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Description

Floating point computations, direct methods for linear systems, interpolation, solution of nonlinear equations, numerical differentiation and integration. 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 MATH410.

Level of Rigor

Advanced

Sample Textbooks

  • An Introduction to Numerical Analysis, by E. Suli & D. Mayers
  • Numerical Analysis by W. Gautschi

Applications

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

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

Math 420, Math 462, Math 464

Additional Notes

  • Duplicate credit with AMSC460 and CMSC460; crosslisted with CMSC466
  • Students interested in grad school in Applied Math should consider this course
  • Students interested in grad school in MATH should consider this course
  • Students interested in grad school in Statistics should consider this course 

Topics

  • Floating point computation (1 week)
  • Properties of machine arithmetic
  • Direct methods for linear systems (4 weeks)
  • Gaussian elimination
  • Pivoting strategies
  • Cholesky factorization
  • Vector and matrix norms
  • Conditioning and the effect of rounding error
  • Interpolation (2 weeks)
  • Polynomial approximation
  • Newton and Lagrange forms
  • Error formula (derived)
  • Solution of nonlinear equations (3 weeks)
  • Bisection, Secant, and Newton's method
  • Fixed point methods
  • Newton's method for systems
  • Numerical differentiation and integration (3 weeks)
  • Numerical differentiation
  • Numerical integration
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