• Distinguished Lectures in Geometric Analysis

    The second in our series of Distinguished Lectures in Geometric Analysis will be given on October 31 and November 2, 2018, by Professor Bo Berndtsson from Chalmers University of Technology in Sweden.  The topic will be Complex Brunn-Minkowski theory. Read More
  • College Welcomes 19 New Faculty Members this Fall

    The College of Computer, Mathematical, and Natural Sciences welcomed 19 new tenured/tenure-track faculty members to the University of Maryland this fall. The brief introductions to the new faculty members can be read on CMNS website. Read More
  • In memory of our colleague David C. Lay

    Our long-time colleague Professor Eneritus David Lay passed away October 12, 2018. David earned his BA at Aurora College in 1962, and his PhD at UCLA in 1966. He then came to Maryland where he rose through the ranks to Professor in 1977. A gifted teacher, he won the campus Read More
  • The Canadian Journal of Statistics Award 2018, to Victor de Oliveira and Benjamin Kedem

    The Canadian Journal of Statistics Award is presented each year by the Statistical Society of Canada to the author(s) of an article published in the journal, in recognition of the outstanding quality of the methodological innovation and presentation. This year’s winner is the article entitled “Bayesian analysis of a density ratio Read More
  • Outstanding Director of Graduate Studies Award

    Professor Konstantina Trivisa has been selected for the Outstanding Director of Graduate Studies (DGS) Award for 2018.  Directors of Graduate Studies are critical partners of the Graduate School in shaping graduate education and ensuring the success of graduate students.  The Outstanding Director of Graduate Studies Award recognizes exceptional contributions made Read More
  • 1
  • 2
  • 3
  • 4
  • 5

Description

Basic computational methods for interpolation, least squares, approximation, numerical quadrature, numerical solution of nonlinear equations, systems of linear equations, and initial value problems for ordinary differential equations. Emphasis on the methods and their computational properties rather on their analytic aspects.

Prerequisites

(MATH 240 and MATH 241) or (MATH 340 and MATH 341); and (CMSC 106 or CMSC131)

Note: Also listed as CMSC 460.

Topics

Computer Arithmetic and Errors

Machine arithmetic
Error analysis
Stability and conditioning

Solving linear systems of equations

Gaussian elimination
well-conditioning vs. ill-conditioning, matrix and vector norms

Software for Gaussian elimination

Interpolation

Polynomial interpolation
Piecewise polynomial interpolation
Spline interpolation
Software for interpolation

Numerical Integration

Elementary integration formulas (midpoint, trapezoidal rules, etc.)
Gaussian quadrature
Adaptive quadrature
Software for adaptive integration

Solution of nonlinear systems of equations

Bisection method, secant method, Newton's method
Methods for systems of equations
Software for solving nonlinear equations

Numerical solution of ordinary differential equations

Stability and stiffness
Basic numerical methods
Stepsize control
Methods for stiff systems
Software for solving initial value problems

Linear least squares problems

Data fitting and least squares
QR factorization
Software for least squares problems

  • 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