Syllabus: 18.01A/2A Calculus - ESG Fall 2007Texts: Simmons: Calculus and Analytic Geometry, (same as regular curriculum).18.01A Supplementary Notes (sold by Copy Tech, Basement Bldg. 11).Instructor: Dennis V. Perepelitsa, (dvp)Class times: MWTR 10, 24-621 (ESG)For ESG to work properly you need to come to all the scheduled classes.Class website: http://web.mit.edu/dvp/18.01A/TA and tutorial hours: Stephanie Cheng (T7-9) Mary-Jane Tsang (M6-8)Schedule: This is just an outline. Detailed reading assignments will be given in theweekly problem sets.18.01A: Single Variable Calculus1. W Sep. 5 Linear and quadratic approximations.2. R Sep. 6 Higher order approximations, Taylor series, Mean-value theorem.3. M Sep. 10 Indeterminate f orms, L’Hospital’s rule, growth rat e of functions.4. T Sep. 11 Definite integral; summation notation, first fund. theorem, properties.W Sep. 12 Discussion, review and catch up.5. R Sep. 13 Second fundamental theorem, ln x as a n integral. Problem Set 1 due6. M Sep. 17 Geometric applications: volumes, area, arclength.7. T Sep. 18 More a pplications: work, average value.W Sep. 19 Discussion, review and catch up.R Sep. 20 Exam 1: covering 1-78. T Sep. 25 Integration: substitution, trigonometric integrals, completing the square.9. W Sep. 26 Integration: partial fractions.10. R Sep. 27 Integration by parts, numerical integration. Problem Set 2 due11. M Oct. 1 Improper integrals.12. T O ct. 2 Infinite series, harmonic series convergence tests.W Oct. 3 Discussion, review and catch up.R Oct. 4 Exam 2: covering 8-1213. W Oct. 10 Geometric series, p ower series, ratio test.14. R Oct. 11 Introduction to probability, discrete random variables. Problem Set 3 due15. M Oct. 15 Continuous random variables, standard deviation.16. T O ct. 16 Normal distributions.W Oct. 17 Discussion, review and catch up. Problem Set 4 dueR Oct. 18 Exam 3: covering 13-16(continued)18.02A (first half): Multivariable Calculus17. M Oct. 22 Vectors, dot product.18. T O ct. 23 Determinants, cross-product.19. W Oct. 24 Matrices, inverses.R Oct. 25 Discussion, review and catch up.20. M Oct. 29 Square matrices/systems, Cramer’s rule, planes.21. T O ct. 30 Parametric equations.W Oct. 31 Discussion, review and catch up.22. R Nov. 1 Vector derivatives: velocity, curvature (2 hours). Problem Set 5 dueM Nov. 5 Continuation.23. T Nov. 6 Continuation, Kepler’s second law.W Nov. 7 Discussion, review and catch up.R Nov. 8 Exam 4: covering 17-2324. T Nov. 13 Functions of several variables, partial derivatives.25. W Nov. 14 Tangent plane, level curves, contour surfaces.26. R Nov. 15 Tangent plane approximation, directional derivatives. Problem Set 6 due27. M Nov. 19 Chain rule.28. T Nov. 20 Max-min problems, least squares.W Nov. 21 No class29. M Nov. 26 Second derivative test, Lagrange multipliers.30. T Nov. 27 Non-indep endent variables, chain rule.W Nov. 28 Discussion, review and catch up.31. R Nov. 29 Double and iterated integrals. Problem Set 7 due32. M Dec. 3 Polar coordinates, double int egrals in polar coordinates.33. T Dec. 4 Change of variable.34. W Dec. 5 Applications of double integration.R Dec. 6 Discussion, review and catch up. Problem Set 8 due35. M Dec. 10 Topic to be decided.T Dec. 11 Discussion, review and catch up.W Dec. 12 Discussion, review and catch up.18.02A midterm: During finals week (Dec 17-21). Day and time
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