18.01A-18.02A Calculus Fall 2008A syllabus is given below; specific readings and exercises are on the problem sets.)Admission Requirements: (strictly monitored for both subjects)18.01A: 4 or 5 on the AB test or on the AB subscore of the BC test, or a comparablegrade on the A-level or IB exams, or in a comparable college calculus subject (show transcriptand syllabus), or a pass on Part I of the M.I.T. 18.01 AP test (given R/O week);18.02A: pass 18.01A, or AP credit for 18.01 through usual mechanismsText: Simmons: Calculus with Analytic Geometry, second edition (McGraw-Hill)18.01A Supplementary Notes (sold by Copy Tech, Basement Bldg. 11)Lectures: T-Th 1, F 2 26-100 18.01A A. Mattuck 2-241 3-4345 [email protected] John Bush 2-392 3-4387 [email protected]: Stevie Gallarelli 2-108 3-4977 [email protected]: M-W; change section on Grade Management (cf. “18.01A Website” below)Problem Sets: Given out Thursdays in lecture; available afterwards on 18.01A website;due on Thursdays, 12:45 in 2-106; returned in recitation following Monday with solutions;unclaimed sets put in horizontal file in 2-108 (left wall) after recitation Monday.18.01A Website: http://math.mit.edu/∼apm/1801A.htmlHas problem sets, practice exams, and corrections in pdf format, and link to GradeManagement website, where you can check your record (grades on exams and problem sets).Tutoring: 2-102 Mon-Tues-Wed-Thurs: 3-5 and 7:30-9:30 PM. (Starts second week.)Exams: 18.01A: One hour-exam; two-hour evening final (dates on syllabus).18.02A (first half): One hour-exam; two-hour midterm during finals week.Students who fail an hour-exam receive e-mail that evening; they can take a make-up examonce during certain hours the following week. (No make-ups for the two-hour exams.)Grading: A grade is given for 18.01A, and a temporary grade for 18.02A (first half). Eachgrade is based on a cumulative total score for that half-semester. For this, each problem setcounts 35-45, each hour-exam 100, each two-hour-exam 200.In addition to this, to pass 18.01A (i.e., be at level C- or better), you must pass the twoexams and make a reasonable effort on three of the four problem sets. Students who do notpass 18.01A Exam 1 (or its makeup) must transfer to 18.01.Exceptions to these for borderline fails will be considered on a case-by-case basis.18.02A second half: Offered twice: IAP (Jan.), and the first half of the spring semester.The final grade for 18.02A will be the average of the grades for each half. (Note that if youfinish 18.02A in the spring, a letter grade (ABC/NR) will appear on your transcript.)Questions: Academic problems and concerns: Recitation TeacherProblems with exams or homework (away games, illness, emergencies): Administrator18.01A SYLLABUSW Sept. 3 0. Rec.: Linear and quadratic approximationsTh Sept. 4 1. Higher order approximations; Taylor seriesF Sept. 5 2. Indeterminate forms 0/0, ∞/∞; L’Hospital’s ruleTu Sept. 9 3. Definite integral; First fundamental theorem; applicationsTh Sept. 11 4. Second fund. theorem; ln x Prob. Set 1 dueF Sept. 12 5. Geometric applications: volumes, arc length, surface areaTu Sept. 16 6. Other applications: work, average valueTh Sept. 18 7. Integration by direct and inverse substitution; trig. integrals Prob. Set 2 dueF Sept. 19 8. Partial fractions decompositionTu Sept. 23 9. (Holiday Mon.) Integration by partsTh Sept. 25 Exam 1, covering Lectures 0-9F Sept. 26 10. Improper integralsTu Sept. 30 11. Infinite series: integral test, convergence ofP1/nkTh Oct. 2 12. Geometric series; ratio test Prob. Set 3 dueF Oct. 3 13. Power series, radius of convergence; short-cuts to expansionsTu Oct. 7 14. Holiday Mon. Intro. to probability: discrete random variables, PoissonTh Oct. 9 15. Continuous random vars; standard deviation Prob. Set 4 dueF Oct. 10 16. Normal distribution; applicationsTu Oct. 14 17. Continuation of probabilityTh Oct. 16 18. Review. Two-hour final in evening, covering 0-18 (No class Fri.)18.02A SYLLABUS: FIRST HALFVectorsM Oct. 20 19. Recit: Intro. to vectorsTu Oct. 21 20. Scalar (dot) productTh Oct. 23 21. Determinants; cross productF Oct. 25 22. Matrices; inverse matricesTu Oct. 28 23. Theorems about square systems; Cramer’s rule, eqns. of planesTh Oct. 30 24. Parametric eqns: eqns. of lines and curves; cycloid Prob. Set 5 dueF Oct. 31 25. Vector derivativesTu Nov. 4 26. Applications; Kepler’s second lawTh Nov. 6 27. Exam 1, covering Lectures 19-26Partial DifferentiationF Nov. 7 28. Intro to fcns. of sev. vars.; graphs, level curves, partial derivs, tangent plane approximationTh Nov. 13 29. Holiday Mon., Tues. 2D-Directional derivative, gradient.F Nov. 14 30. Applications in 3D - contour surfaces, tangent planes.Tu Nov. 18 31. Max-min problems; method of least squaresTh Nov. 20 32. Second derivative criterion. Lagrange multipliers. Prob. Set 6 dueF Nov. 21 33. Chain rule and applications.Tu Nov. 25 34. Chain rule for non-indept. variablesDouble IntegrationTu Dec. 2 35. Holiday Th., Fri. Double and iterated integrals in rect. coord’sTh Dec. 4 36. Polar coordinates. Double integrals in polar coord’s, applications Prob. Set 7 dueF Dec. 5 37. Change of variable in double integrals; jacobiansTu Dec. 9 38. Continuation and reviewcovering 18.02A first half
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