Sep 27, 2023
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
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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