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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, 1995. ISBN: 9780070576421.
"Notes" refers to the course reader: 18.01/18.01A Supplementary Notes, Exercises and Solutions; Jerison, D., and A. Mattuck. Calculus 1.
Readings table.
| SES # |
TOPICS |
READINGS |
| Differentiation |
| 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 |
Continuation and 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 |
Maximum-minimum 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
Definition of Log
|
Notes PI, p.2 [eqn. (7) and example]
Notes FT.
|
| 21 |
Areas Between Curves, Volumes by Slicing |
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. |
| Techniques of Integration |
| 25 |
Trigonometric Integrals |
Text 10.2 and 10.3. |
| 26 |
Exam 3 Covering Ses #18-24 |
|
| 27 |
Integration by Inverse Substitution; Completing the Square |
Text 10.4. |
| 28 |
Partial Fractions |
Text 10.6.
Notes F.
|
| 29 |
Integration by Parts; Reduction Formulas |
Text 10.7. |
| 30 |
Parametric Equations, Arclength, Surface Area |
Text 17.1, 7.5, and 7.6. |
| 31 |
Polar Coordinates; Area in Polar Coordinates |
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. |
| 32 |
Continuation and Review |
|
| 33 |
Exam 4 Covering Ses #25-32 |
|
| 34 |
Indeterminate Forms; L'Hospital's Rule |
Text 12.2 and 12.3. (examples 1-3, remark 1) |
| 35 |
Improper Integrals |
Text 12.4.
Notes INT.
|
| 36 |
Infinite Series
Convergence Tests
|
Text pp. 439-442 (top), pp. 451-3 (skip proof in example 3), and pp. 455-457 (top).
|
| 37 |
Taylor 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 |
|