Applied Mathematics II
| Course Purpose |
|---|
| This course deals with analysis, one of the most significant branch of mathematics, that serves in the engineering field to describe and understand research objects with phenomena surrounding them. The lectures in this course focus on the topics listed below that include: differential equations, Laplace transform, and Fourier analysis. |
| Learning Goals |
| By the end of this course, successful students should be able to: describe the technical terms and key concepts of the topics introduced in the class; apply those mathematical methods to engineering problems; convey the analytical computation. |
| Topic | |
|---|---|
| Session 1 | Complex analysis (1) Complex number, Complex plane Polar coordinate system, Power expression |
| Session 2 | Complex analysis (2) Differential operation Laplace equation, Euler equation |
| Session 3 | Complex analysis (3) Holomorphic function Cauchy-Riemann equation |
| Session 4 | Complex analysis (4) Complex integral Cauchy integral theorem (first theorem) |
| Session 5 | Complex analysis (5) Series, Convergence judgment Taylor series |
| Session 6 | Complex analysis (6) Laurent expansion Residue theorem |
| Sesson 7 | Complex analysis (7) Conformal mapping Riemannian mapping theorem |
| Session 8 | Complex analysis (8) Modeling in complex analysis Electrostatic field, Heat conduction, Flow field |
| Session 9 | Complex analysis (9) Poisson integral formula Dirichlet problem |
| Session 10 | Fourier analysis (1) Periodic function Even function, Odd function |
| Session 11 | Fourier analysis (2) Orthogonal function system Sturm-Liouville equation |
| Session 12 | Fourier analysis (3) Fourier series Complex Fourier series |
| session 13 | Fourier analysis (4) Fourier integral Cosine transform, Sine transform |
| Session 14 | Fourier analysis (5) Discrete Fourier transform (DFT) Fast Fourier transform (FFT) |