Author: Douglas Wilhelm Harder

For every topic, there is a YouTube video and the corresponding slides. The YouTube lectures contain chapters for easier navigation, especially for some of the larger lectures. The videos are on a per-topic basis, and each week is no more than 3 × 50 minutes or two-and-a-half hours of video (see below for a discussion on lecture length). Also included are often links to:

• An in-a-nutshell document that simply summarizes the algorithm in question without covering details.
• A document of questions together with answers.
• Wiki: Links to various web sites, usually Wikipedia.
• Implementations of the algorithms in C++ hosted by replit.com.
• Implementations of the algorithms in Matlab.

The course is broken into twelve weeks, and unfortunately, some week breaks do interrupt a particular topic; however, if you are learning this material on your own, this really should not pose an issue. At the end of each week, an assignment is posted without solutions.

Additional reading (optional—not on the examination)

These are documents that go into greater detail in some cases than the presentations; however, the presentations above contain most of the information needed for the course. Please note, these documents are from a previous offering, and thus there are differences in the emphasis of the material, and there are alternative means of describing some of the algorithms in question. Also, the numbering does not necessarily match, and where explanations differ, this author believes that the presentations above give a much better description.

• 1. Course introduction
• 2. Floating-point representations of real numbers
• 3. Tools for approximating solutions to algebraic and analytic problems
• 4. Categories of numerical problems and error
• 5. Problems of evaluating expressions
• 5.1 Evaluating polynomials, interpolating polynomials, estimating derivatives and estimating integrals
• 5.2 Least-squares approximations to problems in Section 5.1
• 6. Root-finding
• 7. Problems with ordinary-differential equations
• 7.1 First-order initial-value problems
• 7.2 Boundary-value problems
• 8. Problems with partial-differential equations
• 8.1 Laplace's equation
• 9.1 Golden-ratio search

You can look at slides and videos for Laplace's equation, the heat-conduction/diffusion equation and the wave equation at NE 217 and view the 2nd, 4th and 5th laboratories.

A comment on lecture length

Nominally, a week contains three 50-minute lectures, or 150 minutes, together with discussion, etc. For a twelve-week course, this totals to thirty (30) cumulative hours of lectures. However, in-class lectures also includes discussion and questions, which are not possible in an on-line format, so it is unfair to simply pack 150 minutes of lecture material each week. Instead, these lectures contain a total of 1553 minutes or just shy of twenty-six (26) hours of lecture material, with each week containing between two hours and two hours and thirty minutes of lecture material per week with an average just shy of one hundred and thirty (130) minutes per week.