MATH 2120 - Differential Equations

3 sem hrs cr

This course is a study of ordinary differential equations with applications, numerical solutions, power series, and LaPlace transforms. Prerequisite: MATH 1920  

In rare and unusual circumstances, a course prerequisite can be overridden with the permission of the Department Lead for the discipline.

Formerly/Same As (Formerly MAT 2730)

Transfer (UT) or Non-Transfer Course (UN): UT

The goals of instruction in this course are to…

• fulfill the math requirement for pre-engineering, physics, and math majors.
• summarize and review integration techniques from calculus.
• introduce methods for solving linear differential equations.
• introduce methods for solving selected higher-order differential equations.
• use methods of solution of differential equations to solve application problems related to other areas such as physics, chemistry, and biology.
• provide a course that will require students to apply math knowledge acquired in calculus- and pre-calculus-level courses.

Course Objectives

Through the course, students will have the opportunity to…

• review integration, including the following techniques:
  • integration involving exponential and trigonometric functions;
  • integration by parts;
  • integration by substitution; and
  • integration by partial fractions.
• classify differential equations by type, order, and degree.
• verify that a given equation is a solution to a differential equation.
• solve initial-value problems.
• find regions of possible solutions to initial-value problems.
• understand how differential equations arise in applications.
• understand how graphs represent solutions of differential equations.
• solve differential equations using separation of variables.
• recognize and solve first order linear differential equations using integrating factors.
• recognize and solve exact differential equations.
• recognize and solve homogeneous differential equations using the substitutions y=ux and u=vy.
• solve Bernoulli equations.
• understand and use Euler’s Method to solve initial-value problems.
• solve rate of growth/decay, mixture, series circuit and Newton’s Law of Cooling problems using methods of differential equations.
• solve population logistic and second order chemical reaction problems (optional).
• understand basic theory of higher order linear equations, including boundary value problems, homogeneous and non-homogeneous equations, and the differential operator.
• determine whether solutions to differential equations are dependent or independent using Wronskians.
• construct a second solution from a known solution using reduction of order.
• solve higher order homogeneous linear differential equations with constant coefficients using auxiliary equations.
• find the annihilator for polynomial, exponential, and trigonometric functions (optional).
• solve differential equations using the method of undetermined coefficients (this can be done with either the superposition approach or the annihilator approach).
• solve differential equations using variation of parameters.