| 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'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 Rn (x), 14.3-p. 490 (top) and examples 1-5. |
| 38 | Final review | |
| Final exam | ||
Table of Contents
Study Materials
Readings
 When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more. |
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.