CS 314: Numerical Methods

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Details

Program Details

Degree

Courses

Major

Mathematics | Numerical Analysis | Statistics

Area of study

Mathematics and Statistics

Course Language

English

About Program

Program Overview

Department of Computer Science

The Department of Computer Science offers various academic programs, including undergraduate and graduate degrees.

Academic Programs

Undergraduate Program: The undergraduate program provides students with a comprehensive education in computer science, covering topics such as numerical methods, programming languages, and software engineering.
Graduate Program: The graduate program offers advanced degrees in computer science, including master's and doctoral degrees, with research areas in numerical methods, artificial intelligence, and data science.

Courses

CS 314: Numerical Methods: This course covers numerical algorithms, mathematical software, and error analysis, with topics including:
- Numerical Algorithms and mathematical software
- Floating-point computation
- Linear systems: Gaussian elimination and triangular factorization
- Residuals and error estimates in solving linear systems
- Least squares approximation: orthogonal factorization
- Interpolation: existence, uniqueness, and the Vandermonde form of the interpolating polynomial
- Lagrange and Newton forms of the interpolating polynomial, errors in polynomial interpolation, and
- Natural spline interpolation
- Numerical integration: Approximation based on the interpolating polynomial
- Composite rules, Richardson extrapolation
- Spline and adaptive quadrature
- The single nonlinear equation: bisection, Newton method and its variants, including the secant method
- Functional iteration, convergence, and higher order methods
- Initial-value problem for ordinary equations: differential equations, Euler's method
- Taylor and Runge-Kutta methods

Suggested Textbooks

Introduction to Scientific Computing by Charles Van Loan, Prentice Hall
Elementary Numerical Computing with Mathematica by Skeel and Keiper, McGraw-Hill
Lecture Notes by A. Sameh and V. Sarin

Research Areas

The department has research areas in numerical methods, artificial intelligence, and data science, with various research centers and institutes.

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