• Two Math Faculty to Speak at ICM

    Congratulations to faculty members Pierre-Emmanuel Jabin and Xuhua He who have been selected as invited speakers at the International Congress of Mathematics in Rio de Read More
  • Promotions and New Faculty

    We are delighted to announce that faculty members Jacob Bedrossian, Maria Cameron, Amin Gholampour, and Christian Zickert have been promoted to the rank of Associate Read More
  • William E. Kirwan Distinguished Undergraduate Lectures

    Mathematics for Art Investigation: Mathematical tools for image analysis increasingly play a role in helping art historians and art conservators assess the state of conversation Read More
  • Upcoming Conferences

    We would like to draw your attention to several exciting conferences coming up in the Mathematics Department: The Spring Dynamics Conference, Friday, March 31 - Sunday, Read More
  • Putnam Exam

    We would like to congratulate the University Maryland team on their excellent performance on this year's William Lowell Putnam Mathematical Competition, the premier undergraduate math 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: 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

  • William E. Kirwan Hall, home of the Mathematics Department

    William E. Kirwan Hall, home of the Mathematics Department

  • The Experimental Geometry Lab explores the structure of low dimensional space

    The Experimental Geometry Lab explores the structure of low dimensional space

  • Maryland mathematicians help to investigate the inner workings of E_8

    Maryland mathematicians help to investigate the inner workings of E_8

  • Hyperbolic Space Tiled with Dodecahedra

    Hyperbolic Space Tiled with Dodecahedra

  • Isotropoic Gaussian random field with Matern correlation

    Isotropoic Gaussian random field with Matern correlation

  • Part of the proof of the Peter-Weyl theorem

    Part of the proof of the Peter-Weyl theorem