• Maryland finishes fourth in the 2022 Putnam competition

     We are very excited to share the news that the University of Maryland Putnam team ranked fourth among 456 institutions in the 2022 Putnam Competition. This is the best result for our team in more than four decades. The first three teams are MIT, Harvard and Stanford. Our team members,… Read More

  • Congratulations to the 2023 elected Fellows of the Association for Women in Mathematics

    Please join me in congratulating Konstantina Trivisa,  Shelby Wilson (PhD, AMSC, 2012), and Kimberly Sellers (MS, 1998) for being elected as 2023 Fellows of the Association for Women in Mathematics. The official citation reads (see https://awm-math.org/ awards/awm-fellows/2023-awm- fellows/) Konstantina Trivisa, University of Maryland For her tireless efforts and dedication to increase diversity in the mathematical… Read More

  • Abba Gumel & Larry Washington elected as Fellows of the American Mathematical Society

    Please join us in congratulating Abba Gumel and Larry Washington for being elected as Fellows of the American Mathematical Society. Abba was noted for his contributions to the mathematical theory of epidemics, applied dynamical systems, and promoting the use of mathematics to help solve global health challenges. Larry was noted… Read More

  • Dmitry Dolgopyat Named Distinguished University Professor

    Congratulations to Dmitry Dolgopyat (Mathematics), Richard Greene (Physics) and Zhanqing Li (AOSC/ESSIC), who have been named Distinguished University Professors—the highest academic honor bestowed by the university. They will be honored at the Faculty and Staff Convocation on September 14, 2022. These faculty members are world-renowned in their fields and it’s wonderful to see their accomplishments recognized by the university in this way. You can… Read More

  • 2022 Interdisciplinary Competition in Modeling (ICM) Results

    Congratulations to Radu Balan and to the UMD Math Modeling teams. The teams participated in the 2022 Interdisciplinary Competition in Modeling (ICM). This year 12100 teams participated in the ICM competition. The results of our two teams are: Team 2228337 (Sally Zhao, Naveen Raman, Clarissa Xia) has been awarded a Honorable Mention for Problem… Read More
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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. Will use MATLAB.

 

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH340, MATH241); and 1 course with a minimum grade of C- from (CMSC106, CMSC131); and minimum grade of C- in MATH246.

 

Level of Rigor

Standard

 

Sample Textbooks

Numerical Analysis by R. Burden, J. Faires, A. Burden

Numerical Computing with Matlab, by Cleve B. Moler

 

Applications

Computer Science, Economics, Business, Engineering, Physics, Astronomy

 

If you like this course, you might also consider the following courses:

Math 420, Math 416, Stat 430.

 

Additional Notes

Duplicate credit with AMSC466 and CMSC466; cross-listed with CMSC460

Students interested in grad school in Applied Math should consider this course

Students interested in grad school in Statistics should consider this course

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

 

 

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