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Single Variable Calculus >> Content Detail



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Readings

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Listed in the table below are reading assignments for each lecture session.

"Text" refers to the course textbook: Amazon logo 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 #TOPICSREADINGS
Derivatives
0Recitation: graphingNotes G, sections 1-4.
1Derivatives, slope, velocity, rate of changeText 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

3Derivatives of products, quotients, sine, cosineText 3.1, 3.2, and 3.4.
4

Chain rule

Higher derivatives

Text 3.3 and 3.6.
5Implicit 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.

7Hyperbolic functions and exam 1 reviewText 9.7 to p. 326.
8Exam 1 covering Ses #1-7
Applications of Differentiation
9Linear and quadratic approximationsNotes A
10Curve sketchingText 4.1 and 4.2.
11Max-min problemsText 4.3 and 4.4.
12Related ratesText 4.5.
13Newton's method and other applicationsText 4.6. (Text 4.7 is optional)
14

Mean value theorem

Inequalities

Text 2.6 to middle p. 77.

Notes MVT.

15Differentials, antiderivativesText 5.2 and 5.3.
16Differential equations, separation of variablesText 5.4 and 8.5.
17Exam 2 covering Ses #8-16
Integration
18Definite integrals

Text 6.3 though formula (4); skip proofs

Texts 6.4 and 6.5.

19First fundamental theorem of calculusText 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.

21Applications to logarithms and geometryText 7.1, 7.2, and 7.3.
22Volumes by disks, shellsText 7.4.
23Work, average value, probability

Text 7.7 to middle p. 247.

Notes AV.

24Numerical integrationText 10.9.
25Exam 3 review
Techniques of Integration
26Trigonometric integrals and substitutionText 10.2 and 10.3.
27Exam 3 covering Ses #18-24
28Integration by inverse substitution; completing the squareText 10.4.
29Partial fractions

Text 10.6.

Notes F.

30Integration by parts, reduction formulaeText 10.7.
31Parametric equations, arclength, surface areaText 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.
33Exam 4 covering Ses #26-32
34Indeterminate forms - L'Hôspital's ruleText 12.2 and 12.3. (examples 1-3, remark 1)
35Improper integrals

Text 12.4.

Notes INT.

36Infinite series and convergence testsText pp. 439-442 (top), pp. 451-3 (skip proof in example 3), and pp. 455-457 (top).
37Taylor's seriesText 14.4 through p. 498 (bottom); skip everything involving the remainder term Rn (x), 14.3-p. 490 (top) and examples 1-5.
38Final review
Final exam

 








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