MAT 251 - Differential Equations

1. Solve separable and exact ordinary differential equations.
2. Solve a first order linear ordinary differential equation.
3. Solve a homogeneous nth order linear ordinary differential equation with constant coefficients.
4. Solve a nonhomogeneous nth order linear ordinary differential equation with constant coefficients.
5. Apply Laplace transformations to solve ordinary differential equations.
6. Apply selected numerical techniques to solve ordinary differential equations.
7. Obtain a series solution for a differential equation around an ordinary point and around a regular singular point.
8. Solve a partial differential equation by separation of variables.
9. Use the above techniques to solve selected application problems.

1. Basic definitions
2. Separable equations; first order equation; exact equations
3. Theory of the nth order linear ordinary differential equation
4. Solving a homogeneous nth order linear ordinary differential equation with constant coefficients
5. Solve a nonhomogeneous nth order linear ordinary differential equation with constant coefficients: the method of undetermined coefficients and variation of parameters
6. Numerical methods
7. Laplace transform techniques
8. Infinite series solutions around an ordinary point and around a regular singular point
9. Introduction to Partial Differential Equations
10. Selected applications

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