Math 1b Calculus, Series, and Differential Equations

1. Math 1bCalculus, Series, and Differential Equations Harvard University Fall 2005 http://my.harvard.edu/course/math1b

2. Course Goals • Learn the techniques of calculus for analyzing functions • Learn how to model complex situations with mathematics • To read, write, and critique mathematical arguments

3. Course Head • Dr. Matthew Leingangleingang@math.harvard.edu(not leingang@fas)Science Center 323Office Hours: Tues., Weds., 1–3pm.

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9. Other teaching staff • Faculty members or Teaching Fellows in mathematics • Majority of instruction takes place in section, three hours/week • All sections cover same topics and have the same workload

10. Sections • Choose your section by computer: MWF9, 10, 11, 12, T10, 11:30

11. Sections • Choose your section by computer: MWF9, 10, 11, 12, T10, 11:30 With sufficient enrollment • To section from a UNIX prompt: ssh section@ulam.fas.harvard.edu • More information on flyer and at http://math.harvard.edu/sectioning/

12. 発問 Hatsumon Problems you will be able to solve after this course

13. Hatsumon – Volume • What is the volume of a Krispy Kreme Donut?

14. Hatsumon – Microbiology • A population of bacteria reproduces asexually. How can you predict the growth of the population over time?

15. Hatsumon – Fluid Dynamics • A hole is punched near the bottom of a tank • How long does it take for the tank to drain?

16. Hatsumon – Organismal Bio • Owls eat mice. • What will happen to the owl population when the mouse population is halved by starvation? • How long until we notice a change?

17. Hatsumon – Numerical Analysis • What is the 173rd digit of π? • The 1000th? • The millionth?

18. All of these problems (and many more) can be solved with Calculus! “Over three centuries of constant use have not completely dulled this incomparable instrument.”—Nicholas Bourbaki

19. Course Topics

20. Techniques and Applications of Integration • Basic Problem: find the area under a curve • Extends to many concepts besides area: • Volume • Work • Flux

21. Differential Equations • describe the way quantities change with respect to other quantities (for instance, time) • The laws of science are easily expressed by DE • F=ma (more difficult when F depends on position, or on time) • Newton’s Law of Cooling • Population Dynamics

22. Approximate many complicated functions by simple polynomials Solve differential equations Our digital world would be impossible without them—how does your calculator know sin(0.1) to 8 digits? Infinite Series

23. Course Expectations

24. Pre-class Reading Assignments • Reading assignments the night before class • Go to course web site to answer questions • Your teaching fellow will use this information to prepare a customized class

25. Homework • Assigned each day, due the next • No late homework! Please keep up. • Drop one week’s worth in computation of final grade

26. Exams • Technique Test: October 6 and 13 (second is optional; maximum counts) • Two midterm exams: Thursday, October 27 and December 1 • Final Exam (cumulative) tentatively scheduled for January 14

27. Breakdown of your course grade

28. Grading Scale • Could be adjusted for equity (“on the curve”)—up, but not down • Pluses and minuses will also be determined in final analysis

29. Texts • Single Variable Calculus—Concepts and Contexts by James Stewart, ISBN 0-534-41022-7 • Available for purchase at the Coop

30. Texts • Schaum’s Outlines: Precalculus by Fred Safier, ISBN 0-07-057261-5 • Optional • Cheap • Available for purchase at the Coop

31. Prerequisites

32. Logical Prerequisite: Calculus • Derivatives • Definition of the Integral • Fundamental Theorem of Calculus • (Integration by Substitution) • Math 1a or 8 on HMPT2

33. Logical Prerequisite: Precalculus • Functions • Graphs of “famous” functions and manipulating them • Trigonometry • Logarithms • 20 on HMPT1

34. For those who have taken AP Calculus BC • Math 1a and 1b together cover the Calculus BC syllabus • Math 1b does more than what’s on the BC, with different emphasis • You will still find lots to learn in Math 1b

35. For those who have taken AP Calculus AB • Some of your classmates will have seen some of this material before • We are committed to supporting all qualified students

36. Resources • Your section’s problem session • Math Question Center (Sunday–Thursday, 8–10pm, Loker Commons) • Your TF’s office hours • My office hours

37. Math Warm-Up Series • Brush-up on some precalculus topics (trig, logs, algebra) • Advice on study skills and course selection • http://www.math.harvard.edu/mwus/

38. Other Activities • Online Placement Exam http://math.placement.fas.harvard.edu/

39. Other Activities • Math Department advice is ongoing; see http://www.math.harvard.edu/sectioning

40. First Assignments • Read Section 5.1 and 5.2 of the text • Select a section by computer • answer questions online (to appear later this week)

41. Conclusion • I hope you take and enjoy Math 1b! • Web site reminder: http://my.harvard.edu/course/math1b • (Gratuitous baby shot)