MAP2302 - Elementary Differential Equations

Topical Outline with Specific Course Objectives

1. First Order Differential Equations
   1. Understand the Existence and Uniqueness Theorem and its ramifications.
   2. Apply calculus techniques to first order differential equations to determine properties of solutions such as monotonicity, concavity, symmetry, and singularities.
   3. Use graphical techniques such as direction (slope) fields, phase diagrams and orbits to study the relationship between a first order differential equation and its solution.
   4. Investigate the sensitivity of models and their solutions to initial conditions and parameters.
   5. Use numerical methods to approximate solutions to initial value problems and provide error estimates.
   6. Solve first order differential equations which are exact, separable, homogeneous, linear or Bernoulli using symbolic methods.
   7. Construct and analyze models, interpret results, and make predictions within the original context.
2. Higher Order Linear Differential Equations
   1. Use series, graphical, and symbolic methods to generate and analyze solutions to differential equations or boundary value problems.
   2. Solve higher order linear differential equations with constant coefficients using symbolic methods.
   3. Apply the methods of undetermined coefficients and variation of parameters.
   4. Identify and solve Cauchy-Euler equations.
3. The Laplace Transform
   1. Use the Laplace Transform to solve differential equations.
   2. Construct and analyze models, interpret results, and make predictions within the original context.
   3. Use Laplace Transforms to solve systems of linear differential equations.

Department Policies

• Graphing Calculator not allowed on proctored tests or final exam 
• Comprehensive Final