MCCCD Official Course Competencies:

MAT262  1996 Fall – 2011 Summer II

Differential Equations

1.

Solve ordinary differential equations, primarily of first or second order, using the following solution types: exact, implicit, series, or discrete approximations. (I-III)

2.

Solve systems of ordinary linear differential equations of first or second order by differential operator, Laplace, or matrix methods. (IV)

3.

Apply ordinary and systems of differential equations to solving applications. (V)

MCCCD Official Course Outline:

MAT262  1996 Fall – 2011 Summer II

Differential Equations

I. Exact methods of solution

A. First order equations

1. Separable

2. Nonseparable exact

3. Homogeneous

4. Integrating factor techniques

5. Linear coefficient functions

B. Second order equations

1. Homogeneous

2. Nonhomogeneous

3. Cauchy-Euler

II. Power series methods

A. Homogeneous

1. Ordinary point solutions

2. Regular singular point solutions (optional)

B. Nonhomogeneous-Taylor series solutions (optional)

C. Successive approximations (optional)

III. Discrete approximations (optional)

A. Euler and improved Euler

B. Runge-Kutta

C. Adams-Bashforth/Adams-Moulton

IV. Systems of differential equations

A. Laplace transform

B. Differential operator method

C. Matrix method (optional)

V. Applications

A. First order

B. Second order

C. Systems