Description

Modeling with and solving of first- and higher-order ordinary differential equations, systems of linear equations, Laplace Transforms and series solutions of linear differential equations. Methods include numerical, qualitative and analytic approaches. The course will include modeling applications in engineering, chemistry and population studies.

Grading Basis

Graded

Prerequisites

MATH& 152 or Instructor Permission

### Course Learning Outcomes

### Core Topics

- First order differential equations including existence and uniqueness theorem and differential equations of the following types: separable, linear, exact, homogeneous and equations reducible to first order.
- Higher-order linear differential equations including the topics of linear independence and the Wronskian, existence and uniqueness of solutions, homogeneous and non-homogeneous DE with constant coefficients, Cauchy-Euler’s DE.
- Linear systems of differential equations including methods of elimination and matrix methods.
- Method of Laplace transforms to solve DE.
- Series Solutions of second –order linear equations
- Boundary value problems and eigenvalues and eigenfunctions
- Numerical solution techniques including Euler’s, Taylor-series methods.
- Stability analysis and phase plane solution curves.
- Applications for each of the above types of equations which require creating the model and solving the resulting equation or system.