TAM 542: Mathematical Methods II

Class 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

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