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# MAT 262 - Differential Equations [SUN# MAT 2262]

3 Credits, 3 Contact Hours
3 lecture periods 0 lab periods
Introduction to differential equations. Includes first order differential equations, higher order differential equations, systems of linear differential equations, Laplace transforms, and approximating methods. Also includes applications.

Prerequisite(s): MAT 231
Gen-Ed: Meets AGEC - MATH; Meets CTE - M&S.

Course Learning Outcomes
1. Solve first order and higher order differential equations.
2. Solve linear systems of first order differential equations using matrices and eigenvalues.
3. Calculate the Laplace transform of a function, find the inverse transform, and use both to solve linear differential equations with constant coefficients.

Performance Objectives:
1. Solve first order differential equations including separable, linear, and those solved by substitution techniques.
2. Solve higher order linear differential equations with constant and variable coefficients; find a particular solution using undetermined coefficients and variation of parameters; find power series solutions.
3. Solve linear systems of first order differential equations using matrices and eigenvalues.
4. Define and compute the Laplace transform of a function; find the inverse transform; use Laplace transforms to solve linear equations with constant coefficients.
5. Use graphical and numerical methods to interpret and approximate solutions to differential equations.
6. Use differential equations to model and interpret scientific and mathematical applications.

Outline:
1. First Order Differential Equations
1. Separable
2. Linear
3. Exact (optional)
4. Solvable by substitution
5. Applications
2. Higher Order Linear Differential Equations
1. Wronskian and linear independence of functions
2. Reduction of Order
3. Homogeneous equations
4. Non-homogeneous equations
1. Undetermined coefficients
2. Variation of parameters
5. Cauchy-Euler equations (optional)
6. Power series solutions
7. Applications
3. Systems of Linear First Order Differential Equations
1. Method of eigenvalues
2. Applications
4. Laplace Transforms
1. Definitions and existence
2. Properties
3. Inverse Transform
4. Applications to solutions of linear equations with constant coefficients
5. Approximating Methods
1. Numerical
2. Graphical
6. Applications
1. First order
2. Higher order
3. Linear systems
4. Laplace Transforms

Effective Term:
Fall 2015