Supplementary Notes to Math 551-Numerical Methods, Spring 2013 Tom DeLillo, WSU Math Dept. May 9, 2013 1 Introductory remarks-Lecture 1/22/13 I will try to maintain here a record of my lectures, with varying levels of detail, as a supplement to our text [CM]. This is not meant to replace or completely reproduce the lectures. Please let me know if you spot any typos or errors. I will also post pdf files of older notes when necessary and type them up here in this latex file as frequently as I can manage. (Students who want to learn latex, can volunteer to help! I will send you the latex file as a sample to help you get started.) A good supplement to our text is the book [CVL]. It contains some more detailed derivations and some analysis (one theorem per chapter) of the many of the methods we will be discussing. Some of my notes here and in class will follow [CVL]. Another text to be aware of in [TB] which we use frequently in our Math 751, Numerical Linear Algebra course offered each Fall. I will adopt the idea there of introducing the singular value decomposition almost immediately, since it sheds so much light on the properties of matrices and linear systems Ax = b which will be an ongoing concern to us. A glance at the table of contents of our text [CM] will show you that this course will probably draw from every undergraduate math course that you have taken from calculus to differential equations to linear algebra. The point of this course is to develop efficient, accurate, and reliable methods for computing numerical solutions to many of the problems you have discussed in your core mathematics courses. You will need access to MATLAB and are advised to get the Student Edition of MATLAB . 1
Table 1: Approximate syllabus Week Tuesday lecture Thursday lecture 1 Sec. 1.7 difference quotient error 2 lin. alg. rev.: Sec. 2.9 norms . . . , matrix norms, Sec. 10.1 SVD 3 SVD cont. SVD, oper. counts 4 oper. counts, start Chap. 2 Chap. 2... 5 lutx, bslashtx, oper. counts det( A ) , A - 1 6 tridisolve sec. 3.1-poly. interp. 7 3.2,3.3 pw cubic, spline 3.4, 3.5 spline, periodic 8 finish Chap 3 4.1,4.2, Newton, Picard iter. 9 4.3,4.4 secant Exam I thru 4.4 10 11 12 13 14 15 I’ll include here some short, unpolished pieces of MATLAB code to il- lustrate the discussion. I’ll try to make these available on my web page eventually, but many of them are short enough that you can just type them in yourself. Numerical methods, along with theory and experiment, are fundamen- tal to modern applied science and engineering. For an incisive overview of the field of numerical analysis, read Nick Trefethen’s essay in the Appendix of [TB] on The Definition of Numerical Analysis or on his web site [LNT]— read it now and at the conclusion of this course. For those of you who consider yourselves to be pure mathematicians, you might take the attitude that you don’t fully understand a topic unless you know how to compute effectively!
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