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

Department of
Mathematics University of Illinois at Urbana-Champaign 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Telephone: (217) 333-3350 Fax (217) 333-9576 office@math.uiuc.edu |