| 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
§7.6+7.7 Determinants, Cramer’s Rules
HW#2 |
| 第3週 |
§7.8 Inverse of a Matrix, Gauss-Jordan Elimination
HW#3 |
| 第4週 |
第一次小考
Chapter 8 Linear Algebra: Matrix Eigenvalue Problems
§8.1 Eigenvalues, Eigenvectors
§8.2 Applications
|
| 第5週 |
§8.3+8.5 Special Matrices and Forms
§8.4 Eigenbases, Diagonalization, Quadratic Forms
HW#4 |
| 第6週 |
Chapter 4 Systems of Differential Equations
§4.2+4.3 Homogeneous Linear Systems with Constant Coefficients
§4.6 Nonhomogeneous Linear Systems with Constant Coefficients
Chapter 12 Partial Differential Equations
§ Basic Concepts |
| 第7週 |
校慶補假
§ Methods for Solving PDE
A. Introduction of New Variables |
| 第8週 |
第一次期中考(Chapter 7+Chapter 8+§4.2+§4.3+§4.6)
B. Separation of Variables
(a) homogeneous PDE
(i) homogeneous B.C.’s
Solution by Fourier series
HW#5 |
| 第9週 |
Solution by Fourier integral
(ii) nonhomogeneous B.C.’s
Superposition method
HW#6 |
| 第10週 |
第二次小考
(b) nonhomogeneous PDE
Variation of parameters
C. Combination of Variables
HW#7 |
| 第11週 |
D. Laplace Transform
E. Fourier Transform
Chapter 9 Vector Differential Calculus
§9.1 Vector Algebra
§9.2 Inner (Dot) Product
§9.3 Vector (Cross) Product |
| 第12週 |
第二次期中考(Chapter 12)
§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13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14週 |
第三次小考
§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15週 |
§10.7 Triple Integrals, Divergence Theorem of Gauss
§Application in Transport Phenomena
§10.9 Stokes’s Theorem |
| 第16週 |
期末考(Chapter 9+Chapter 10)
|
自主學習
內容 |
02.閱覽產業及學術相關多媒體資料
觀看工程數學相關線上教學影片與多媒體資料
演算工程數學相關線上教學題目與多媒體資料題目
複習各次期中考及期末考題目 |