TAM 541: Mathematical Methods I

Class Description:

Vector and tensor algebra, introduction to complex-variable methods; ordinary differential equations, qualitative questions of existence and uniqueness; analytic solution methods, numerical methods, power-series solution and special functions; eigenvalue problems, Green|#39;s functions, Laplace transforms, stability of solutions; engineering applications drawn from mechanics. Prerequisite: MATH 241 (formerly MATH 243) or MATH 380; one of MATH 385, MATH 386, MATH 441. 4 graduate hours.

Textbook:

Michael Greenberg, Advanced Engineering Mathematics, Prentice-Hall

Topics:

Introduction
Linear algebra and linear vector spaces (6 hr)
Introduction to complex analysis, examples from mechanics (10 hr)

Ordinary differential equations
ODEs in mechanics (2 hr)
Existence, uniqueness and stability of solutions (4 hr)
Solution methods for various classes of ODEs (6 hr)
Series solutions of scalar ODEs, special functions (8 hr)
Sturm|ndash;Liouville problem, eigenvalues; mechanics applications (6 hr)
Green|rsquo;s function, Laplace transforms (6 hr)
Solution methods for systems of ODEs (4 hr)
Qualitative theory of solutions of ODEs; mechanics applications (6 hr)

Midterm (2 hr)
TOTAL HOURS: 60

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