MAT 212 - Differential Equations

4 credit hours - Four hours weekly; one term.
This course meets the Mathematics General Education Requirement

Analyze and solve ordinary differential equations of various types: separable, exact, linear equations of all orders and systems of linear equations. Master techniques including integrating factors, undetermined coefficients, the Wronskian, variation of parameters, reduction of order, power series, Laplace transforms and numerical approximations. Solve systems of linear equations using operator methods, numerical approximations and matrix methods. Apply these techniques to various applications including trajectories, mixing, growth, decay, vibrating springs, electric circuits and resonance. Use a mathematical software system as an integral and substantial part of the course.

Prerequisite(s): MAT 192 .

Crosslisted: Also offered as MAT 212H ; credit is not given for both MAT 212 and MAT 212H .

Location(s) Typically Offered: Arnold Main Campus (MC) and Online (OL)

Term(s) Typically Offered: Fall, spring, and summer

Course Outcomes:
Upon successful completion of this course, a student will be able to:

Analyze first-order Initial Value Problems (IVPs) using direction fields and Euler approximations.
Solve first-order IVPs including separable, linear, and exact equations.
Model various phenomena including mixing, growth, decay, fluid dynamics, and circuits as first-order IVPs.
Solve higher-order linear IVPs by modeling various phenomena, such as springs and electric circuits.
Solve higher-order IVPs using exponential functions, Euler’s formula, reduction of order, power series, and Laplace transforms.
Solve systems of linear IVPs using both matrix and numerical methods.
Approximate solutions to IVPs and systems of IVPs using Runge-Kutta methods.
Use a mathematical software system to analyze or solve IVPs for equations and systems.