| 週次 |
授課內容 |
| 第1週 |
Chapter 7 Linear Algebra: Matrices, Vectors, Determinants, Linear Systems
§7.1 Matrices, Vectors: Addition and Scalar Multiplication
§7.2 Matrix Multiplication
§7.3 Linear Systems of Equations, Gaussian Elimination
§7.4 Linear Independence, Rank of a Matrix, Vector Space
HW#1 |
| 第2週 |
§7.5 Solutions of Linear Systems: Existence, Uniqueness
HW#2 |
| 第3週 |
§7.6+7.7 Determinants, Cramer’s Rules
HW#3 |
| 第4週 |
§7.8 Inverse of a Matrix, Gauss-Jordan Elimination
第一次小考
|
| 第5週 |
Chapter 8 Linear Algebra: Matrix Eigenvalue Problems
§8.1 Eigenvalues, Eigenvectors
§8.2 Applications
§8.3+8.5 Special Matrices and Forms
HW#4 |
| 第6週 |
§8.4 Eigenbases, Diagonalization, Quadratic Forms
Chapter 4 Systems of Differential Equations
§4.2+4.3 Homogeneous Linear Systems with Constant Coefficients
§4.6 Nonhomogeneous Linear Systems with Constant Coefficients |
| 第7週 |
自主學習(複習+演算+問題解答) |
| 第8週 |
第一次期中考(Chapter 7+Chapter 8+§4.2+§4.3+§4.6)
Chapter 12 Partial Differential Equations
§ Basic Concepts |
| 第9週 |
§ Methods for Solving PDE
A. Introduction of New Variables
B. Separation of Variables
(a) homogeneous PDE
(i) homogeneous B.C.’s
Solution by Fourier series
HW#5 |
| 第10週 |
B. Separation of Variables
(a) homogeneous PDE
(i) homogeneous B.C.’s
Solution by Fourier series
Solution by Fourier integral
第二次小考 |
| 第11週 |
(ii) nonhomogeneous B.C.’s
Superposition method
(b) nonhomogeneous PDE
Variation of parameters
HW#6 |
| 第12週 |
C. Combination of Variables
D. Laplace Transform
E. Fourier Transform
HW#7 |
| 第13週 |
第二次期中考(Chapter 12)
Chapter 9 Vector Differential Calculus
§9.1 Vector Algebra
§9.2 Inner (Dot) Product
§9.3 Vector (Cross) Product |
| 第14週 |
§9.4 Vector and Scalar Functions, Derivatives
§9.5 Curves, Tangent, Arc Length
§9.7 Gradient of a Scalar Field, Directional Derivative
HW#8 |
| 第15週 |
§9.8 Divergence of a Vector Field
§9.9 Curl of a Vector Field
§ Application in Transport Phenomena
Chapter 10 Vector Integral Calculus and Integral Theorems
§10.1 Line Integral
HW#9
第三次小考 |
| 第16週 |
§10.2 Line Integrals Independent of Path
§10.3 Double Integrals
§10.4 Green’s Theorem in Plane
§10.5 Surfaces
§10.6 Surface Integrals
HW#10 |
| 第17週 |
§10.7 Triple Integrals, Divergence Theorem of Gauss
§ Application in Transport Phenomena
§10.9 Stokes’s Theorem |
| 第18週 |
期末考(Chapter 9+Chapter 10) |