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Computational Methods - CMSC / AMSC 460 (Section 0401), Fall 2024
Course Description

Instructor Information
         Howard Elman
         Department of Computer Science
         Email: helman@umd.edu
         Office: 4210 Iribe
         Office hours: Tu 11-12, Th 3:30-4:30, or by appointment
 
Overview
The course is an introduction to the properties and computational implementations of basic methods of scientific computing. The main thrust is intelligent use of mathematical software, although important theoretical results are explained. Students are expected to have a good working knowledge of calculus, linear algebra and programming, and some exposure to ordinary differential equations. Assignments will include significant programming, which can be done in MATLAB or Python, or alternatives subject to instructor approval.
 
Outline of Topics Covered
  • Interpolation and approximation of functions
    • polynomial and piecewise polynomial interpolation
    • accuracy of interpolation
    • least squares approximation
  • Numerical integration
    • Newton-Cotes rules
    • error analysis
    • adaptive quadrature
    • Gauss quadrature
  • Direct solution of linear systems of equations
    • Gaussian elimination
    • effects of pivoting and conditioning
    • bandsolvers
  • Nonlinear equations and optimization
    • rootfinding and minimization of scalar functions
    • systems of equations
    • minimization of mulivariate functions
  • Numerical solution of ordinary differential equations
    • one-step and multistep methods
    • stability of problems and methods
    • stiff systems
 
Required Text
 
Grading
Grades will be determined as follows:
  • 5-7 homework assignments: 30%
  • Midterm examination: 25%
  • Final examination: 45%
Homework assignments will contain a large component of programming. Knowledge of MATLAB or Python or the ability to learn at least one of them quickly is required.

Information about MATLAB can be found at:
      http://www.mathworks.com/academia/student_center/tutorials/launchpad.html
Information about Python can be found at:
      https://docs.python.org/3/tutorial/index.html
Search "Matlab tutorial" or "Python tutorial" for other sources.

Due dates of assignments are listed on them, typically 11:59PM on the due date. Late assignments will be accepted within 48 hours of the due date and not later. The value of late assignments will decrease according to the following rule:
  • within 24 (weekday) hours after the due date: 85% of the original value
  • within 48 (weekday) hours after the due date: 70% of the original value
No makeups will be given for the midterm exam. If the exam is missed and a valid medical excuse is provided, then grading will be determined by increasing the weights of the final exam and homework. The final grade will be on a curve. A grade of A is guaranteed with an average of 90% or better, a grade of B with 80% or better, etc.
 
Plagiarism: You are welcome to discuss assignments in a general way among yourselves, but you may not use other students' written work or programs. Use of external references for your work should be cited. Clear similarities between your work and others will result in a grade reduction for all parties. Flagrant violations will be referred to appropriate university authorities.
 
[Last updated July 21, 2024]