, Prentice-Hall
Calculus of Variations, Robert Weinstock, Dover Publications
Topics:
Introduction
Partial differential equations in mechanics (4 hr)
Elements of functional analysis (8 hr)
Partial differential equations
Basic theory of second-order PDEs (4 hr)
Examples from mechanics: the heat equation, Laplace|rsquo;s equation, the wave equation (6 hr)
Separation of variables (4 hr)
Eigenfunction expansions (6 hr)
Integral transforms and fundamental solutions; Green|rsquo;s functions (6 hr)
Method of characteristics (4 hr)
Hyperbolic conservation laws; generalized weak solutions (6 hr)
Calculus of variations with applications to mechanics (10 hr)
Midterm (2)
TOTAL HOURS: 60