### 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 ]

Course Forum: Piazza (requires login)

### Textbooks

[ PDF ] Numerical Methods in Practice - (in progress)

### Lectures

01 [ PPTX ] | Introduction to numerical methods, quantization errors, and programming tools |

02 [ PPTX ] 2.1 [ YouTube ] 2.2 [ YouTube ] |
Computational complexity, Horner's algorithm, polynomial derivatives |

03 [ PPTX ] 3.1 [ YouTube ] 3.2 [ YouTube ] |
Numerical representation, error, loss of precision HexEdit website: hexed.it |

04 [ PPTX ] | Methods for mitigating precision loss, re-arranging terms, Maclaurin series |

05 [ PPTX ] | Roots of Equations and Optimization |

06 [ PPTX ] | Linear Systems, Gaussian elimination, and instabilities |

07 [ PPTX ] | Stable methods for solving linear systems |

Review 1 [ PPTX ] | |

08 [ PPTX ] | Properties of linear systems, conditioning, stability |

09 [ PPTX ] | Probability, random number generators |

Review 2 [ PPTX ] | |

10 [ PPTX ] | Finite difference calculus |

11 [ PPTX ] | Numerically solving partial differential equations |

12 [ PPTX ] | Numerical integration, Monte-Carlo methods |

13 [ PPTX ] | Least squares fitting |

Review 3 [ PPTX ] |

### Homework and Programming Assignments

Homework 1 | Review Chapters 1 and 2 (math and C/C++ review) Get an account on Tuxedo (Engineering Computer Lab) a program that echos user input.Submit:input:(assuming your executable is the default "a.out")./a.out repeat this text
echo: "repeat this text" |

Homework 2 | Read Chapter 3 P3.1, P3.2Submit: |

Programming 1A | Chapter 3, Programming Assignment Horner's Method ( )no submission yet |

Homework 3 | Read Chapters 5 and 6 5.1 #6, 5.2 #2, 5.3 through 5.10, 6.4, 6.12, 6.16 |

Programming 1 | Chapter 7 Programming Assignment Implement the Newton Horner Method |

Practice Exam #1 | Practice Exam #1 Answers |

Homework 4 | 8.1, 9.1A, 9.7, 10.1, 10.2 |

Programming 2 | Implement partial pivoting Example input matrices: geometric8.txt geometric9.txt rand_perm.txt |

Practice Exam #2 | Practice Exam #2 Answers |

Programming 3: instructions slides |
Implement the Kessel RunCluster files:cluster1.mat |

Practice Exam #2 | Practice Exam #3 Answers |