• Adam Kanigowski Awarded European Mathematical Society Prize

    He is the first member of UMD’s Department of Mathematics to receive this prestigious award for young mathematicians. The European Mathematical Society (EMS) awarded a 2024 EMS Prize to Adam Kanigowski, a Polish-born associate professor in the University of Maryland’s Department of Mathematics. Established in 1992, the prize is presented every four years to… 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

  • Alfio Quarteroni receives the Blaise Pascal Medal in Mathematics

    Congratulations to Alfio Quarteroni for winning the 2024 Blaise Pascal Medal in Mathematics The message from the European Academy of Sciences reads: We are excited to announce that Professor Alfio Quarteroni has been awarded the esteemed 2024 Blaise Pascal Medal in Mathematics for his outstanding contributions to the field, particularly in… Read More

  • Archana Receives the Donna B. Hamilton Award

    Archana Khurana has been selected to receive the Donna B. Hamilton Award for Excellence in Undergraduate Teaching in a General Education Course.  Awards are based solely on student nominations and are solicited from across campus.  From the many nominations received, the selection committee was very impressed by the student experience… Read More

  • Yanir Receives a Do Good Campus Fund Grant

    Yanir’s proposal on “Incorporating outreach into the curriculum via experiential learning” is one of the only 27 projects out of 140 submissions that were funded by the UMD Do Good Campus Fund. 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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