# Math 246 Description and Prerequisites

** Math 246,
Differential Equations for Scientists and Engineers (3 credits) **
This course is an introduction to ordinary differential equations.
The course introduces the basic techniques for solving and/or
analyzing first and second order differential equations, both linear
and nonlinear, and systems of differential equations. Emphasis is
placed on qualitative and numerical methods, as well as on formula
solutions. The use of a mathematical software system (MSS), either
Mathematica or MATLAB, is an integral and substantial part of the
course.
More detailed outlines of some of the topics to covered can be found
below and at
http://www.math.umd.edu/undergrad/syllabi240.351.html#math246 .

## * Course Prerequisites *

- Math 141 (Calculus II) or equivalent;
- Either Math 240, ENES 102, Phys 161, Phys 171, or some other
course with an adequate coverage of vectors.

## * A More Detailed Outline *

** Introduction to and Classification of
Differential Equations **

** First Order Equations **

Linear, separable and exact equations

Introduction to symbolic solutions using a MSS

Existence and uniqueness of solutions

Properties of nonlinear vs. linear equations

Qualitative methods for autonomous equations

Plotting direction fields using a MSS

Models and applications

** Numerical Methods **

Introduction to a numerical solver in a MSS

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 and variation
of parameters for non-homogeneous equations

Symbolic and numerical solutions using a MSS

Mechanical and electrical vibrations

** Laplace Transforms **

Definition and calculation of transforms

Applications to differential equations
with discontinuous forcing functions

** First Order Linear Systems **

General theory

Eigenvalue-eigenvector method for systems
with constant coefficients

Finding eigenpairs and solving linear systems
with a MSS

The phase plane and parametric plotting
with a MSS

** First Order Systems in the Plane **

Autonomous systems and critical points

Stability and phase plane analysis of almost linear systems

Linearized stability analysis and plotting vector fields
using a MSS

Numerical solutions and phase portraits of nonlinear systems
using a MSS

Models and applications