Math 342 is an introduction to numerical analysis. We will focus on the big ideas and problems in numerical analysis, including error analysis, root finding methods, systems of linear equations, interpolation, numerical integration, and solving differential equations.
| Week | Topic | Notes |
|---|---|---|
| 1 | Floating point numbers | Week 01 |
| 2 | Taylor series | Week 02 |
| 3 | Bisection & Newton’s method | Week 03 |
| 4 | Secant method, fixed point iteration | Week 04 |
| 5 | LU decomposition | Week 05 |
| 6 | Norms & condition numbers, Midterm 1 | Week 06 |
| 7 | Newton & Lagrange polynomials | Week 07 |
| 8 | Interpolation error | Week 08 |
| 9 | Numerical integration, Newton-Cotes formulas | Week 09 |
| 10 | Gaussian quadrature, improper integrals | Week 10 |
| 11 | Least squares regression, continuous least squares | Week 11 |
| 12 | Orthogonal functions, Gram-Schmidt, Midterm 2 | Week 12 |
| 13 | Initial value problems, Euler’s method | Week 13 |
| 14 | Runge-Kutta methods | Week 14 |
The schedule above is tentative, and may be subject to change. Changes will be announced in class, and you are responsible for knowing about any changes even if you miss the class when they are announced.
Attendance in this class is required. Repeated absences may result in a forced withdrawal from the course. You are responsible for any material you miss due to absence. Please let me know ahead of time if you know that you will not be able to attend class.
The term grade will be based on the following factors.
| Component | Proportion |
|---|---|
| Workshops | 40% |
| Midterm 1 | 15% |
| Midterm 2 | 15% |
| Final Exam | 30% |
Most weeks we will have one or more in-class workshops. We will use the Python programming language for many of these workshops, and will use Google Colab for convenient access to Python. If you already have Python installed on your laptop, then you can use that instead of Google Colab. If you would like to install Python on your laptop, I recommend downloading Anaconda Individual Edition which is free.
We will do (or at least start) each workshops in class. Any in-class work that you do not finish will become homework that you will need to complete before the next class period.
There will be two in-class midterm exams and a cumulative final. These exams will be announced in advance, and you will know exactly what concepts will be covered on each exam.
My office hours are shown on my weekly schedule. I am also available by appointment. If you can’t stop by during my regular office hours, just ask me after class or by e-mail, and I’ll be happy to make an appointment that works for both of us.
Students who think they may need accommodations in this course because of the impact of a disability are encouraged to meet with me privately at the beginning of the semester. Students also should contact Melissa Wood, Title IX/504 Coordinator (mwood@hsc.edu, 434-223-6061) to verify their eligibility for reasonable accommodations. Early contact will help to avoid unnecessary inconvenience and delays.