## Course Description

Computational methods for solving numerical problems in science, engineering and business. Linear and non-linear equations, approximation, optimization, interpolation,integration and differentiation. The aim is to give students a basic understanding of floating-point arithmetic and the implementation of algorithms used to solve numericalproblems, as well as a familiarity with current numerical computing environments.Course concepts are crucial to a wide range of practical applications such as computational finance and portfolio management, graphics and special effects, data mining and machine learning, as well as robotics, bioinformatics, medical imaging and others.

See the Syllabus for more information.

## Course Staff and Contact

**Instructor:** Lisa Zhang**Office Hours:** MF11:00-12:00, W13:00-14:00**Office:** DH3068**Email:** lczhang [at] cs [dot] toronto [dot] edu**Teachin Assistants:** Vlad, Hossein

Please include "CSC338" in your subject.

All announcements will be made on Piazza and Quercus

## Textbook

Michael Heath, Scientific Computing: An Introductory Survey, Second Edition, McGraw Hill, 2002.

Roughly the first half of the book will be covered. The relevant chapters have been made available by McGraw Hill in the textbook store at a special price.

## Tentative Schedule

The course schedule is tentative and subject to change.

Date | Course Material | Deadline | |
---|---|---|---|

Week 1 | Jan 7 | Lecture- Introduction
- Errors in Scientific Computing
- Lecture Notes [pdf]
Tutorial- Python and Jupyter Notebook
- Homework 1
Reading- Chapter 1 Slides 1-23 [pdf]
- Textbook Chapters 1.1, 1.2,
| |

Week 2 | Jan 14 | Lecture- Floating Point Numbers
- Lecture Notes [pdf]
- Notebook Output [pdf]
Tutorial- Floating Point Numbers [pdf]
Reading- Chapter 1 Slides 24-44 [pdf]
- Textbook Chapters 1.3-1.3.10
| Homework 1 (Jan 21 9pm) |

Week 3 | Jan 21 | Lecture- Systems of Linear Equations
- Gauss Elimination
- LU Factorization
- Lecture Notes [pdf]
Reading- Chapter 2 Slides 1-7, 23-39 [pdf]
- Textbook Chapters 2.1, 2.2, 2.4-2.4.4
Review- Essense of Linear Algebra by 3Blue1Brown [YouTube playlist]
Tutorial- Numpy [link]
Additional Reading | |

Week 4 | Jan 28 | Lecture- Vector and Matrix Norms
- Conditioning of Ax=b
- Gauss Elimination With Partial Pivoting
- Lecture Notes [pdf]
- Notebook Output [pdf]
Reading- Chapter 2 Slides 8-22, 40-42 [pdf]
- Textbook Chapters 2.3, 2.4.5
| Homework 2 (Feb 4 9pm) |

Week 5 | Feb 4 | University Closed due to Snow StormTutorial- Midterm Review [pdf]
| |

Week 6 | Feb 11 | Lecture- Midterm (3:10pm-4:10pm)
- Complete Pivoting, Iterative Refinement, Modified Problem (4:30pm-5pm)
- Lecture Notes [pdf]
Tutorial- Midterm Take-up
Reading- Chapter 2 Slides 43-51, 57-71, 76 [pdf]
- Textbook Chapters 2.4.9-2.5.1
| |

Reading Week | |||

Week 7 | Feb 25 | Lecture- Cholesky Factorization
- Linear Least Squares: The Normal Equation
- Lecture Notes [pdf]
Reading | |

Week 8 | Mar 4 | Lecture- Linear Least Squares Conditioning & Sensitivity
- Householder Transform
- Lecture Notes [pdf]
Tutorial- Curve Fitting (slides 4-8, 35-39)
Reading- Chapter 3 Slides 4-8, 14-16, 24-39 [pdf]
- Textbook Chapters 3.3, 3.4.3-3.5.1
| Homework 3 (Mar 10 9pm) |

Week 9 | Mar 11 | Lecture- Nonlinear Equations
- Interval Bisection
- Fixed-Point Iteration
- Lecture Notes [pdf]
- Notebook Output [pdf]
Tutorial- Fixed-Point Iteration
- Notebook Output [pdf]
Reading- Chapter 5 Slides 1-23 [pdf]
- Textbook Chapters 5.1-5.5.2
| |

Week 10 | Mar 18 | Lecture- Fixed-Point Iteration
- Newton's Method; Secant Method
- Lecture Notes [pdf]
Tutorial- Nonlineare Equations Review [pdf]
Reading- Chaper 5 Slides 16-31, 41-45 [pdf]
- Textbook Chapters 5.2-5.4, 5.6-5.6.2
| Homework 4 (Mar 25 9pm) |

Week 11 | Mar 25 | Lecture- Optimization
Reading- Book Slides [pdf]
- Textbook Chapters 6 (TBD)
| |

Week 12 | Apr 1 | Lecture- Optimization
Reading- Book Slides [pdf]
- Textbook Chapters 6 (TBD)
| Homework 5 (Apr 5 9pm) |

Final Exam |