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    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

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    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

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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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