MCCCD Program Description

Modern Differential Equations

Course: MAT276

First Term: 2009 Fall

Lecture 4.0 Credit(s) 4.0 Period(s) 4.0 Load
Subject Type: Academic
Load Formula: S

Description: Introduces differential equations, theoretical and practical solution techniques with applications. Problem-solving using MATLAB

MCCCD Official Course Competencies
1. Solve analytically and numerically ordinary differential equations, primarily of first or second order, using exact, implicit, or discrete approximation solution types. (I, II, III) 2. Solve analytically and numerically systems of ordinary linear differential equations using matrix methods and Laplace Transforms or differential operator methods. (III, IV) 3. Solve application problems using differential equations. (I, II, III, IV) 4. Linearize non-linear systems and describe the long-term behavior of solutions. (IV) 5. Read and interpret quantitative information when presented numerically, analytically or graphically. (I, II, III, IV) 6. Compare alternate solution strategies, including technology. (I, II, III, IV) 7. Justify and interpret solutions to application problems. (I, II, III, IV) 8. Communicate process and results in written and verbal formats. (I, II, III, IV)
MCCCD Official Course Competencies must be coordinated with the content outline so that each major point in the outline serves one or more competencies. MCCCD faculty retains authority in determining the pedagogical approach, methodology, content sequencing, and assessment metrics for student work. Please see individual course syllabi for additional information, including specific course requirements.

MCCCD Official Course Outline
I. Exact methods of solution A. First order equations 1. Separable 2. Exact 3. Homogeneous 4. Integrating factor techniques 5. Linear equations 6. Slope fields 7. Applications and computer investigations B. Second order equations 1. Homogeneous 2. Non-homogeneous 3. Applications and computer investigations C. Laplace Transform 1. First Order Linear Equations 2. Second Order Linear Equations 3. Linear Systems 4. Applications II. Discrete approximations A. Euler and improved Euler methods B. Runge-Kutta C. Applications and computer investigations III. Linear Systems of differential equations A. Laplace transform B. Matrix methods C. Phase plane D. Applications and computer investigations E. Differential operator method IV. Introduction to Nonlinear Systems A. Linearization of autonomous systems B. Stability analysis of equilibrium C. Phase portrait analysis D. Hamiltonian E. Applications and computer investigations

MCCCD Governing Board Approval Date: 5/26/2009

All information published is subject to change without notice. Every effort has been made to ensure the accuracy of information presented, but based on the dynamic nature of the curricular process, course and program information is subject to change in order to reflect the most current information available.