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.
| Date | Section | Topic | Notes |
|---|---|---|---|
| 1/17 | 1.3 | Floating point numbers | |
| 1/19 | 1.2 | Intro to Python: The Babylonian algorithm | Week 1 |
| 1/21 | 1.3 | Overflow & underflow errors | |
| 1/24 | 1.1 | Calculus review: Taylor’s theorem | |
| 1/26 | 2.2 | The bisection method | Week 2 |
| 1/28 | 2.3 | Newton’s method | |
| 1/31 | 2.3 | Newton’s method - con’d | |
| 2/02 | 2.1 | Error analysis for iterative methods | Week 3 |
| 2/04 | 2.3 | Limitations of Newton’s method | |
| 2/07 | 2.4 | Secant method | |
| 2/09 | 2.6 | Fixed point iteration | Week 4 |
| 2/11 | 2.7 | Higher order fixed point iteration | |
| 2/14 | Linear algebra review: systems of linear equations | ||
| 2/16 | LU factorization | Week 5 | |
| 2/18 | LU factorization with pivots | ||
| 2/21 | Norms of vectors and matrices | ||
| 2/23 | Ill-conditioned systems | Week 6 | |
| 2/25 | Midterm 1 | ||
| 2/28 | 3.1 | Polynomial interpolation | |
| 3/02 | 3.1 | Lagrange & Newton polynomials | Week 7 |
| 3/04 | 3.1 | Divided differences | |
| 3/14 | 3.2 | High degree polynomial interpolation | |
| 3/16 | 3.3 | Hermite interpolation | Week 8 |
| 3/18 | 3.4 | Spline interpolation | |
| 3/21 | 4.1 | Newton-Cotes formulas for integration | |
| 3/23 | 4.2 | Composite Newton-Cotes formulas | Week 9 |
| 3/25 | 4.2 | Composite Newton-Cotes formulas - con’d | |
| 3/28 | 4.3 | Gaussian quadrature | |
| 3/30 | 4.5 | Improper integrals | Week 10 |
| 4/01 | 4.6 | Numerical differentiation | |
| 4/04 | 5.1 | Discrete least squares | |
| 4/06 | 5.1 | Discrete least squares - con’d | Week 11 |
| 4/08 | 5.2 | Continuous least squares | |
| 4/11 | 5.3 | Gram-Schmidt orthogonalization | |
| 4/13 | 5.3 | Orthogonal polynomials | Week 12 |
| 4/15 | Midterm 2 | ||
| 4/18 | Solving ODEs: Euler’s method | ||
| 4/20 | Euler’s method examples | Week 13 | |
| 4/22 | Error in Euler’s method | ||
| 4/25 | Runge-Kutta methods | ||
| 4/27 | Runge-Kutta methods - con’d | Week 14 | |
| 4/29 | Review |
Attendance in this class is expected, and you are responsible for any material that you miss. However, if you have a fever or are not feeling well, then please do not come to class that day. As long as you let me know the reason for your absence, I will do my best to help you stay caught up and make up any material that you missed. The key is to communicate with me when you aren’t able to attend class.
My office hours are shown above on my weekly schedule. I am also available by appointment. My office is Blake B-02, which is one of the Blake apartments. You can find it on this map. It looks like a student apartment, but I am using it as my office while the new science building is being built. During my regularly scheduled office hours the front door should be unlocked, so feel free to come in. I’ll be right upstairs. If you would prefer to schedule online office hours, let me know and I’ll be happy to set up a Zoom meeting.
The term grade will be based on the following.
| Component | Proportion |
|---|---|
| Workshops | 50% |
| Midterm 1 | 15% |
| Midterm 2 | 15% |
| Final Exam | 20% |
There will be two in-class midterm exams and a cumulative final.
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 GoogleColab 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, so you will need to bring a laptop to class. If you do not have a laptop that you can bring to class, please let me know so we can make other arrangements. Any in-class work that you do not finish will become homework that you will need to complete before the next class period.
In compliance with the Hampden-Sydney College policy and equal access laws, I am available to discuss appropriate academic accommodations that may be recommended for students with disabilities. Requests for academic accommodations are to be made at the beginning of the semester (except for unusual circumstances) so that appropriate arrangements can be made. Students are required to contact the Office of Academic Success in order to verify their eligibility for appropriate accommodations.
If we need to switch to an online virtual course at any point during the semester, the basic outline and schedule of topics for the course will remain the same. I will provide asynchronous video guided notes and workshops to help learn the material. I will also divide the class into smaller groups and schedule Zoom meetings during our regular class time (MWF 10:00 - 11:10am & R 2:30 - 3:40pm) where we can go over the material in more detail. I may also incorporate a short oral examination as part of one or more of the midterm or final exams. If you know that you will have trouble with Zoom from home, please let me know.