Ordinary Differential Equations

1. Exact forms Mdx+Ndy=0
2. 積分因子        積分因子(李群觀點)
3. Homogeneous nonlinear equations
4. Applications of first order equtions
5. Linear second order equations

(1)   Homogeneous  The Wronskian and Abel formula

(2)  Nonhomogeneous linear equations

(3)   The method of undetermined coefficients

(4)  Riccati equations   KdV equation

(5)  Reduction of order  (6)  Variation of parameters

6. Applications of linear second order equations

(1)   Spring-mass system   (2)   RLC circuits  (3)  Motion of an object under a central force

7. Series solutions of linear second equations

7.4 Euler equation  7.5 The method of Frobenius

8. Laplace transforms     (1) Laplace Transform (2)Inverse Laplace

9. Linear higher order equations
10. Linear system Abel公式

(1)  Basic theory of homogeneous linaer syetem

11. Boundary Value Problems and Fourier expasions
12. Fourier solutions of partial differential
13. Phase flows
14. D'Alembert method
15. 正交曲線族   人造衛星的軌道方程  Escape velocity
16. 單擺      懸鍊線(catenary)
17. Green定理的應用
18. ODE with discontinuous forcing function
19. Numerical Methods (1)Euler's method (2)Runge-Kutta method

習作 [Ex001]

1. Elementary Differential Equations and Boundary Value Problems     William E. Boyce   Richard C. DiPrima
2. Elementary Differential Equations and Boundary Value Problems     William F. Trench   [Student Solution Manual]
3. Ordinary Differential Equations      V.I.Arnold
4. Symmetry Methods for Differential Equations      Peter E. Hydon
5. Galois Theory of Linear Differential Equations    Marius van der Put   [ResearchGate]
6. 微分方程      劉睦雄  劉任業
7. 微分方程式  王振華
8. Solved Problems