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.