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INTRODUCTION TO NUMERICAL METHODS

COMPSCI 412
과목 설명

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.

선수과목

MATH 222 and (COMPSCI/MATH 240 or MATH 234 ) and (COMPSCI 200 , COMPSCI 300 , 301, 302, COMPSCI 310 , or placement into COMPSCI 300 ) or graduate/professional standing or declared in the Capstone Certificate in Computer Sciences for Professionals

충족 요건

This course does not satisfy any prerequisites.

학점

미보고

개설 시기

미보고

평점
2.79

-4.74% 과거 데이터 대비

수료율
87.18%

-3.81% 과거 데이터 대비

A 비율
23.08%

-10.05% 과거 데이터 대비

학급 규모
39

-32.52% 과거 데이터 대비

Cumulative Grade Distribution

강사 (2026 Summr)

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유사 과목

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.)

LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS

MATH 320

An introduction to linear algebra and differential equations with emphasis on the relationship between the theory of linear algebra and analytical and numerical techniques for solving differential equations. Linear algebra topics include linear systems, matrices and their algebra, vector spaces and linear transformations, eigenvalues and eigenvectors. Topics from differential equations include first order ODE, homogeneous and nonhomogeneous linear systems, and numerical methods.

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.

NUMERICAL ANALYSIS

COMPSCI/MATH 514

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.

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).