Math 246 Description, Textbooks and Other Information

UM Undergraduate Catalog Course Description

Math 246, Differential Equations for Scientists and Engineers (3 credits) An introduction to the basic methods of solving ordinary differential equations. Equations of first and second order, linear differential equations, Laplace transforms, numerical methods, and the qualitative theory of differential equations. All sections will use Matlab.

Required Resources

There are two required texts:

The bookstore provides three ways to buy them (please check with the bookstore for the most up-to-date information):

See here for more details.
Feel free to check prices and choose your most advantageous solution, at bookstore or elsewhere.

MATLAB Computer Program:

This software is available in most OIT WAM labs, so you do not have to buy it.

Course Prerequisites

Our More Detailed Outline

Introduction to and Classification of Differential Equations
First Order Equations
     Linear, separable and exact equations
     Introduction to symbolic solutions using MATLAB
     Existence and uniqueness of solutions  
     Properties of nonlinear vs. linear equations
     Qualitative methods for autonomous equations
     Plotting direction fields using MATLAB
     Models and applications
Numerical Methods
     Introduction to a numerical solver in MATLAB
     Elementary numerical methods: Euler, improved Euler, Runge-Kutta
     Local and global error, reliability of numerical methods
Higher Order Linear Equations
     General theory of linear equations
     Homogeneous linear equations with constant coefficients
     Reduction of order
     Methods of undetermined coefficients, variation of parameters, and Green functions for nonhomogeneous equations
     Symbolic and numerical solutions using MATLAB
     Mechanical vibrations
Laplace Transforms
     Definition and calculation of transforms
     Applications to differential equations with piecewise continuous forcing functions
First Order Linear Systems
     General theory
     Systems with constant coefficients and matrix exponentials
     Eigenpairs and special solutions
     Finding eigenpairs and solving linear systems with MATLAB
     The phase plane and parametric plotting with MATLAB
First Order Systems in the Plane
     Autonomous systems and stationary solutions
     Linearized stability and phase plane analysis
     Linearized stability analysis and plotting vector fields using MATLAB
     Numerical solutions and phase portraits of nonlinear systems using MATLAB
     Models and applications