# MA 341: Applied Differential Equations

Instructor: Petr Kaplicky
Credits: 3
GEP: Elective

*Prerequisite: MA 242 or (MA 132 and MA 231).

### Course Description

Differential equations and systems of differential equations. Methods for solving ordinary differential equations including Laplace transforms, phase plane analysis, and numerical methods. Matrix techniques for systems of linear ordinary differential equations. Credit is not allowed for both MA 301 and MA 341.

### Learning Outcomes

Upon successful completion of this course, students will be able to:

• Determine if a given function is a solution to a particular differential equation; apply the theorems for existence and uniqueness of solutions to differential l equations appropriately;
• Distinguish between
a) linear and non-linear differential equations;
b) ordinary and partial differential equations;
c) homogeneous and non-homogeneous differential equations;
• Solve ordinary differential equations and systems of differential equations using:
a) Direct integration
b) Separation of variables
c) Methods of undetermined coefficients and variation of parameters
d) Laplace transform methods
• Determine particular solutions to differential equations with given initial conditions.
• Analyze real-world problems such as the motion of a falling body compartmental analysis, free and forced vibrations, etc.; use the analytic technique to develop a mathematical model, solve the mathematical model and interpret the mathematical results back into the context of the original problem.
• Apply matrix techniques to solve systems of linear ordinary differential equations with constant coefficients.
• Find the general solution for a first order, linear, constant coefficient, homogeneous system of differential equations; sketch and interpret phase plane diagrams for systems of differential equations.