Listed in the table below are reading assignments for each lecture session.
“Text” refers to the course textbook: 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 | 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’Hôspital’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 R_{n} (x), 14.3-p. 490 (top) and examples 1-5. |
38 | Final review | |
Final exam |