Linear Methods of Applied Mathematics
Evans M. Harrell II and James V. Herod*
version of 9 January 2000
This is a WWW textbook written by Evans M. Harrell II and James V. Herod, both of Georgia Tech. In case it should move from this location someday, a link will be maintained at
In the past Georgia Tech was on the quarter system, and the text was used for two distinct 10-week courses. The "red syllabus" has been used for Math 4582, which emphasizes Fourier series, other orthogonal series, and the method of separation of variables. It is essentially Chapters I-XII, which were entirely written by Evans Harrell. (More about the red syllabus.)
The "green syllabus" has been used for Math 4348, which emphasizes integral operators and the method of Green functions; it follows Chapters I,II, and XII-XIX. These chapters originated with extensive classnotes by Jim Herod, with additions and Web translation provided by Evans Harrell. Note: If the emphasis in a course is to be integral equations and Green functions, the instructor may wish to begin with a lecture on the Model Problems of Chapter XIII to provide motivation, before Chapter I.
Two recommended 15-week course syllabuses are:
These syllabuses assume little review. If students are less well prepared than we expect ours to be, a semester-long course could be made by reviewing linear algebra or ordinary differential equations before the red or green syllabus. For the green syllabus one of the appendices could be used to review linear algebra. In our experience, this is not feasible in a 10-week course.
We regard the text as suitable for students who are quite comfortable with calculus and are mainly interested in problem solving. For that reason, we do not stress proofs, although we try to give careful statements of theorems and to discuss the technical assumptions. Also, we do not spend much time with material like methods to calculate the integrals arising in Fourier analysis, choosing instead to appeal to software to do some calculations. Currently, this is usually done with Mathematica, although some parts of the text are also available using Maple. It is not at all necessary to have previous experience with mathematical software, since the calculations in the text are self-explanatory. On the other hand, there are links to many more detailed calculations done in Mathematica notebooks, which will be useful for those who are familiar with Mathematica or who are learning it. Many Georgia Tech students have also found Matlab to be useful for calculations like those in this text.
Both we and our students have enjoyed this experiment in Web publishing. While it is still not clear what effect the World Wide Web will have on publishing, we believe that the effect will be very great. Experiments like this are valuable and necessary to learn the potential of the new forms of communication, and to help us reach this potential we welcome your commentary. In particular, if you would like to use the book at another university, we would be quite interested, and are ready to discuss the mechanics of doing this.
By the way, the Web implementation of most of this text, including all of the red syllabus, should work with any browser, including text-only browsers like lynx. We have made an effort to keep the text as widely accessible as possible, although access controls will probably be implemented in the future.
Some may hesitate to use a Web text because they like the convenience of a printed text which can be read without being at a computer or terminal, and for that reason it may be reassuring a nicely formatted hard copy is available. This can be obtained by purchasing disks from Evans Harrell or by downloading files from the Web (at this time files can be downloaded only for the red syllabus). The format of these files is Microsoft Word. (Mac 5.0 or Windows 6.0 on the disk, or rtf files on the Web. Microsoft's rtf format is a text-only format which should be properly interpreted and opened by Word.) Locally at Georgia Tech printed copies are available for photocopying.
This takes care of the only obvious disadvantage to using a Web text, but there are many distinct advantages:
Finally, a word about reading the book on the Web. Web browsers as of this date are not terribly uniform. The book has been prepared with a word processor and has been viewed with Netscape 3.0 and later. We went to some effort to make the interface somewhat universal, especially by inserting text alternatives to the graphics, for those with non-graphic Web browsers. Much of the book has been viewed with lynx, but not all. Please inform the authors of any problems you have viewing the book.
Good luck and happy browsing!
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