一、課程簡介:

6. Linear algebra: matrices, vectors, determinants
Basic concept
Matrix multiplication
Gauss elimination
Rank of a matrix
Solutions of a linear system
Determinants, Cramer’s rule
Inverse of a matrix, Gauss-Jordan elimination
Vector spaces, inner product spaces, linear transformation

7. 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

8. 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

9. 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

10. Complex numbers
Complex number, complex plane
Polar form of complex numbers, powers and roots
Curves and regions in complex plane
Limit, Derivative, Analytic function
Cauchy-Riemann equation
Exponential and Logarithmic function
Trigonometric functions and Hyperbolic functions

11. Complex integral
Line integral in the complex plane
Two integration method
Cauchy-Gourset Integral Theorem
Existence of Indefinite Integral
Cauchy`s Integral Formula
Derivative of Analytic function

12. Series and Residue
Sequences and series
Tayloe series
Laurent series
Zeros and Poles
Residues and Residue theorem
Evaluation of real integral



二、先修課程:微積分

三、參考書目:
E. Kreyszig, “ Advanced Engineering Mathematics”, John Wiley & Sons, INC.