| ses # | TOPICS | readings |
|---|---|---|
| 1 | Velocity and Rates of Change | § 2.1-2.4. |
| 2 | Slope and Derivative Limits and Continuity | Notes C. |
| 3 | Differentiation Formulas: Products and Quotients | § 3.1-3.2. |
| 4 | Chain Rule and Implicit Differentiation | § 3.3, 3.5-3.6, and 8.1-8.2. |
| 5 | The Derivatives of Exponential and Logarithm Functions | § 8.3-8.4. |
| 6 | The Derivatives of Trigonometric Functions | § 9.1-9.2, and 9.4. |
| 7 | Review for Exam 1 | |
| Unit 1 Exam | ||
| 8 | Approximations Mean Value Theorem | Notes A, MVT. |
| 9 | Curve Sketching | § 4.1-4.2. |
| 10 | Max-Min Problems | § 4.3-4.4. |
| 11 | Related Rates | § 4.5. |
| 12 | Inequalities, Zeros, and Newton's Method | § 4.6 and 2.6, pp. 76-77. |
| Unit 2 Exam | ||
| 13 | Differentials and Indefinite Integrals | § 5.1-5.3. |
| 14 | Definite Integrals | § 6.1-6.4. |
| 15 | The Fundamental Theorem of Calculus | § 6.5-6.6. |
| 16 | Properties of Definite Integrals | Notes PI, Notes FT, and § 6.7. |
| 17 | Differential Equations and Separation of Variables | § 5.4 and 8.5. |
| 18 | Numerical Integration and Review of Unit 3 | § 10.9. |
| Unit 3 Exam | ||
| 19 | Areas between Curves, Volumes of Revolutions, and Slicing | § 7.1-7.3. |
| 20 | Volumes by Shells and Average Values | Notes AV, § 7.4. |
| 21 | Parametric Equations and Arc Length | § 17.1 and 7.5. |
| 22 | Surface Area and Polar Coordinate Graphs | § 7.6 and 16.1-16.3. |
| 23 | Area and Arc Length in Polar Coordinates | § 16.4-16.5. |
| Unit 4 Exam | ||
| 24 | Inverse Trigonometric Functions and Hyperbolic Functions | Notes G.7-G.9, § 9.5 and 9.7. |
| 25 | Integration by Inverse Substitution | § 10.4-10.5. |
| 26 | Integration by Partial Fractions | Notes F, § 10.6. |
| 27 | Integration by Parts | § 10.7-10.8. |
| Unit 5 Exam | ||
| 28 | Indeterminate Forms and L'Hospital's Rule | § 12.1-12.3. |
| 29 | Improper Integrals | Notes INT, § 12.4. |
| 30 | Infinite Series | § 13.1-13.3. |
| 31 | Power Series | § 14.1 and 14.4. |
| 32-33 | Final Review |
Table of Contents
Study Materials
Readings
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For each date, there is required reading from sections in the textbook and sections in the course reader. You are to read the material before the lecture.
Textbook
Simmons, George F. Calculus with Analytic Geometry. 2nd ed. New York, NY: McGraw-Hill, October 1, 1995. ISBN: 0070576424.
Readings in the textbook are listed by section numbers (e.g., § 2.1-2.4 means read sections 2.1 through 2.4.)
Course Reader
MIT students will be provided with a copy of the Course Reader: Jerison, D., and A. Mattuck. Calculus1. Readings in the Course Reader are listed as "Notes". (Not available to OCW users.)