Math. 311, Sec. 200 (Honors) Spring, 2002Topics in Applied Mathematics I(linear algebra and vector calculus)Prerequisites: multivariable calculus (M. 251 or equivalent); differential equations(M. 308 or equivalent) at least concurrently.Classes: MWF 12:40–1:30, Blocker 156Instructor: S. A. Fulling620H Blocker [email protected] I am not in my office, you can leavea note in my mailbox (in the roomopposite the math department office,6thfloorofBlocker)orintheplasticpouch beside my office door.Our class’s home page on the World Wide Web ishttp://calclab.math.tamu.edu/~fulling/m311/s02/Tentative office hours: M 10:10–11:00, W 1:40–2:30, R 3:00–3:45Permanent office hours will be announced later.Required textbook:• S. A. Fulling, Linearity (World Scientific, 2000).Recommended books and resources:1. M. R. Spiegel, Vector Analysis (Schaum’s Outline Series).2. A large amount of material from previous semesters is available from the Web page.This includes old tests with solutions and the beginnings of a student-written solutionsmanual for the book. Also, there is a list of “learning objectives” for each week; thismay be helpful in keeping your focus in a class format where not all the material isdelivered in a traditional lecture.Other textbooks that students have found helpful:3. S. J. Leon, Linear Algebra with Applications.4. B. Kolman, Elementary Linear Algebra (in any of its many editions).5. H. M. Schey, Div, Grad, Curl, and All That.Grading system: Hour tests: 100 × 3 = 300Final exam: 200Homework: ≤ 130Reviewing and class participation: ≥ 70Total 700The “curve” will be at least as generous as the “standard” scale [i.e., 90% (= 630 pts) willguarantee an A, etc.].Page 2Schedule: Homework will usually be due on Mondays, as follows.Assignment Date Sections1 1/18 (Fri) 1.1–1.42 1/28 2.1–2.33 2/4 2.4–3.24 2/11 3.3–3.5Test on Chapters 1–3 on February 13 (Wed).5 2/18 4.16 2/25 4.2–4.47 3/4 4.5–5.18 3/18 5.2–5.4Test on Chapters 4 and 5 on March 20 (Wed) .9 3/25 5.5–6.110 4/3 (Wed) 6.2–6.411 4/10 (Wed) 7.1–7.412 4/17 (Wed) 7.5–7.6Test on Chapters 6 and 7 on April 19 (Fri) .13 4/26 (Fri) 8.1–8.2Final exam on Monday, May 6, 10:30–12:30Educational philosophy: The procedures in this class are designed to avoid wastinghonors students’ time on routine things and to facilitate some deeper learning. In part, thisclass is intended as a prototype of a “W course” (a future addition to the Core Curriculumin which students will get extra academic credit for writing experience). Lectures androutine homework assignments will be deemphasized. Instead, class participation, carefuland focused writing, constructive criticism of others’ writing, and cooperative study willbe encouraged. These activities are hard to grade by precise criteria; we will all be happierif you avoid a fixation on “points” and rest assured that the class participation and writtenwork grades will be generous overall. It is vital that you read the relevant sectionsof the textbook BEFORE coming to class, since the classes will usually be usedfor discussion, not lecture presentation. You should read the relevant textbooksections approximately a week before the “due date” listed above.In comparison with other Math. 311 sections, we will give more attention to theapplications of linear algebra to differential equations, ordinary and partial. As timepermits, there will be occasional brief special lectures on advanced topics, such as Gr¨obnerbases and quantum computing.We will be using the Internet and the World Wide Web for communications. Therefore,you will be provided with an account on the math department’s calclab computer system(without paying an extra lab fee). Although not strictly necessary, the capability to viewDVI files (the output of TEX) over the Web will be helpful; if you have a DOS/WindowsPC, I can provide you with software for that.Page 3Groups: You’ll be organized into groups of two or three. After each test the membershipof the groups may be adjusted. The groups will serve two main functions, both furtherexplained below: (1) reviewing homework papers, and (2) working problems in class.Homework: As always, you are expected to work as many of the homework problems asyou can, for the sake of learning. Indeed, you should try to finish the problems well beforethe “due date”, so as to benefit from class discussion and to study for tests.However, each week you will turn in only two homework problems (in some weeks,only one). Each of these is to bea carefully written, complete, formal solution, comparable to a worked-out example in a textbook.In this way your class will build up its own solutions manual. For tips on goodwriting, please start by reading the attached “Guidelines for Reviewers (and Authors!)”.Your paper should be self-contained, so you should either copy the problem from the book,or reformulate the problem briefly in your own words at the beginning of the solution (e.g.,“We are asked to find a vector that satisfies ... ”), or (in an on-line solution) give a linkto the proper “problem template” on the Web.Problems may be individually assigned, or you may be allowed to choose one. Inthe latter case, roughly speaking, you should choose the hardest problem that you areconfident you know how to do well.For the time being, the limited availability of technology and lack of a standard formatfor electronic presentations forces us to use paper as the primary medium of presentation.However, you can earn 2extrapointsper problem by making your work also accessiblevia the World Wide Web. Acceptable formats include:1. plain ASCII text, using “pidgin TEX” for mathematical symbols. (An explanation ofthis will come later.)2. HTML3. DVI (TEX output)4. PostScript or PDF (less satisfactory than the others because of file size)Optical scanning of a handwritten page is discouraged (worth only one extra point). Pro-prietary formats such as Microsoft Word .doc are not acceptable for Web display; outputthe file as HTML instead.You are strongly urged to keep a copy (or at least a rough draft) of your paper whenyou turn it in. Since your paper may be photocopied or put into a binder, please followthese technical guidelines: Use standard 8.5 ×11-inch paper, not too flimsy. Avoid yellowpaper, blue pens, and faint pencil. Don’t write too close to the edge of the page! (Leavemargins of about an inch.) Use one side of the