18.01 - Syllabus (Fall 2017)

 Date (click on date for lecture notes) Reading (recommended before class) Topics First recitation Notes G: sections 1 - 4 graphing 9-7-17 Text: 2.1 - 2.4 derivatives, slope, velocity, rate of change 9-8-17 Notes C; Text: 2.5 (bottom pp. 70-73; concentrate on examples, skip the ε - δ definition); Text: 2.6 to pg. 75; learn definition (1) and the proof of "differentiable => continuous" at the end limits, continuity, trigonometric limits 9-12-17 Text: 3.1, 3.2, and 3.4 derivatives of products, quotients, sine, cosine 9-14-17 Text: 3.3 and 3.6 chain rule, higher derivatives 9-15-17 Text: 3.5; Notes G: section 5; Text: 9.5 (bottom pp. 313 - 315) implicit differentiation, inverses 9-19-17 Notes X (Text 8.2 has some of this); Text: 8.3 to middle of pg. 267, Text: 8.4 to top of pg. 271; Text: 9.7 to pg. 326 exponential and log, logarithmic differentiation, hyperbolic functions 9-21-17 Notes A linear and quadratic approximations 9-22-17 Text: 4.1 and 4.2 curve sketching 9-26-17 Text: 4.3 and 4.4 min-max problems 9-28-17 Midterm # 1 9-29-17 Holiday Holiday 10-3-17 Text: 4.5 related rates 10-5-17 Text: 4.6 (4.7 is optional) Newton's method and other applications 10-6-17 Text: 2.6 to middle of pg. 77; Notes: MVT mean value theorem, inequalities 10-10-17 Holiday Holiday 10-12-17 Text: 5.2 and 5.3 differentials, antiderivatives 10-13-17 Text: 5.4 and 5.8 differential equations, separation of variables 10-17-17 Text: 6.3 though formula (4); skip proofs; Text: 6.4 and 6.5 definite integrals 10-19-17 Review for Midterm #2 10-20-17 Midterm #2 10-24-17 Text: 6.6, 6.7 to top of pg. 215 (skip the proof pp. 207-8, which will be discussed in Ses #20) first fundamental theorem of calculus 10-26-17 Notes: PI, pg. 2 [eqn. (7) and example]; Notes: FT second fundamental theorem of calculus 10-27-17 Text: 7.1, 7.2, and 7.3 applications to logarithms and geometry 10-31-17 Text 7.4 volumes by disks, shells 11-2-17 Text: 7.7 to middle of pg. 247; Notes: AV work, average value, probability 11-3-17 Text: 10.9 numerical integration 11-7-17 Text: 10.2 and 10.3 trigonometric integrals and substitutions 11-9-17 Text: 10.4 and 10.5 integration by inverse substitution, completing the square 11-10-17 Holiday Holiday 11-14-17 Review for Midterm # 3 11-16-17 Midterm # 3 11-17-17 Text: 10.6; Notes: F partial fractions 11-21-17 Text: 10.7 integration by parts, reduction formulas 11-23-17 Holiday Holiday 11-24-17 Holiday Holiday 11-28-17 Text: 17.1, 7.5, and 7.6 parametric equations, arclength, surface area 11-30-17 Text: 16.1; (Text: 16.2 lightly, for the pictures), Text: 16.3 to top of pg. 570; Text: 16.5 to middle of pg. 581 polar coordinates, area in polar coordinates 12-1-17 Text: 12.2 and 12.3 (examples 1-3, remark 1) indeterminate forms - L'Hôspital's rule 12-5-17 Text: 12.4; Notes: INT improper integrals 12-7-17 Text: pp. 439-442 (top), pp. 451-453 (skip proof in example 3), and pp. 455-457 (top) infinite series and convergence tests 12-8-17 Midterm #4 12-12-17 Text: 14.4 through p. 498 (bottom); skip everything involving the remainder term Rn (x); Text: 14.3-pg. 490 (top) and examples 1-5 Taylor's series