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