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Apr 27, 2024
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MAT 251 - Differential Equations
Credits: 3
3 Lecture Hours
Prerequisites: MAT 202 or Equivalent
Description
This is an introductory course in the fundamental concepts of ordinary differential equations that prepares the student for further study in mathematics, engineering or science. Students explore first order equations, nth order equations and Laplace Transforms. Additionally, students solve differential equations using various numerical solution techniques and infinite series. An introduction to partial differential equations and selected applications is also discussed.
Learning Outcomes
Upon successful completion of the course, the student will:
- Implement techniques to produce solutions for separable, exact and first order linear differential equations.
- Solve homogeneous and non-homogeneous nth order linear ordinary differential equations with constant coefficients.
- Apply Laplace Transformations to solve ordinary differential equations.
- Compute solutions to ordinary differential equations using selected numerical techniques.
- Obtain a series solution for a differential equation around an ordinary point and around a regular singular point.
- Solve a partial differential equation by separation of variables.
- Apply the above techniques to solve selected application problems.
Listed Topics
- Separable equations
- First order linear equations
- Exact equations
- Nth order linear ordinary differential equations
- Homogeneous nth order linear ordinary differential equation with constant coefficients
- Non-homogeneous nth order linear ordinary differential equation with constant coefficients: the method of undetermined coefficients and variation of parameters
- Numerical methods
- Laplace Transform techniques
- Infinite series solutions around an ordinary point and around a regular singular point
- Systems of differential equations
- Introduction to partial differential equations
- Selected applications
Reference Materials
Each student is required to have a textbook/e-book/homework system adopted by the Mathematics Department at the specific campus.
Students who successfully complete this course acquire general knowledge, skills and abilities that align with CCAC’s definition of an educated person. Specifically, this course fulfills these General Education Goals: - Critical Thinking & Problem Solving
- Quantitative & Scientific Reasoning
Approved By: Dr. Quintin B. Bullock Date Approved: 5/8/2023
Last Reviewed: 5/8/2023
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