# (2016 Spring) Math 2352: Differential Equations

This course covers: first order equations, second order equations, Laplace transform method, numerical solution of initial value problems, boundary-value problems.

There are several problems to be solved for each week. The problems are given in “Work Sheets”, and solutions “Answer Sheets”.

## Work Sheets

1. Complex Numbers & Separable Equations

2. Linear First-Order Equations

3. Second-Order Homogeneous ODEs

4. Inhomogeneous ODEs

5. The Laplace Transform

6. Series Solutions

7. Cauchy-Euler Equations

8. Systems of Equations

9. Normal Modes

10. Fixed Points and Linear Stability

11. Fourier Series

### Errata

1. In wk06_ans.pdf, at the last line of problem 2, the denominator of the coefficient of $x^2$ should be $120$ (instead of $240$).

2. In wk07_ans.pdf, problem 3-b), the second $e$ in the final result should be instead $1$

3. In wk08_ans.pdf, problem 2-b), the $2$ in $x_1(t)$ should be deleted (check the program above to see the correct answer). Similarly, in 3-a), there is a missing bracket in $x_1(t)$.

### Acknowledgement

Special thanks to Mr. Yuqi Zhao for providing several solution sheets (those without attributes).

##### Xiaoyu Wei
###### Postdoctoral Research Associate

My research interests include high-order numerical methods for PDEs, integral equation methods and fast algorithms.