MATH 282 - Differential Equations

First order differential equations; higher order linear differential equations and systems of linear equations; solution by power series and numerical methods; the Laplace transform and some applications. PREREQUISITE(S): A grade of C or better in MATH 182 or equivalent, or consent of department. Three hours each week.

3 semester hours

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

Use qualitative and numerical methods to analyze the family of solutions to a first-order differential equation, particularly an autonomous equation.
Solve first-order separable and linear differential equations and corresponding initial-value problems.
Determine the domain of a solution and describe long-term behavior of a solution.
Know and be able to apply the theorem for existence and uniqueness of solutions to a first-order differential equation.
Write and solve a first-order initial-value problem that models a practical situation involving a rate of change.
Rewrite a second-order differential equation as a system of first-order equations.
Use qualitative and numerical methods to describe and analyze the family of solutions to a first-order system.
Write a first-order system in matrix form, find the eigenvalues and write the general solution to the system.
Assume exponential solutions and solve a homogeneous or non-homogeneous linear second-order differential equation with constant coefficients.
Understand and interpret the solutions to a second-order equation in terms of harmonic oscillator.
Use Laplace transforms to solve first- and second-order initial-value problems when the differential equation may be forced by a continuous or discontinuous function.
Use an advanced software tool (Maple, MATLAB, Mathematica, ODE software, and the like) appropriately and effectively to aid in understanding the behavior of solutions to differential equations.

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