### MATH 2403 Differential Equation

### Spring 2012

### Monday 9:30-11:00, Thursday 8:30-10:00 Yellow room.

### Office Hours: MT 11-12, room 215.

Methods for obtaining numerical and analytic solutions of elementary
differential equations. Applications are also discussed with an
emphasis on modeling.
The text that will be used is:

*Differential Equations* by Brennan and Boyce, Wiley 2nd
Edition

The syllabus can be found here.

There will be two midterm.

The exercise listed are for HW collection. I will collect them
every
two weeks and grade 2 or 3 exercises among the one assigned.

The final grade will be based on the following rules: 45%
final, 35%
midterms, 20% HW. Curving will be done on the final result.

#### Arguments covered.

- Introduction and Euler's method: 1.1-1.4

- First Order Differential equations: 2.1-2.8
- Systems of two first order equations: 3.1-3.7
- Second order linear equations: 4.1-4.8
- Systems of first order equations: 6.1-6.7
- Nonlinear Differential Equations and Stability 7.1-7.6
- Laplace Transform Methods: 5.1-5.9

**First week**

Material covered:

- 1.1 Mathematical Models, Solutions and Direction Foelds

Exercises:

- (1.1) 15-20, 29, 35 (this two last exercises are missing in the first edition. Here are the relevant pages of the second edition: ex. 29 and ex. 35.)

Second Week

Material Covered:

- 1.2 Linear Equation: Methods of Integrating Factors (this is section 2.1 of the 1st edition.)

- 1.3 Numerical Approximations: Euler's Methods
- 1.4 Classification of Differential Equation

Exercises:

- (1.2) 2, 6, 26, 39 (same numbers but from section 2.1 for people with the first edtion.)

- (1.3) 10, 15, 17

- (1.4) 1, 3, 5

Third Week

Material Covered:

- 2.1 Separable Equations

- 2.2 Modelling with First Order Equations

- 2.3 Difference Between Linear and Nonlinear Equations

Exercises:

- (2.1) 12, 24 , 28

- (2.2) 3, 8, 14, 17, 29

- (2.3) 21, 22

Fourth Week

Material Covered:

- 2.4 Autonomous Equation and Population Dynamics

- 2.5 Exact Equation and Integrating Factors

Exercises:

- (2.4) 7, 15, 22

- (2.5) 1, 2, 3, 4, 5, 6 (only point (a), (b))

FifthWeek

Material Covered:

- 2.6 Accuracy of Numerical Methods

Exercises:

SixthWeek

Material Covered:

- 3.1 System of Two Linear Algebraic Equation
- 3.2 System of Two First Order Linear Differential Equation

Exercises:

- (3.1) 13, 14, 21, 22, 35

- (3.2) 10(a), 12(a), 19, 22

SeventhWeek

Material Covered:

- 3.3 Homogeneous Linear System with Constant Coefficients

- 3.5 Repeated Eigenvalue

Exercises:

- (3.3) 13, 15, 26

- (3.5) 9, 10, 14

EighthWeek

Material Covered:

- 3.4 Complex Eigenvalue

- 3.6 A Brief Introduction to Nonlinear Systems
- 3.7 Numerical Methods for Systems of First Order Eqaution

Exercises:

- (3.4) 8, 9, 13

- (3.6) 9, 11, 23

- (3.7)

The next homework will be due on Thursday April 5th. We will have a second midterm on Tuesday April 24th based on the second part of the class.