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Single Variable Calculus >> Content Detail



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


Amazon logo 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.)


ses #TOPICSreadings
1Velocity and Rates of Change§ 2.1-2.4.
2Slope and Derivative

Limits and Continuity
Notes C.
3Differentiation Formulas: Products and Quotients§ 3.1-3.2.
4Chain Rule and Implicit Differentiation§ 3.3, 3.5-3.6, and 8.1-8.2.
5The Derivatives of Exponential and Logarithm Functions§ 8.3-8.4.
6The Derivatives of Trigonometric Functions§ 9.1-9.2, and 9.4.
7Review for Exam 1
Unit 1 Exam
8Approximations

Mean Value Theorem
Notes A, MVT.
9Curve Sketching§ 4.1-4.2.
10Max-Min Problems§ 4.3-4.4.
11Related Rates§ 4.5.
12Inequalities, Zeros, and Newton's Method§ 4.6 and 2.6, pp. 76-77.
Unit 2 Exam
13Differentials and Indefinite Integrals§ 5.1-5.3.
14Definite Integrals§ 6.1-6.4.
15The Fundamental Theorem of Calculus§ 6.5-6.6.
16Properties of Definite IntegralsNotes PI, Notes FT, and § 6.7.
17Differential Equations and Separation of Variables§ 5.4 and 8.5.
18Numerical Integration and Review of Unit 3§ 10.9.
Unit 3 Exam
19Areas between Curves, Volumes of Revolutions, and Slicing§ 7.1-7.3.
20Volumes by Shells and Average ValuesNotes AV, § 7.4.
21Parametric Equations and Arc Length§ 17.1 and 7.5.
22Surface Area and Polar Coordinate Graphs§ 7.6 and 16.1-16.3.
23Area and Arc Length in Polar Coordinates§ 16.4-16.5.
Unit 4 Exam
24Inverse Trigonometric Functions and Hyperbolic FunctionsNotes G.7-G.9, § 9.5 and 9.7.
25Integration by Inverse Substitution§ 10.4-10.5.
26Integration by Partial FractionsNotes F, § 10.6.
27Integration by Parts§ 10.7-10.8.
Unit 5 Exam
28Indeterminate Forms and L'Hospital's Rule§ 12.1-12.3.
29Improper IntegralsNotes INT, § 12.4.
30Infinite Series§ 13.1-13.3.
31Power Series§ 14.1 and 14.4.
32-33Final Review

 








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