MATH 21b, FALL 2006:LINEAR ALGEBRA WITH DIFFERENTIAL EQUATIONSTopics: An introduction to linear algebra, including linear transformations,determinants, eigenvalues/eigenvectors, inner products, and vector spaces,with applications to linear (and some nonlinear) differential equations.Course Head: Noam D. Elkies, SC 335, 495-4625, [email protected](elkies@math is sufficient from most Harvard computers).Sections: This course is taught entirely in se ctions (taught by teaching fel-lows, TFs), with an additional weekly problem session (conducted by a courseassistant, CA).Grades: Your course grade will be determined according to the followingweights:• homework 20%,• two midterms 20% each,• final exam 40%.(The homework scores may be adjusted for disparities between the sections.)Midterm examinations:First midterm Monday, October 23, 7:45–9:15pm, classroom TBA.Second midterm Monday, November 20, 7:45–9:15pm, classroom TBA.No calculators will be allowed in the exams.(If any student feels that they may not be able to take the midterms at thesetimes for religious reasons they should contact the course head immediately.)Text: For most of the course we will closely follow the textbook Linear Al-gebra with applications by Otto Bretscher. (3rd edition, 2005; Prentice Hall,available at the Coop.) In addition there will be handouts for some of thematerial on differential equations.This is a fast-paced course which covers a lot of material. We will coverone section of the text per lecture; your TF will highlight the key conceptsintroduced in the text, but there will not be enough time to cover all thetopics. You will need to study the text to fill in the details.Reading the text is an integral part of the course. It is preferable to readthrough each section before it is covered in class and then again after it hasbeen covered. On the tests you will be responsible for all the material discussedin the text, including the handouts for sections 10.1–10.4, unless specificallyexcluded (some sections of the later chapters may have to be omitted).1Homework: Homework problems are an integral part of this course. It is im-possible to understand the material and do well on the exams without workingthrough the homework problems in a thoughtful manner. Don’t just crankthrough computations and write down answers — think about the problemsposed, your strategy, the meaning of the computations you perform, and theanswers you get. Nothing prevents you from trying a few more problems in agiven section if you feel it may do you some good. (We will usually suggesta few extra problems that show a previously introduced idea in a new light,or hint at later developments, but of course you are not limited to these.)More generally the only way to learn any topic in mathematics is to work outexamples for yourself.Many homework problems will look different from problems discussed in classand in the text. This is not an accident: We want you to think about thematerial and to learn to apply it in unfamiliar settings and interpret it indifferent ways. Only if you understand the material (as opposed to merelyknowing it) will you be able to go beyond the information you are given.Some students seem to subscribe to the “Ten Minute Rule”: If you can notsolve it in ten minutes, you cannot solve it at all. Nothing could be furtherfrom the truth: you will learn most from those problems which keep you busymore than ten minutes, whether you ultimately solve them or not.You are encouraged to discuss the course with other students, your CA and/oryour TF, and to use the Question Center in Science Center B10 (8:30–10:30PM). It is much easier to learn mathematics if you have other people who willhelp you test your understanding and surmount problems. It is fine to discusshomework problems with other students, but you should always write yourhomework solutions out yourself in your own words.Your homework is due at the start of class on the due date. Your course as-sistant will return your corrected homework to you at the end of the followingclass. He/she will also put homework solutions on reserve at Cabot Library,and/or on the course webpage, within 1 week of the due date. If you hand inyour homework late there will be a 25% penalty for the first week of delay (orany part of it), and an additional 25% for any longer delays. Homework willno longer be accepted five days after the beginning of reading period. In cal-culating the total grade for your homework your 4 worst individual homeworkgrades will be dropped.You are strongly encouraged to keep up to date with the homework, otherwiseyou will find that you do not get all you should out of the classes. It will alsobecome increasingly difficult to catch up again.2Technology: In some of the homework problems you w ill be asked not to useany technology (calculators or software packages). If no restriction is made,you may use the form of technology of your choice (for example, a TI-85calculator or one of the packages MATLAB or Maple). Make sure to haveaccess to some form of technology; a few calculators are on reserve at CabotLibrary. See also the section on “computers and computation” in the Prefaceof the textbook (pages xi-xii).No calculators will be allowed in the exams.Web Page: www.courses.harvard.edu/~math21bHomework Assignments: The following are the provisional homework as-signments up to the second midterm examination.Section Assignment extras Due Date— — — Monday, September 251.1 6,10,20,26,30 35,43 Wednesday, September 271.2 10,12,30,32,40 29,37 Friday, September 291.3 4,14,24,36,50 25,57 Monday, October 22.1 6,14,24,34,42 25-30,43,44 Wednesday, October 42.2 6,16b,18,26,34 29,32 Friday, October 6— HOLIDAY — Monday, October 92.3 12,20,30,38,40 45,49 Wednesday, October 112.4 14,28,38,56,76 86,87 Friday, October 133.1 2,20,32,34,44,54 49,50 Monday, October 163.2 18,24,32,38,46,50 39,42 Wednesday, October 183.3 22,30,32,38,44 53,56 Friday, October 203.4 28,30,44,56 64,78 Monday, October 23— MIDTERM — Monday, October 23,7:45 – 9:15 PM (Classroom TBA)5.1 6,26,28,36,38 13,14 Wednesday, October 255.2 4,14,32,34 Friday, October 275.3 32,34,38,40,66 64,67 Monday, October 305.4 10,20,22,30,36 38,39 Wednesday, November 16.2 4,16,20,30,40 44,50 Friday, November 37.1 8,20,24,36,52 7,54 Monday, November 67.2 10,12,16,22,32 28,36 Wednesday, November 8— HOLIDAY — Monday, November 107.3 12,20,26,36,44 47,48 Monday, November 137.4 12,16,30,32,54 38,58
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