### 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:
• (2.6)
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.