Course Description
This course is an introduction to numerical analysis with an emphasis on practical applications, implementation, and algorithm design. The primary objective of this course is to gain an understanding of the algorithms and pitfalls encountered when performing numerical operations on computational systems. The secondary objective is to gain practical programming experience with C/C++ and Matlab, including algorithm design and the proper understanding and use of available numerical algorithms.
Syllabus [ PDF ]
Textbooks
[ PDF ] Numerical Methods in Practice - (in progress)
Course Information
| 01 [ PPTX ] | Introduction to numerical methods, quantization errors, and programming tools |
| Homework 1 | Review Chapters 1 and 2 (math and C/C++ review) Get an account on Tuxedo (Engineering Computer Lab) Submit: a program that echos user input. input: (assuming your executable is the default "a.out") ./a.out repeat this text output: echo: "repeat this text" |
| 2.1 [ YouTube ] [ PDF ] 2.2 [ YouTube ] [ PDF ] |
Computational complexity, Horner's algorithm, polynomial derivatives |
| Homework 2 | Read Chapter 3 Submit: P3.1, P3.2 |
| 3.1 [ YouTube ] [ PDF ] 3.2 [ YouTube ] [ PDF ] 3.3 [ YouTube ] [ PDF ] |
Numerical representation, error, loss of precision HexEdit website: hexed.it |
| 4.1 [ YouTube ] [ PDF ] 4.2 [ YouTube ] [ PDF ] |
Methods for mitigating precision loss, re-arranging terms, Maclaurin series |
| Homework 3 | Read Chapters 5 and 6 5.1 #6, 5.2 #2, 5.3 through 5.10, 6.4, 6.12, 6.16 |
| 5 [ YouTube ] [ PDF ] | Roots of Equations and Optimization |
| Programming 1 | Python Benchmark: roots_benchmark.py
Usage: |
| Review 1 [ PDF ] | Practice Exam #1 Answers |
| 6.1 [ YouTube ] [ PDF ] 6.2 [ YouTube ] [ PDF ] 6.3 [ YouTube ] [ PDF ] |
Linear Systems, Gaussian elimination, and instabilities |
| 7 [ YouTube ] [ PDF ] | Probability, random number generators |
| Homework 4 | 8.1, 9.1A, 9.7, 10.1, 10.2 |
| Programming 2 | Python Benchmark: lup_benchmark.py
Usage: |
| 8 [ YouTube ] [ PDF ] | Finite difference calculus |
| 9 [ YouTube ] [ PDF ] | Numerically solving partial differential equations [ Python ] [ MATLAB ] |
| Review 2 [ PDF ] | Practice Exam #2 Answers |
| 10 [ YouTube ] [ PDF ] | Numerical integration, Monte-Carlo methods |
| 11 [ YouTube ] [ PDF ] | Least squares fitting |
| 12 [ YouTube ] [ PDF ] | Interpolation |
| 13 [ YouTube ] [ PDF ] | Kessel Run Programming Assignment MATLAB Euler example |
| Review 3 [ PDF ] | Practice Exam #3 Practice Exam #3 Answers |