Math 2320   “Differential Equations”

Course Syllabus

Fundamentals of Differential Equations by:

Nagle, Saff, and Snider  (Sixth Edition)

 

 

Introduction:

1)                 Show that certain functions solve same differential equation

2)                 Direction Fields

 

Study of First-Order Differential Equations

1)                 Separable Equations

2)                 Linear Equations

3)                 Exact Equations

4)                 Integrating Factors

5)                 Substitution and Transformations

 

Study of Linear Second-Order Equations

1)                 Homogeneous Linear Equations: The General Solution

2)                 Auxiliary Equations

3)                 Nonhomogeneous Equations

a)                 Undetermined Coefficients

b)                 Variation of Parameters

 

Study of Higher-Order Linear Differential Equations

1)                 Basic Theory

2)                 Homogeneous Equations with Constant Coefficients

3)                 Method of Undetermined Coefficients

4)                 The Annihilator Method

5)                 Method of Variation of Parameters

 

La Place Transforms

1)                 Definition of the La Place Transform

2)                 Properties

3)                 The Inverse La Place Transform

4)                 Solving Initial Value Problems

5)                 Transforms of Discontinuous and Periodic Functions

6)                 Convolution

 

Series Solutions of Differential Equations

1)                 Power Series and Analytic Functions

2)                 Power Series Solutions of Differential Equations

3)                 Equations with Analytic Coefficients

4)                 The Cauchy-Euler Equation

5)                 Find a Second Independent Solution

 

Linear Systems of Differential Equations

1)                 Linear Systems in Normal Form

2)                 Homogeneous Linear Systems with Constant Coefficients

3)                 Complex Eigenvalue

4)                 Non-homogeneous Linear Systems

5)                 The Matrix Exponential Function