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Math 487. /ECE 493. Advanced Engineering Math

Prerequisite: Calculus III and Differential Equations

Text: Michael D. Greenberg: Advanced Engineering Mathematics. (2nd Ed) Prentice Hall, Upper Saddle River. 1998.

The crux of this course is to learn Fourier analysis for solving boundary value problems, to study Sturm-Liouville Systems, and to use complex variables to study Fourier and Laplace transforms and their inversions.

Emphasis I: Linear Algebra (4 weeks)
1. Euclidean geometry: vectors, dot products, Rn
2. Matrix algebra: matrices, solving equations, eigendecompositions
3. Calculus: derivatives, change of coordinates

Emphasis II: Differential Equations (4 weeks)
1. Linear systems: matrix exponentials
2. Nonlinear equations: fixed points and linearization
3. PDEs: separation of variables

Emphasis III: Complex Variables (4 weeks)
1. Fourier theory: transforms, applications to ODEs, PDEs
2. Contour integration: Cauchy-Riemann, poles
3. More general integration: Differential operators, Green/Gauss/Stokes