• 2023 Putnam Competition Result

    We very excited to report that our Putnam team ranked 8th, honorable mention, among 471 institutions in the 2023 Putnam math competition.Our team members this year were Vincent Trang, Daniel Yuan, Omar Habibullah, and Andrew Parker.Vincent Trang ranked 43rd and Daniel Yuan ranked 64th among 3,857 participants. Read More
  • Simons Fellows - Darvas, Kanigowski, Rubinstein

    Congratulations to Tamas Darvas, Adam Kanigowski, and Yanir Rubinstein for being named Simons Fellows. Read More
  • Doron Levy is elected 2024 Class of Fellows of the AMS

    Congratulations to Dr. Doron Levy, as Fellow of the American Mathematical Society, Class of 2024 (https://www.ams.org/cgi-bin/fellows/fellows_by_year.cgi)!  Dr. Levy was elected  ``For his contributions to Mathematical Oncology and Mathematical Biology".  Read More
  • Scott Wolpert to lead NSF-funded project on DEI in mathematics and statistics

    Congratulations to Scott Wolpert, professor emeritus of mathematics, who was named principal investigator of a new project to improve diversity, equity and inclusion in mathematics departments. The project is funded by a $600,000 grant from the NSF, and it will provide DEI training to six representatives of math and statistics departments Read More
  • Abba Gumel Featured in Scientific American Article

    Congratulations to Abba Gumel being featured in a new Scientific American Article. The title is “How Mathematics Can Predict and Help Prevent the Next Pandemic” (link to the article). What a great advertisement to Maryland. It is a great honor to have Abba as our colleagues.   Congratulations Abba! Read More
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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

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