Topical Outline with Specific Course Objectives
- First Order Differential Equations
- Understand the Existence and Uniqueness Theorem and its ramifications.
- Apply calculus techniques to first order differential equations to determine properties of solutions such as monotonicity, concavity, symmetry, and singularities.
- 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.
- Investigate the sensitivity of models and their solutions to initial conditions and parameters.
- Use numerical methods to approximate solutions to initial value problems and provide error estimates.
- Solve first order differential equations which are exact, separable, homogeneous, linear or Bernoulli using symbolic methods.
- Construct and analyze models, interpret results, and make predictions within the original context.
- Higher Order Linear Differential Equations
- Use series, graphical, and symbolic methods to generate and analyze solutions to differential equations or boundary value problems.
- Solve higher order linear differential equations with constant coefficients using symbolic methods.
- Apply the methods of undetermined coefficients and variation of parameters.
- Identify and solve Cauchy-Euler equations.
- The Laplace Transform
- Use the Laplace Transform to solve differential equations.
- Construct and analyze models, interpret results, and make predictions within the original context.
- Use Laplace Transforms to solve systems of linear differential equations.
Department Policies
- Graphing Calculator not allowed on proctored tests or final examÂ
- Comprehensive Final