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