https://github.com/jamesquinlan/cos374-numerical
Introduction to Numerical Analysis
https://github.com/jamesquinlan/cos374-numerical
Last synced: 27 days ago
JSON representation
Introduction to Numerical Analysis
- Host: GitHub
- URL: https://github.com/jamesquinlan/cos374-numerical
- Owner: jamesquinlan
- License: gpl-3.0
- Created: 2022-04-13T01:50:20.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2024-07-10T15:36:44.000Z (10 months ago)
- Last Synced: 2025-03-29T10:53:41.673Z (about 1 month ago)
- Language: TeX
- Size: 150 KB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README-une405.md
- License: LICENSE
Awesome Lists containing this project
README
# Introduction to Numerical Analysis
Numerical analysis studies the methods used to solve problems involving continuous variables and is an applied branch of mathematics and computer science. The goal of this numerical analysis course is to provide students with opportunities to learn to devise, evaluate, and use methods for computing approximate but accurate solutions to various numerical problems that arise in mathematics, physics, biology, and data science. MAT 405 covers the analysis associated with direct methods of solution of linear systems, zeros of non-linear equations, approximation and interpolation, numerical integration, and initial value problem for ordinary differential equations, with attention to generation and propagation of numerical errors and to computational speed.
## Topics
- Programming Primer
- Mathematical preliminaries (review of calculus) and error analysis
- Solutions of equations in one variable (root finding techniques: Bisection, Newton's and Secant methods)
- Interpolation and polynomial approximation
- Numerical differentiation and integration
- Direct and indirect methods for solving linear systems
## Learning Outcomes
Students successfully completing this course will: % \footnote{Evaluation item listed in parenthesis)}:
- Apply basic programming constructs to solve numerical problems
- Show how numbers are represented on the computer and how errors from this representation affect arithmetic
- Apply numerical methods for accurate solutions to scientific problems
- Demonstrate how numerical methods presented in the course work for solving various standard mathematical problems in realistic settings.
- Select the appropriate algorithm to solve the problem based on the criterion of its suitability for present-day computers.
- Apply numerical algorithms presented in the course effectively based on ready-to-use computer programs.
- Understand issues of algorithm complexity and programmability
- Interpret machine output and provide a good understanding of the problems of error analysis and convergence of algorithms
## Textbook
Burden, R. L., Faires, J. D., & Burden, A. M. (2015). _Numerical analysis_. Cengage learning.
```
@book{burden2015numerical,
title={Numerical analysis},
author={Burden, Richard L and Faires, J Douglas and Burden, Annette M},
year={2015},
publisher={Cengage learning}
}
```
## Homework
Homework will be assigned and collected regularly. You are expected to hand in homework that is your own work. Homework will account for 30% of your grade.
Homework must be neat, organized, detailed, and stapled. Homework that does not meet these specifications will not be accepted, no exceptions. In addition to written homework assignments, you may be given electronic homework assignments. One point per day will be deducted for late homework. Use MATLAB's dairy function to copy and paste MATLAB commands and code into your documents.