Mathematics / Computer Science 340

Numerical Analysis (3)

Dr. Chris Caldwell

What? | | | Success | | | Grade | | | Text | | | Homework | | | Files |

Numerical analysis addresses two problems: "how do we find an approximate numerical solution to a given mathematics problem?" and "how do we bound the error in our approximations?" The type of problems that are most amenable to approximation are those involving (at least piecewise) continuous functions, so many of the the main tools of numerical methods come from Calculus. The problems we will look at involve approximating functions, their zeros and integrals; solutions to differential equations; and solutions to systems of equations. Here is the catalog description of the course:

Formulation of numerical problems for solution on a digital computer. Error analysis and control, nonlinear equations, differentiation, integration, systems of equations, differential equations, curve fitting, eigenvalue problems.

Though the title of our course is *numerical analysis*, not *numerical
methods*,
we have traditionally taught it as if it were a methods course. This
means the emphasis is more on the selection and applications of methods than
on the mathematical theory required to derive them. This is not a proof
course, but will test your memory of first year Calculus (251-252). We
will quickly review any required Linear Algebra (310) as it is needed.

The prerequisites also include CSCI 221. That is because we will program these methods, in Maple, to better understand their use. Why Maple? Because it will allow us to use the full power of an algebraic operating system and graphical interface, which still doing numerical approximations where appropriate. It is a bit awkward to program in, but we will learn as we go. (Our text is also strongly linked to the use of Maple.)

See also the department syllabus.

The text for this course is: *Numerical Methods * by
J. Douglas Faires and Richard Burdon, 3rd edition. Publisher-Thompson
and Brooks/Cole. ISBN: 0-534-40761-7. We will cover much
of chapters one through eight (or nine). This is a very standard text
(well, actually their Numerical Analysis is very standard and Numerical Methods
covers roughly the same material without the emphasis on deriving all of the
methods.)

The suggestions are the same for most any mathematics class:

- Come to class and do the homework
- Always seek to understand, not just memorize.
- Study with a friend. Make a new friend if necessary!
- Use other books as references. Get familiar with the library.
- Stay ahead of the class in the text.
- Come by my office. Do not hesitate because I look busy. I rarely just sit around, but you are my top priority.
- Do not fall behind.
- Do the homework (maybe extra even).

I want you to succeed and will gladly
help you, but you must start by working on the homework and reading the
text. Dr. L. Kolitsch, Mr. Eskew and many of the other
faculty member *might* also
be able to answer some questions (if they have time).

Homework will be assigned daily but sporadically collected. At the beginning of the following class period I may ask students to present parts of the homework as "board problems." I expect you to use your homework as notes. We will have three or four, fifty minute tests and a comprehensive final. The homework should give you an idea what the test question will look like. The course grade will probably be determined as follows:

Letter grades will then be assigned at my discretion.

Animations from John Matthew's Numerical Analysis Modules: secant method, false position, Newton's method,