The numbers and letters in the Readings column correspond to sections of the textbook, George F. Simmons, Calculus with Analytic Geometry, 2nd ed., or sections of the course reader (D. Jerison and A. Mattuck, Calculus 1.) For instance, for Session 1, the assigned reading is Sections 2.1--2.4 of Simmons, and for Session 2, the assigned reading is Notes C in the 18.01 course notes. It is most useful if you read the material before the lecture. Even skimming the material for 10 or 15 minutes will allow you to get much more out of lecture. (Note: The course reader is currently not available to OCW users.)
| 1 |
Velocity and Rates of Change
|
Sections 2.1–2.4 |
| 2 |
Slope and Derivative
Limits and Continuity |
Notes C |
| 3 |
Differentiation Formulas: Products and Quotients |
Sections 3.1–3.2 |
| 4 |
Chain Rule and Implicit Differentiation |
Sections 3.3, 3.5 |
| 5 |
Higher Derivatives, Exponential and Log Functions |
Sections 3.6, 8.1–8.2 |
| 6 |
Calculus of the Exponential and Log Functions |
Sections 8.3–8.4 (through Example 1) |
| 7 |
Unit 1 Exam |
|
| 8 |
Trigonometric Functions |
Sections 9.1–9.2, 9.4 |
| 9 |
Approximations |
Notes A |
| 10 |
Curve Sketching |
Sections 4.1–4.2 |
| 11 |
Max-Min Problems |
Sections 4.3–4.4 |
| 12 |
Related Rates |
Section 4.5 |
| 13 |
Inequalities, Zeros, and Newton’s Method |
Sections 4.6, 2.6 (pp. 76–77) |
| 14 |
Unit 2 Exam |
|
| 15 |
Differentials and Indefinite Integrals |
Sections 5.1–5.3 |
| 16 |
Definite Integrals |
Sections 6.1–6.4 |
| 17 |
The Fundamental Theorem of Calculus |
Sections 6.5–6.6 |
| 18 |
Properties of Definite Integrals |
Section 6.7, Notes PI, Notes FT |
| 19 |
Differential Equations and Separation of Variables |
Sections 5.4, 8.5 |
| 20 |
Numerical Integration and Review of Unit 3 |
Section 10.9 |
| 21 |
Unit 3 Exam |
|
| 22 |
Areas between Curves, Volumes of Revolutions and Slicing |
Sections 7.1–7.3 |
| 23 |
Volumes by Shells and Average Values |
Section 7.4, Notes AV |
| 24 |
Parametric Equations and Arclength |
Sections 17.1, 7.5 |
| 25 |
Surface Area and Polar Coordinate Graphs |
Sections 7.6, 16.1–16.3 |
| 26 |
Area and Arclength in Polar Coordinates |
Sections 16.4–16.5 |
| 27 |
Unit 4 Exam |
|
| 28 |
Inverse Trig Functions and Hyperbolic Functions |
Sections 9.5, 9.7, Notes G.7–G.9 |
| 29 |
Integration by Direct Substitution |
Sections 10.1–10.3 |
| 30 |
Integration by Inverse Substitution |
Sections 10.4–10.5 |
| 31 |
Integration by Partial Fractions |
Section 10.6, Notes F |
| 32 |
Review of Unit 5 |
|
| 33 |
Unit 5 Exam |
|
| 34 |
Integration by Parts |
Sections 10.7–10.8 |
| 35 |
Indeterminate Forms and L'Hospital's Rule |
Sections 12.1–12.3 |
| 36 |
Improper Integrals |
Section 12.4, Notes INT |
| 37 |
Infinite Series |
Sections 13.1–13.3 |
| 38 |
Survey of 18.02 |
|
| 39 |
Final Review |
|
|