Meeting Schedule: Tuesdays, Thursdays 11:00 am - 12:15 pm
Location: Fariborz Maseeh Hall (FMH) 419
Instructor: Will Pazner
Email: pazner@pdx.edu
Office: FMH 462B
Office hours: Tuesdays 12:30 pm - 1:30 pm, Thursdays 3:00 pm - 4:00 pm (FMH 462B), and by appointment.
Course Description: Computer arithmetic. Solution of nonlinear equations. Interpolation. Numerical integration and differentiation. Solution of linear equation systems. Eigenvalue problem, least square, Chebyshev, trigonometric and rational function approximation. Numerical solution of differential equations. This is the first course in a sequence of three: MTH 451/551, MTH 452/552, and MTH 453/553 which must be taken in sequence.
The goal of this course is to provide a solid foundation in numerical analysis, which concerns the design and analysis of algorithms for efficiently and accurately approximating solutions of mathematical problems arising in science and engineering.
Credits: 3
Prerequisites: knowledge of a programming language such as MATLAB, Python, or C/C++, MTH 253Z and MTH 261.
In this course, students will learn to identify the types of problems that require numerical techniques for the solution, see examples of the error propagation that can occur when numerical methods are applied and learn typical techniques for estimating error bounds for the approximations.
Textbook: Numerical Mathematics by Jeffrey S. Ovall, published by SIAM.
The book is available at https://epubs.siam.org/doi/10.1137/1.9781611978070. A 20% discount can be applied using the code BKOVAD.
The course grade will be based on assignments (30%), quizzes (10%), one midterm exam (30%), and the comprehensive final exam (30%).
There is one midterm exam (Thursday 10/29), which take place at the regular class time and room.
The final exam is cumulative, and will take place during exam week, on Thursday 12/10, from 11:10 am - 1 pm in the normal classroom (FMH 419).
There will be four homework assignments. These will be selected questions from the textbook. Students enrolled in MTH 551 will have some extra questions.
You are welcome (and encouraged) to discuss the assignments with other students, but your write-ups should reflect your own work and understanding. Use of AI for homework assignments is prohibited.
Late policy: Each student may use one free extension during the term, which allows one assignment to be turned in up to three days late with no penalty, without any explanation needed. One other late homework will be accepted up to three days after the due date with a 10% penalty. After that, late work won’t be accepted, because solutions will be posted. If you have a serious emergency (illness, family emergency, etc.), please contact me as soon as possible and we will make an arrangement.
There will be four in-class quizzes, listed on the lecture schedule. Each quiz will cover material from recent lectures and homework. Solutions will be presented in class, and there will be an opportunity to correct your quiz answers.
| Lecture | Date | Topic | Textbook Reference |
|---|---|---|---|
| 1 | Tue 9/29 | Taylor’s Theorem | 1.1 |
| 2 | Thu 10/1 | Taylor’s Theorem; Orders of convergence | 1.1, 1.2 |
| 3 | Tue 10/6 | (Quiz 1, §1.1) Orders of convergence | 1.2, 1.3 |
| 4 | Thu 10/8 | Floating-point arithmetic | 1.4 |
| 5 | Tue 10/13 | Root bracketing methods | 2.1 |
| 6 | Thu 10/15 | (Homework 1 due) Newton and secant methods | 2.2 |
| 7 | Tue 10/20 | (Quiz 2, §2.1, 2.2) Functional iteration and fixed points | 2.3 |
| 8 | Thu 10/22 | Building polynomials | 3.1 |
| 9 | Tue 10/27 | (Homework 2 due) Midterm Review | - |
| - | Thu 10/29 | Midterm Exam | - |
| 10 | Tue 11/3 | Building polynomials | 3.1 |
| 11 | Thu 11/5 | Lagrange interpolation in Lagrange and barycentric forms | 3.2 |
| 12 | Tue 11/10 | (Quiz 3, §3.1, 3.2) Lagrange interpolation: error estimates | 3.4 |
| 13 | Thu 11/12 | Basic quadrature | 4.1 |
| 14 | Tue 11/17 | Basic quadrature | 4.1 |
| 15 | Thu 11/19 | (Homework 3 due) Finite difference approximations of derivatives | 4.2 |
| 16 | Tue 11/24 | (Quiz 4, §4.1, 4.2) Finite difference approximations of derivatives | 4.2 |
| - | Thu 11/26 | Thanksgiving Day: No Class | |
| 17 | Tue 12/1 | Gaussian quadrature | 4.3 |
| 18 | Thu 12/3 | (Homework 4 due) Exam Review | - |
| - | Thu 12/10 | Final Exam, 11:10 am-1 pm, FMH 419 | - |
I am committed to creating an accessible and inclusive learning environment for all students. If you encounter any accessibility barriers or challenges in this course, please reach out to me via email (pazner@pdx.edu). I will work with you and our campus partners to evaluate the issue and find solutions.