工程數學一｜臺大課程網

課程概述
This course is an introduction to the methods of mathematical physics used in the environmental and hydrologic sciences. It is presented in the context of basic mathematical methods and their application in the environmental and hydrologic contexts. The lecture introduces ordinary differential equations (ODEs) and vectors. Both analytical and numerical methods of solution of differential equations are introduced. Analytical solutions 1. First-order ODEs 2. Second-order Linear ODEs 3. Higher Order Linear ODEs 4. System of ODEs (Eigenvalue Problems for Systems of ODEs) Series Solutions 5. Series Solutions of ODEs (Special Functions) Transforms 6. Laplace Transforms Some of the contents in the below chapters are merged into chapters 1 to 6 Linear algebra 7. Matrices, Vectors, Determinants, Linear system 8. Eigenvalue and Eigenvectors 9. Vector differential and integral calculus (Optinal) Numerical methods 20. Numeric Linear Algebra (20.6 – 20.8) 21. Numerics for ODEs (21.1 – 21.3)

課程目標
Primarily introduces analytical methods for solving commonly used mathematical equations in the fields of physics and engineering. Cultivates students' abilities to interpret and handle mathematical equations in their professional fields.

課程進度

9/6第 1 週	9/6	Introduction
9/13第 2 週	9/13	Linear 1st order ODEs (modeling, separation variables, Euler’s method)
9/20第 3 週	9/20	Linear 1st order ODEs (Linear Equ., Exact Equ., Bernoulli Equ.)
9/27第 4 週	9/27	Linear 2nd ODEs with constant coefficients (homogeneous ODE, non-homogeneous ODE, Mass-Spring System)
10/4第 5 週	10/4	Linear 2nd ODEs with constant coefficients (non-homogeneous ODE, Resonance)
10/11第 6 週	10/11	Midterm
10/18第 7 週	10/18	System of Linear ODEs （Eigenvalue, Eigenvector, system ODEs with constant coefficients）
10/25第 8 週	10/25	System of Linear ODEs (homogeneous and nonlinear)
11/1第 9 週	11/1	Linear 2nd ODEs with variable coefficients and serious solutions (special functions) I
11/8第 10 週	11/8	Linear 2nd ODEs with variable coefficients and serious solutions (special functions) II
11/15第 11 週	11/15	No class 校慶停課
11/22第 12 週	11/22	Midterm
11/29第 13 週	11/29	Laplace transform （Linearity, first shifting theory, derivatives and integrals)
12/6第 14 週	12/6	Laplace transform (Unit step function, Heaviside function, second shifting theory)
12/13第 15 週	12/13	Laplace transform (convolution, solve ODEs)
12/20第 16 週	12/20	Final