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
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
2)
Homogeneous
Linear Systems with Constant Coefficients
3)
Complex
Eigenvalue
4)
Non-homogeneous
Linear Systems
5)
The
Matrix Exponential Function