• Congrats to 3 CMNS Students Named Goldwater Scholars

    Congratulations to UMD’s 3 Goldwater Scholars this year, all from CMNS: Junior physics and mathematics double-degree student Yash Anand Sophomore atmospheric and oceanic science and physics double-degree student Malcolm Maas Junior biological sciences and mathematics double-degree student Jerry Shen Over the last 15 years, UMD’s nominations yielded 49 scholarships—No. 2… Read More

  • Maria Cameron Receives the 2024 MURI Award

    Congratulations to Maria Cameron for her MURI award. MURI are multidisciplinary university research initiative grants that are awarded by the department of defense. Cameron’s grant is sponsored by the office of naval research. Her team includes Balakumar Balachandran (ME) and Miao Yu (ME). This is a project on “disorder-influenced collective… Read More

  • A $27.2M Gift to the Math Department by the Brin Family

    The university announced today a big gift to the Math Department. The very generous gift of $27.2M was made by Michael & Eugenia Brin. The gift will endow the Brin Mathematics Research Center, establish an endowed chair, and launch a summer camp for high school students. The official university’s press… Read More

  • 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
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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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