NUMERICAL ANALYSIS

COMPSCI/MATH 514

Course Description

Polynomial forms, divided differences. Polynomial interpolation. Polynomial approximation: uniform approximation and Chebyshev polynomials, least-squares approximation and orthogonal polynomials. Numerical differentiation and integration. Splines, B-splines and spline approximation. Numerical methods for solving initial and boundary value problems for ordinary differential equations.

Prerequisties

(MATH 320 , MATH 340 , MATH 341 , or MATH 375 ), (MATH 322 , MATH 376 , MATH 421 , or MATH 521 ), and (COMPSCI 200 , COMPSCI 220 , COMPSCI 300 , COMPSCI 310 , or 301 prior to Spring 2020, or placement into COMPSCI 300 ); grad/professional standing; member of the Pre-Masters Mathematics (Visiting International) Program

Satisfies

This course does not satisfy any prerequisites.

Credits

Offered

Fall

Grade Point Average

3.02

0.29% from Historical

Completion Rate

88.37%

-4.14% from Historical

A Rate

41.86%

37.43% from Historical

Class Size

-1.15% from Historical

2025 Fall Grade Distribution

Instructors (2025 Fall)

Sorted by ratings from Rate My Professors

Laurel OHM

[email protected]

4.1

Rating

Similar Courses

INTRODUCTION TO NUMERICAL METHODS

COMPSCI 412

Interpolation, solution of linear and nonlinear systems of equations, approximate integration and differentiation, numerical solution of ordinary differential equations, Data fitting (such as least squares) by polynomials and splines. Knowledge of matrix algebra recommended, such asMATH 340.

METHODS OF COMPUTATIONAL MATHEMATICS I

COMPSCI/MATH 714

Development of finite difference methods for hyperbolic, parabolic and elliptic partial differential equations. Analysis of accuracy and stability of difference schemes. Direct and iterative methods for solving linear systems. Introduction to finite volume methods. Applications from science and engineering. Students are strongly encouraged to have programming skills (e.g.COMP SCI 200) and some undergraduate numerical analysis (e.g.MATH/COMP SCI 514orCOMP SCI 412), analysis and differential equations (e.g.MATH 322andMATH 521) and linear algebra (e.g.MATH 341).

NUMERICAL LINEAR ALGEBRA

COMPSCI/MATH 513

Direct and iterative solution of linear and nonlinear systems and of eigenproblems. LU and symmetric LU factorization. Complexity, stability, and conditioning. Nonlinear systems. Iterative methods for linear systems. QR-factorization and least squares. Eigenproblems: local and global methods.

METHODS OF COMPUTATIONAL MATHEMATICS II

COMPSCI/MATH 715

Introduction to spectral methods (Fourier, Chebyshev, Fast Fourier Transform), finite element methods (Galerkin methods, energy estimates and error analysis), and mesh-free methods (Monte-Carlo, smoothed-particle hydrodynamics) for solving partial differential equations. Applications from science and engineering. Applications from science and engineering. Students are strongly encouraged to have programming skills (e.g.COMP SCI 200), undergraduate numerical analysis (e.g.MATH/COMP SCI 514orCOMP SCI 412), analysis (MATH 322and521) and linear algebra (e.g.MATH 341or equiv.)

TECHNIQUES IN ORDINARY DIFFERENTIAL EQUATIONS

MATH 319

Review of linear differential equations; series solution of linear differential equations; boundary value problems; Laplace transforms; possibly numerical methods and two dimensional autonomous systems.