Syllabus for Numerical Analysis

Course purpose

Numerical analysis in the 21st century is largely the art of (approximately) solving the problems of applied mathematics on a computer. In this course we will:

Learn the mathematics behind the fundamental algorithms of numerical computing By the fundamental algorithms of numerical computing, we mean the computational techniques to find approximate solutions to elementary problems of applied mathematics. These include solving equations and systems of equations, interpolation of data, evaluating derivatives and integrals, and solving differential equations. These problems are central to a wide variety of applications.
Learn the computational issues behind these algorithms Numerical analyisis has developed largely as a technique to solve applied problems on a computer. Thus, we will implement these algorithms on the computer using a procedural programming paradigm. Implementation introduces it's own complications. For example, given two mathematically equivalent expressions, one might be more numerically stable than the other. Even the representation of numbers on a computer introduces issues to study.
Learn to use a powerful numerical tool We will implement some of the basic algorithms we learn in Python as part of our learning experience. We will will also learn how to use several, high level Python libraries for numerical analysis.

Materials

Text: I will use the open source text, Tea Time Numerical Analysis to assign problems and organize the class.
Python: We will be programming a fair amount in Python this semester. I recommend that you download and install Anaconda, which is the easiest way to get a full scientific Python distribution with all the libraries we'll need this semester.
Numeric Talk: I've set up a discussion forum for this class. Note that participation is mandatory. We'll talk about it in class and there is an onsite topic explaining it's use and role in the class.

Grades

HW/Computer Labs: We will have homework in the form of computer labs throughout the semester. These will often be short 10-20 point assignments, though there will also be one or two more involved labs worth 40-50 points. All labs will be written in a literate style, meaning that they will contain exposition as well as working code.
Numeric Talk: Several individualized assigments will be assessed via our discussion forum.
Quizzes: There will be two quizzes during the semester worth about 40 points apiece. Likely dates for those quizzes are:
- Wednesday, February 21
- Wednesday, April 4
Exams: There will be two exams during the semester worth about 100 points apiece. Likely dates for the exams are:
- Wednesday, March 7
- Wednesday, April 18
Final exam: There is a comprehensive, final exam worth around 180 points scheduled for 11:30 AM on Monday, May 7.
Final grades: I will determine final grades using a scale not more stringent than the standard 90-80-70-60 scale. You will be apprised of your standing as the term progresses.
Late work: In general, I don't accept late work.

Your rights and responsibilities

It's worth understanding your rights and responsibilities as a student at UNCA. One of my responsibilities is to make sure you have the information that you need to do that. Since this is common to all classes, I've got that information on this legalese document.