Course Description
First- and second-order ordinary differential equations, including physical and biological applications, numerical solutions, and mathematical modeling.
Athena Title
Elem Differential Equations
Equivalent Courses
Not open to students with credit in MATH 2700, MATH 2700H
Non-Traditional Format
This course will be taught 95% or more online.
Prerequisite
MATH 2260 or MATH 2260E or MATH 2260H or MATH 2310H or MATH 2410 or MATH 2410H
Grading System
A - F (Traditional)
Student learning Outcomes
- Students will understand the fundamental ideas of differential equations and systems of differential equations.
- Students will learn how to model physical and biological processes with differential equations.
- Students will learn how to find general solutions explicitly or implicitly to simple classes of differential equations and to interpret these solutions in reference to the processes they model.
- Students will learn how to get qualitative (graphical) information and approximate solutions for important classes of differential equations whose general solutions cannot be found explicitly.
Topical Outline
- 1. Introduction to Differential Equations: Definitions and Terminology, Initial-Value Problems, Differential Equations as Mathematical Models.
- 2. First-Order Differential Equations: Solution Curves Without a Solution - Direction Fields, Autonomous First-Order DEs, Separable Equations, Linear Equations, Exact Equations, Solutions by Substitutions, Numerical Method.
- 3. Modeling with First-Order Differential Equations: Linear Models, Nonlinear Models, Modeling with Systems of First-order DEs.
- 4. Higher-Order Differential Equations: Preliminary Theory—Linear Equations, Initial-Value and Boundary-Value Problems, Homogeneous Equations, Nonhomogeneous Equations, Reduction of Order, Homogeneous Linear Equations with Constant Coefficients, Undetermined Coefficients—Annihilator Approach, Variation of Parameters, Cauchy-Euler Equations, Solving Systems of Linear DEs by Elimination, Nonlinear Differential Equations.
- 5. Modeling with Higher-Order Differential Equations: Linear Models: Initial-Value Problems, Spring/Mass Systems; Nonlinear Models.
- 6. Systems of Linear First-Order Differential Equations: Preliminary Theory—Linear Systems, Homogeneous Linear Systems, Distinct Real Eigenvalues, Repeated Eigenvalues, Complex Eigenvalues.
- 7. The Laplace Transform: Definition of the Laplace Transform, Inverse Transforms and Transforms of Derivatives, Operational Properties. The Dirac Delta Function and Convolutions, Systems of Linear Differential Equations.
General Education Core
CORE III: Quantitative Reasoning
