Calculus II
Calculus II
Textbook : Thomas' Calculus; Early Transcendentals, 12 ed , Pearson,2010.
Course Content:
1. Applications of Definite Integrals. (7 Lectures)
6.1. Volumes Using Cross-Sections.
6.2. Volumes Using Cylindrical Shells.
6.3. Arc Length.
6.4. Area of Surfaces of Revolution.
Suggested Problems:
Page (371-374): 2, 4, 6, 10, 15, 18, 24, 25, 28, 32, 35, 40, 44, 47, 49, 52, 54.
Page (379-381): 2, 4, 6, 10, 13, 16, 20, 22, 24, 26, 28, 29, 32, 36, 38, 40, 46, 48.
Page (386-387): 1, 3, 6, 10, 12, 16, 18, 20, 24, 26, 30.
Page (391-393): 2, 4, 6, 8, 12, 16, 19, 21, 24.
2. Integrals and Transcendental Functions (5 Lectures)
7.1 The Logarithm Defined as an Integral.
7.2 Hyperbolic Functions.
Suggested Problems:
Page (425-427): 1, 3, 5, 8, 10, 13, 16, 17, 20, 23, 26, 29, 32, 36, 40, 43, 46,48, 50, 52, 53, 54, 55.
Page (441-444): 1, 4, 8, 10, 14, 17, 20, 23, 26, 29, 32, 35, 38, 42, 44, 47, 50, 53,56, 60, 62, 64, 66, 69, 72, 74, 79, 81, 82.
3. Techniques of Integration (10 Lectures)
8.1 Integration by Parts.
8.2 Trigonometric Integrals.
8.3 Trigonometric Substitution.
8.4 Integration of Rational Functions by Partial Functions.
8.7 Improper Integration.
Suggested Problems:
Page (459-461): 2, 5, 8, 11. 14, 17, 20, 23, 26, 29, 32, 35, 38, 40, 42, 43, 47, 50, 52, 54, 56, 58.
Page (466-467): 4, 7, 12, 18, 20, 23, 26, 28, 32, 34, 38, 42, 45, 48, 52, 56, 58, 62, 64, 68, 69, 71, 72.
Page (470-471): 1, 4, 7, 10, 13, 18, 21, 24, 27, 30, 34, 38, 41, 44, 47, 50, 52, 54, 56, 57.
Page (479-480): 1, 4, 7, 10, 13, 16, 20, 22, 26, 29, 32, 34, 38, 41, 43, 46, 49, 52, 54.
Page (505-506): 2, 5, 8, 11, 14, 17, 20, 24, 27, 30, 33, 36, 40, 42, 46, 50, 56, 59, 65,67, 70.
4. Infinite Sequences and Series (18 Lectures)
10.1 Sequences.
10.2 Infinite Series.
10.3 The Integral Test.
10.4 Comparison Test.
10.5 The Ratio and Root Test.
10.6 Alternating Series, Absolute and Conditional Convergence.
10.7 Power Series.
10.8 Taylor and Maclaurin Series.
10.9 Convergence of Taylor Series.
10.10 The Binomial Series and Application of Taylor Series.
Suggested Problems:
Page (559-562): 1, 3, 5, 8, 11, 14, 17, 20, 23, 28, 30, 33, 36, 39, 43, 46, 49, 54, 58, 60, 64, 67, 70, 73, 76, 79, 81, 84, 87, 90, 93, 96, 107, 112, 116.
Page (569-570): 1, 4, 6, 9, 12, 14, 16, 18, 21, 24, 28, 30, 31, 34, 36, 38, 40, 44, 46, 48, 52, 56, 59, 63, 66, 68, 70, 72, 75, 78.
Page (575-576): 1, 3, 6, 8, 10, 12, 13, 16, 21, 25, 30, 32, 35, 37, 40.
Page (580-581): 1, 4, 5, 6, 7, 8, 10, 13, 15, 17, 20, 23, 24, 25, 29, 32, 36, 39, 42, 45, 48, 49, 50.
Page (585-586): 1, 3, 5, 7, 9, 11, 14, 16, 18, 20, 21, 23, 25, 29, 32, 35, 38, 40, 44, 47, 50, 53, 56, 59.
Page (591-592): 1-6, 11, 13, 16, 18- 26, 31, 35, 37, 39, 41, 43, 46, 48, 58.
Page (600-602): 1- 8, 16- 22. 28, 32, 36, 38-40, 42, 46, 48, 52, 54.
Page (606-607): 1, 3, 5, 7, 9, 13, 16, 23, 27, 37.
Page (613-614): 1, 4, 6, 8, 9, 11, 13, 15, 18, 19, 22, 24, 27, 29, 32, 33.
Page (620-622): 1, 4, 8, 16, 20, 26, 28, 31, 35.
5. Parametric Equations and Polar Coordinates (6 Lectures)
11.3 Polar Coordinates.
11.4 Graphing in Polar Coordinates.
11.5 Areas and Lengths in Polar Coordinates.
Suggested Problems:
Page (648-649): 2, 4, 6, 8, 10, 11, 18, 20, 23, 25, 27, 31, 33, 35, 37, 42, 46, 49, 52, 56, 62, 66.
Page (652-653): 1, 5, 9, 12, 14, 17, 19, 21, 22, 25.
Page (656-657): 1-8, 9, 12, 15, 18, 20, 22, 24, 27, 29.