|
週次 |
日期 |
單元主題 |
|
第1週 |
|
8. Linear algebra: matrix eigenvalue problems Eigenvalues, Eigenvectors |
|
第2週 |
|
Application of Eigenvalue problems Symmetric, skew-symmetric and orthogonal matrix |
|
第3週 |
|
Hermitian, Skew-Hermitian, Unitary matrix Similarity Matrices, Basis, Diagonalization |
|
第4週 |
|
11. Fourier series, integrals and transforms Periodic function Fourier series Function of any period |
|
第5週 |
|
Half-range Expansion Complex Fourier series Forced oscillation |
|
第6週 |
|
Approximation by Trigonometric polynomials Fourier integrals Fourier sine and cosine transforms |
|
第7週 |
|
Fourier transforms.期中考一 |
|
第8週 |
|
12. Partial differential equations Modeling: vibrating string, wave equation |
|
第9週 |
|
Separation of variables D’alembert’s solution of wave equation |
|
第10週 |
|
Heat equation: solution by Fourier series Heat equation: solution by Fourier integral and transform |
|
第11週 |
|
Two-dimensional wave equation Rectangular membrane Laplacian in Polar coordinates |
|
第12週 |
|
Circular membrane Laplace equation in Cylindrical and Spherical coordinates Solutions by Laplace transform |
|
第13週 |
|
期中考二 13 Complex Numbers Complex number. Complex plane Polar form of a complex numbers. Powers and Roots |
|
第14週 |
|
curves and region in complex plane Limit, Derivative, Analytic function Cauchy-Riemann Equation Exponential and Logarithmic function Trigonometric functions and Hyperbolic functions |
|
第15週 |
|
14 Complex Integration Line integral in the complex plane Two integration methods Cauchy-Gourset Integral Theorem |
|
第16週 |
|
Existence of Indefinite Integral Cauchy’s Integral Formula Derivative of Analytic Function |
|
第17週 |
|
15 Series & Residue Sequences and Series Taylor Series Laurent Series Zeros and Poles Residues and Residue theorem Evaluation of Real Integral |