• Sergei Novikov wins the 2020 Russian Academy of Sciences Gold Medal

    Congratulations to our colleague Sergei Novikov for receiving the 2020 Russian Academy of Sciences Gold Medal.Sergei and John Milnor will be sharing the award. For more details about the award, follow this link: https://nauka.tass.ru/nauka/10085945 congratulate our colleague Sergey Novikov for receiving the 2020 Russian Academy of Sciences Gold Medal.Sergey and Read More
  • 2020 Alexander Prize Recipients

    Xue Ke and Patrick Daniels won the 2020 James C. Alexander Prize for Graduate Research in Mathematics.Xue Ke PhD dissertation title is “Affine Pavings of Hessenberg Ideal Fibers”. The dissertation was directed by Patrick Brosnan.Patrick Daniels PhD dissertation title is “A Tannakian Framework for G-Displays and Rapoport-Zink Spaces”. The dissertation Read More
  • Adjunct Professor, Gail Letzer named AWM Fellow

    Our Adjunct Professor, Gail Letzter, was named a Fellow of the Association for Women in Mathematics.   The AWM Fellows Program recognizes individuals who have demonstrated a sustained commitment to the support and advancement of women in the mathematical sciences, consistent with the AWM mission: “to encourage women and girls Read More
  • Cleve Moler joins the Math Department

    We would like to welcome Cleve Moler to our department.  Cleve is the founder and Chief Mathematician of Mathworks.  He was the driving force in the development of Matlab. He is a highly distinguished scientist, with honors including the National Academy of Engineering, the SIAM Prize for distinguished service to the profession, and the Read More
  • Vadim Kaloshin receives the 2020 ICCM Best Paper Award ( Gold Medal)

    We are pleased to announce that Vadim Kaloshin will receive a gold medal from the International Consortium of Chinese Mathematics (ICCM) for his joint paper with Guam Huang and Alfonso Sorrentino, “Nearly circular domains which are integrable close to the boundary are ellipses”. The award is given to 20 papers 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