MAT-2460 Differential Equations

Credits: 4
In this course, students study first order differential equations, including but not limited to separable, linear, exact, and Bernoulli. Next, students solve higher order linear homogeneous and non-homogeneous differential equations. Students also solve systems of differential equations, using Laplace transform and matrix methods. Students then apply these equations to problems of motion, vibration, mixture, population, and others. Students apply several types of solution techniques, including various analytical methods, Laplace transform, and numerical methods. Students use various types of mathematical software to visualize and analyze solutions of differential equations and systems of equations and assess numerical methods’ accuracy and computational efficiency. Additionally, students explore solutions and phase portraits using mathematical software to analyze nonlinear systems and phenomena.  

Prerequisite(s): MAT-2420 completion with grade C or higher.

Course Outcomes

Classify ordinary differential equations and systems of equations.
Solve separable, linear, exact and Bernoulli equations of first order and use them in mathematical modeling for rate of change problems in various areas of science including motion and mixing.
Solve linear homogeneous and non-homogeneous equations with constant coefficients of second order and higher.
Apply second order linear equations to model and solve mechanical and electrical vibrations problems.
Use mathematical software to obtain both symbolic and numerical solutions for various differential equations.
Apply Laplace transformation to solve differential equations and systems of differential equations.
Solve systems of linear differential equations of first order using matrix methods.
Analyze nonlinear systems and phenomena using mathematical software exploring solutions and phase portraits.