Readings

Listed in the table below are reading assignments for each lecture session.

"Text" refers to the course textbook: Buy at Amazon Simmons, George F. Calculus with Analytic Geometry. 2nd ed. New York, NY: McGraw-Hill, October 1, 1996. ISBN: 9780070576421.

"Notes" refers to the course reader: 18.01/18.01A Supplementary Notes, Exercises and Solutions; Jerison, D., and A. Mattuck. Calculus 1.

SES # TOPICS READINGS
Derivatives
0 Recitation: graphing Notes G, sections 1-4.
1 Derivatives, slope, velocity, rate of change Text 2.1-2.4.
2

Limits, continuity

Trigonometric limits

Text: 2.5 (bottom pp. 70-73; concentrate on examples, skip the ε - δ definition)

Text 2.6 to p. 75; learn definition (1) and proof "differentiable => continuous" at the end.

Notes C

3 Derivatives of products, quotients, sine, cosine Text 3.1, 3.2, and 3.4.
4

Chain rule

Higher derivatives

Text 3.3 and 3.6.
5 Implicit differentiation, inverses

Text 3.5.

Notes G, sections 5

Text 9.5 (bottom pp. 913 - 915)

6

Exponential and log

Logarithmic differentiation; hyperbolic functions

Notes X (Text 8.2 has some of this)

Text 8.3 to middle p. 267

Text 8.4 to top p. 271.

7 Hyperbolic functions and exam 1 review Text 9.7 to p. 326.
8 Exam 1 covering Ses #1-7  
Applications of Differentiation
9 Linear and quadratic approximations Notes A
10 Curve sketching Text 4.1 and 4.2.
11 Max-min problems Text 4.3 and 4.4.
12 Related rates Text 4.5.
13 Newton's method and other applications Text 4.6. (Text 4.7 is optional)
14

Mean value theorem

Inequalities

Text 2.6 to middle p. 77.

Notes MVT.

15 Differentials, antiderivatives Text 5.2 and 5.3.
16 Differential equations, separation of variables Text 5.4 and 8.5.
17 Exam 2 covering Ses #8-16  
Integration
18 Definite integrals

Text 6.3 though formula (4); skip proofs

Texts 6.4 and 6.5.

19 First fundamental theorem of calculus Text 6.6, 6.7 to top p. 215 (skip the proof pp. 207-8, which will be discussed in Ses #20.)
20

Second fundamental theorem

Notes PI, p. 2 [eqn. (7) and example]

Notes FT.

21 Applications to logarithms and geometry Text 7.1, 7.2, and 7.3.
22 Volumes by disks, shells Text 7.4.
23 Work, average value, probability

Text 7.7 to middle p. 247.

Notes AV.

24 Numerical integration Text 10.9.
25 Exam 3 review  
Techniques of Integration
26 Trigonometric integrals and substitution Text 10.2 and 10.3.
27 Exam 3 covering Ses #18-24  
28 Integration by inverse substitution; completing the square Text 10.4.
29 Partial fractions

Text 10.6.

Notes F.

30 Integration by parts, reduction formulae Text 10.7.
31 Parametric equations, arclength, surface area Text 17.1, 7.5, and 7.6.
32

Polar coordinates; area in polar coordinates

Exam 4 review

Text 16.1, (Text 16.2 lightly, for the pictures), Text 16.3 to top p. 570, and Text 16.5 to middle p. 581.
33 Exam 4 covering Ses #26-32  
34 Indeterminate forms - L'H├┤spital's rule Text 12.2 and 12.3. (examples 1-3, remark 1)
35 Improper integrals

Text 12.4.

Notes INT.

36 Infinite series and convergence tests Text pp. 439-442 (top), pp. 451-3 (skip proof in example 3), and pp. 455-457 (top).
37 Taylor's series Text 14.4 through p. 498 (bottom); skip everything involving the remainder term Rn (x), 14.3-p. 490 (top) and examples 1-5.
38 Final review  
  Final exam