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