MAT 238 - Differential Equations

Objectives

1. Define a differential equation.
2. Identify and classify equations.
3. Recognize initial-value problems.
4. Find the general solutions of a differential eqution.
5. Apply this solution to velocity and acceleration.
6. Show the existence and uniqueness of solutions.
7. Separate the variables in a diferential equation.
8. Apply this technique to ntural growth and to cooling and heating problems.
9. Examine linear first order equations.
10. Examine substitution methods including Bernoulli's equations.
11. Find a method of solution for exact equations.
12. Define second order linear equations.
13. Define integrating factors for a linear equation.
14. Establish linear depedence and independence of second order equations.
15. Distinguish homogeneous from nonhomogeneous second order equations.
16. Study the solutions for homogneous equations with constant coefficents.
17. Apply solutions of second order equations to mechanical vibration problems.
18. Look at the methods of reducion of order and Euler-Cauchy equations.
19. Discuss the method of variations of parameters to find a particular solution of nonhomogeneous equations.
20. Review power series including definition, types and radius of convergence.
21. Examine the power series method of solving linear equations.
22. Look at series solutions near ordinary points.
23. Look at series solutions near singular points.
24. Introduce Bessel's and Legendre's equations.
25. Define Laplace transforms and inverse transforms.
26. Apply Laplace transforms to solve a linear differential equation with constant coefficients.
27. Use the inverse transform to solve rational functions by first using partial function decomposition. (optional)
28. Look at derivatives, integrals and products of transforms.(optional)

Optional

Back to the top

Syllabus

Back to the top

Outline

Back to the top

Text

Back to the top

Examples of Objectives

Back to the top