Math 310 - Applied Ordinary Differential Equations

Credits: 3

Course Description: A comprehensive study of the nature of ordinary differential equations. The course includes qualitative analysis of properties of solutions, as well as standard methods for finding explicit solutions to important classes of differential equations. It presents many applications, particularly for linear equations.

Pre-Requisites: [MATH 240] AND [MATH 260 or PHYSICS 114].

Frequency: This course is offered every semester (Fall-Spring-Summer).

Current Textbook: Fundamentals of Differential Equations, 6th Edition, by Kent Nagle, Edward Saff & Arthur Snider, published by Addison Wesley, 2003. ISBN: 0321145720. Check with your instructor to make sure this is the textbook used for your section.

Chapter 1:

1.1 Motivational background.
1.2 Solutions; initial value problems.
1.3 Direction fields.
1.4 Euler's approximation method.

Chapter 2:

2.2 Separable Equations.
2.3 Linear Equations.
2.6 Substitutions and Transformations.

Chapter 3:

3.2 Compartmental Analysis.

Chapter 4:

4.1 Introduction to the Mass-Spring Oscillator.
4.2 Homogeneous Linear Equations: General Solution.
4.3 Auxiliary Equations with Complex Roots.
4.4 Nonhomogeneous Equations: Undetermined Coefficients.
4.5 Superposition Principle using undetermined Coefficients.
4.8 Free Mechanical Vibrations.
4.9 Forced Mechanical Vibrations.

Chapter 5:

5.2 Constant Coefficients Systems: Elimination Methods.
5.4 Phases Plan introduction.

Chapter 6:

6.2 Homogeneous Linear Equation with Constant Coefficients.

Chapter 7:

7.2 Laplace Transform: Definition.
7.3 Laplace Transform: Properties.
7.4 Inverse Laplace Transform.
7.5 Solving Initial Value Problems.
7.6 Transforms of Discontinuous & Periodic Functions.

Chapter 8:

8.1 Taylor Polynomial Approximations.
8.2 Power Series and Analytic Functions.
8.3 Power Series solution of Linear Differential Equations.
8.4 Differential Equations with Analytic Coefficients.
8.5 Cauchy-Euler (Equidimensional) Differential Equations.
8.6 Frobenius Method at Regular Singular Points.