COURSE NUMBER AND TITLE: MATH 3020 Differential Equations

CREDIT HOURS: 3

CATALOG DESCRIPTION: A study of first-order and linear second-order differential equations with applications. Topics include solution techniques, qualitative behavior, numerical methods, Laplace transformations, and the use of series.

PREREQUISITE(S): MATH 2012 or permission of instructor.

SUGGESTED TEXT(S):
Elementary Differential Equations by Boyce and DiPrima
A First Course in Differential Equations by Zill

COURSE OUTLINE:

1. First Order Differential Equations
   • Separable Equations
   • Exact Equations
   • Linear Equations
   • Substitutions (May include homogeneous, Bernoulli, Riccatti, Clairaut equations)
   • Applications of linear and nonlinear first order equations
2. Linear Equations of Higher Order
   • Linear equations of higher order, linear independence, The Wronskian
   • Reduction of order
   • Homogeneous linear equations with constant coefficients
   • Differential operators
   • Non-homogeneous linear equations and undetermined coefficients
   • Non-homogeneous linear equations and variation of parameters
   • Applications of higher order equations; Harmonic motion, Electrical circuits, etc.
   • Cauchy-Euler equations
3. Power Series methods
   • Power Series Solutions About Ordinary Points
   • Power Series Solutions About Singular Points (The Method of Frobenius)
   • Bessel functions and Legendre Polynomials
4. Laplace Transform Methods
   • The Laplace Transform and Inverse Laplace Transform
   • Translation Theorems; Derivatives of Transforms
   • Transforms of Derivatives, Integrals, Periodic Functions
   • Applications
5. Numerical Methods
   • Euler Methods
   • Runge-Kutta Methods
   • Other Numerical Methods
6. Optional Additional Advanced Topics may include:
   • Direction fields
   • Autonomous equations and phase planes
   • Systems of differential equations
   • Eigenvalues and eigenvectors