Michael D. Greenberg, Advanced Engineering Mathematics (second Edition; 0-13-221431-1), Prentice-Hall, 1998.
Math 527, or permission of the instructor
A second semester graduate course intended primarily for students in mechanical and aerospace engineering, biomedical engineering, and other engineering programs. There will be three parts:
1. Complex variable theory, with topics chosen from the differential and integral calculus of functions of a complex variable, conformal mapping, Taylor series, Laurent series, the residue theorem, and applications to partial differential equations and to fluid mechanics.
2. Calculus of variations, including the motivation of variational principles from physical laws, derivation of Euler-Lagrange equations, stability criterion, and linearization.
3. Perturbation methods, including applications to ode systems, examples of boundary layer, multiple-scale problems, and eigenvalue problems.