- Instructor: Professor Anne Gelb, Mathematics Department, Dartmouth College
- Course Time: 10A T-Th 10:10am-12:00pm (x-hour F 3:30pm-4:20pm)
- Course Location: Kemeny TBD
- Office: Kemeny 207 Office Hours: T Th 3:30-4:20; and by appointment.
- Jonathan Lindbloom (TA) Office: Kemeny 219 Office Hours: TBD.

**Course Description:**
Numerical analysis is a fundamental topic in applied mathematics. Many practical problems that scientists try to solve are based on mathematical models, but few can be solved analytically, mainly due to their large size. Therefore computational algorithms are needed for approximating these solutions. It is critically important to maintain the important mathematical properties of the underlying system when developing numerical algorithms, and moreover to ensure accuracy, efficiency and convegence. Numerical analysis is about developing good computational techniques for broad based problems and demonstrating that these properties hold both theoretically and computationally. Numerical analysts make sure that computational algorithms are trustworthy so that domain scientists can be confident in the results of their experiments. Numerical analysts also answer the question, ``what assumptions of the underlying problem are necessary for this computational method to succeed?'' In this course we will focus on numerical linear algebra, interpolation and approximation, which are all essential when solving problems in data science, signal and image processing, and evolutionary dynamics. We will use MATLAB to verify our understanding of the theoretical results, but developing programming skills are not the main focus of the course.

**Prerequisites:**
Math 22 or instructor approval. Some experience in MATLAB or another programming language is expected.

**Textbooks:**

*Lambers, James V., Sumner Mooney, Amber C., and Montiforte, Vivian (2021), Explorations in Numerical Analysis: Python Edition, World Scientific Press*(required). 2016 preprint of book (in MATLAB).*Ascher, Uri M. and Greif, Chen. (2011) A First Course in Numerical Methods, SIAM*(suggested).

**Grading:** Grades in the class will be based on homework sets which will ensure mastery of theoretical and computational skills. There will also be two take home exams, which will not have computational components. Students may work together on the homework, but will need to turn in their own assignments. Students may not work together on take home exams. It is strongly recommended that all homework assignments, especially those involving programming problems, be started early.

**Grading formula:**
(i) Homework sets (50%); (ii) two take home exams (40%); (iii) Participation & Attendance (10%).

- First day of class: January 4 2023.
- 5 homework problem sets due approximately every ten days. Homework sets will be available on CANVAS. Due to the varying complexity of the material, some homework sets will naturally be more challenging than others. Regardless, each homework set is weighted the same for the final grade.
- First exam: Hand out: TBD. Due: TBD
- X Hours: Some X hours will be used during the early part of the term, mainly to review class concepts by discussing the ``exploration excercises'' (see textbook). The X hours may be held remotely (check the announcements on CANVAS).
- Participation & attendance: Students are expected to attend most classes and X hours (when scheduled).
- Last day of class: March 7 2023
- Second exam due: TBD

Week | Lecture |
---|---|

Weeks 1 & 2 | Chapters 1 & 2: Preliminaries. The first X-hour will be an introduction to Python in context of the exercises in Chapter 1 (taught by Jonathan Lindbloom). |

Week 3 | Chapter 3: Direct Methods for Linear Systems. |

Weeks 4 | Chapter 4: Least Square Problems. |

Week 5 | Chapter 7: Polynomial Interpolation. |

Week 6 | Chapter 8: Approximation of Functions |

Week 7 | Chapter 9: Differentiation and Integration |

Week 8 | Chapter 10: Zeroes of Nonlinear Functions |

Week 9 | Chapter 5: Iterative Methods for Linear Systems |