Department of Mathematics - Math 246 - Differential Equations for Engineers

Eugenia Brin, Longtime Supporter of Science and Performing Arts at UMD, Dies

Eugenia Brin, a Russian immigrant and retired NASA scientist who, with her family of accomplished Terps, became an important benefactor of the University of Maryland, died on Dec. 3, 2024. She was 76 years old. The rest of the article can be read here: https://cmns.umd.edu/news-events/news/eugenia-brin-1948-2024 Read More

2024 Michael Brin Dynamical Systems Prize for Young Mathematicians Awardees

Math is excited to announce that Francisco Arana-Herrera has been awarded the 5th Michael Brin Dynamical Systems Prize for Young Mathematicians. The prize was shared between Francisco and Rohil Prasad. Details about eh prize and previous winners can be found at https://science.psu.edu/math/research/dynsys/dynamical-systems-prize-young-mathematicians Read More

UMD Launches Award to Recognize Dual Majors in Computer Science and Mathematics

Starting Spring 2025, the Grant Family Outstanding Achievement Undergraduate Student Award will recognize graduating seniors excelling in both fields. Link to the article can be read here: https://www.cs.umd.edu/article/2024/11/umd-launches-award-recognize-dual-majors-computer-science-and-mathematics Read More

Jonathan Poterjoy and Kayo Ide join new $6.6 million NOAA consortium

Congratulations to AOSC's Jonathan Poterjoy and Kayo Ide (also of math and IPST) on joining a new NOAA consortium to improve the accuracy of weather forecasts. Called CADRE, the $6.6 million initiative will focus on data assimilation, which uses observations to improve model predictions of natural systems, like Earth's atmosphere, over time.… Read More

Description

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 mathematical software system is an integral and substantial part of the course. Beginning Spring 2003, all sections of the course will use the software system MATLAB. Credit will be granted for only one of the following: MATH 246 or MATH 341.

Prerequisites

Required: a C- or better in MATH 141. Recommended: MATH240 or ENES102 or PHYS161 or PHYS171.

Topics

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

Second Order Equations

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

Systems of First Order Linear Equations

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

Nonlinear Systems and Stability

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