Math 172-01 Course page Fall 2003

Math172-01 Fall 2003 (08/25/03 - 12/10/03)
Calculus B

Course Information:

Instructor:	Shangbing Ai, MDH 320, Phone: (256) 824-2229, Email: ais@email.uah.edu, Webpage: www.math.uah.edu/ai
Class meetings:	MTWF 9:10-10:05 am, MDH 301
Office Hours:	MTWF 11:00-12:00 am or by appointment
Prerequities:	MA 171 with a grade of C or better.
Textbook:	Calculus, by James Stewart, Early Transcendentals, 4th Edition.
Grading:	Weekly Quizzes (15%), three in class tests (20%+20%+15%), the final (30%). The worst quiz will be dropped.
Test Dates:	Test 1 (Monday, 9/22), Test 2 (Friday, 10/17), Test 3 (Friday, 11/14), Final (12/10, 8:00 - 10:30 am).
Calculus Workshop:	UAH Calculus Resourses (MW: 1:00 - 2:30 pm, MDH 308)
Course Objectives:	Techniques of integration, applications of the integral, polar coordinates, sequences, series, and conic sections.

Main Topics and Schedule (tentative)

Chapter 6. Applications of Integration

Sec. 6.1 Areas between Curves (area between curves, area enclosed by two curves)
Exercises (pp. 438-439): 1, 2, 3, 4, 5, 7, 8, 9, 11, 15, 17, 24, 26, 29, 40
Quiz 1 (Quiz 1 will be on Friday, Aug. 29. The problems are from 6.1.)
Sec. 6.2 Volumes by Cross Sections (cross section method, the volumn formulas, Examples 1 - 8)
Exercises (pp. 448): 1, 3, 5, 7, 9, 11, 13, 15, 17, 31, 35, 46, 47, 48, 50
Quiz 2 ( quiz 2 is given on Fri., Sept. 5. The problems are from 6.2)
Sec. 6.3 Volumes by Cylindrical Shells (the method of cylindrical shells, Examples 1 - 4)
Exercises (pp. 454): 1, 2, 5, 6, 7, 8, 11, 14, 18, 20, 44
Sec. 6.4: Work (Examples 1 - 4)
Exercises (pp. 458): 3, 4, 5, 6, 11, 12, 16, 17 - 20
Sec. 6.5: Average Value of a Function (definition for average of a function over [a,b], the mean value theorem for integrals, the geometric interpretation of the average value of a function)
Exercise (pp. 462): 5, 7, 8, 14, 15, 20
Quiz 3 ( quiz 3 is given on Fri., Sept. 12. The problems are from 6.4 and 6.5)

Chapter 7. Techniquses of Integration

Sec. 7.1: Integration by Parts (Integration parts formulas)
Exercises (pp: 474): 1 -- 32, 37 -- 43, 48, 51, 53, 63
Sec. 7.2: Trigonometric Integrals (know how to calculate 4 typical k inds of integrals)
Exercises (pp. 481): 1 -- 17, 19 -- 31, 41 -- 46
Sec. 7.3: Trigonometric Substitution ( 3 typical integrals and 3 typical trig. substitutions)
Exercises (pp. 488): 1 - 29 (with odd numbers), 35
Sec. 7.4: Integrations of Rational Functions
Exercises (pp: 498): 13 -- 41 (with odd numbers), 43 -- 52, 58
Quiz 4 (Quiz 4 is given on Friday, Sept. 19. The problems are from 7.1 and 7.2)
Test 1 (Test 1 will be on Monday, Sept. 22. It covers the materials of Chapter 6 and 7.1 -- 7.2)
Test 1 (used in the summer)
Sec. 7.4: Integration for Rational Functions
Exercises (pp: 498): 1, 6, 10, 13, 21, 25, 27, 37, 41, 45, 50, 51, 52, 59, 60
Sec. 7.7: Approximate Integration (midpoint rule, trapezoidal rule, Simpson's rule, error estimates)
Exercises (pp. 520): 1, 5 -- 8, 21, 24, 32, 33
Sec. 7.8: Improper Integrals (two types of improper integrals, comparison tests)
Exercises (pp. 531) 5 -- 40, 49 -- 59, 74
Quiz 5 (Quiz 5 is given on Wen. Oct. 8. The problems are from 7.8)

Chapter 8. Furhter Applications of Integration

Sec. 8.1: Arc Length
Exercises (pp. 546): 3, 4, 7, 8, 10, 11, 23, 25
Sec. 8.3: Moments and Center of Mass (moments and centers of mass, Theorem of Pappus)
Exercises (pp. 563): 19, 20, 21, 23, 25, 27, 29, 30 -- 32, 36, 37, 39, 40

Chapter 9. Differential Equations

Sec. 9.1: Modeling with differential equaitons
Exercises (pp. 585): 1, 3, 5
Sec. 9.3: Separable Equations
Exercises (pp. 600): 1 -- 16, 29
Quiz 6 (Quiz 6 is given on Wen. Oct. 15. The problems are from 8.1 and 8.3)
Test 2 (time is changed) (Test 2 is given on Fri., Oct. 24. The problems are from Sections 7.3, 7.4, 7.7, 7.8, 8.1, 8.3, 9.1 and 9.3)
Test 2 (used in the summer. Our test may contain different type problems)

Chapter 10. Parametric Equaitons and Polar Coordinates

Sec. 10.1: Curves Defined by Parametric Equations
Exercises (pp. 645) 5, 6, 13, 14, 38
Sec. 10.2: Tangents and Areas
Exercises (pp. 653): 1, 3, 5, 7, 13, 15, 18, 41
Sec. 10.3: Arc Length and Surface Area
Exercises (pp. 659): 1, 3, 5, 7, 17, 29, 30
Sec. 10.4: Polar Coordinates
Exercises (pp. 668): 1 -- 14, 15 -- 26, 29, 31, 33, 37, 49, 41, 47, 56
Sec. 10.5: Areas and Lengths in Polar Coordinates
Exercises (pp. 674): 5, 6, 7, 8, 11, 14, 21, 22, 25, 27, 45, 49, 51
Test 2 (Retaken on Monday, Nov. 3) (The test will cover the same materials as well as those in Sections 10.1 -- 10.5)
Solution to Test 2

Chapter 11. Infinite Sequences and Series

Sec. 11.1: Sequences (definition of the limit, monotone convergence theorem)
Exercises (pp. 720): 1, 2, 12, 13, 14, 15--38, 45, 50, 54, 55, 56, 60, 62, 63, 66, 68, 69, 70
Hand-in Homework (pp. 702): 16, 20, 22, 28, 33, 37
Sec. 11.2: Infinit Series
Hand-in Homework (pp. 711): 12, 14, 19, 24, 28, 30, 34, 39
Sec. 11.3: Integral Test
Hand-in Homework (pp. 720): 1, 7, 17, 19, 20, 22, 30
Sec. 11.4: The Comparison Test
Hand-in Homework (pp. 725): 10, 11, 13, 14, 18, 27, 28, 29, 36, 37
Sec. 11.5: Altetnating Series
Hand-in Homework (pp. 730): 12, 13, 14, 16, 17, 24, 30, 32, 34
Sec. 11.6: Absolute convergence
Hand-in Homework (pp. 736): 7, 11, 12, 17, 18, 25, 26, 33
Test 3 (Tuesday, Nov. 25): The test will cover the materials in Sections 11.1 -- 11.7. It includes the concept check problems, true-false problems similar to those on pages 775 - 776. Most problems in the test are about to determine the convergence or divergence of given series. You have to know the convergence of geometric series and its sum, the convergence of telecoping series, the convergence of p-series. Those series are used to be compared with many other series in order to decide the convergence of those series. The following tests for positive series are required: the integral test, the comparison test, the limit comparison test, the ratio test, the root test. When using them, you may decide which one is better for the given series. The test for alternating series is also required. Also, the error (remainder) estimates from integral test and the alternating series test are required. I will try to make the test problems close to the homework problems I assigned.)
Sec. 11.8: Power Series
Hand-in Homework (due 12/2) (pp. 744): 5 -- 27 (with odd numbers), 33 (a).
Sec. 11.9: Representations of Functionss Power Series
Hand-in Homework (due 12/3) (pp. 749): 3, 7, 9, 11, 17, 19, 25
Sec. 11.10: Taylor Series and Maclaurin Series
Exercises (pp. 760): 3, 5, 9, 11, 13, 21, 23, 37, 38, 53, 55, 60
Final Test (Dec.10: 8:00-10:30am): The final test is comprehensive and contains similar materials covered in our tests 1, 2, 3 and the materials from Sections 11.8 and 11.9. Please look at those tests, the examples in the book, and homework in Sections 11.8 and 11.9. Please stop by office if you have any questions.
Solution to Test 1, Solution to Test 2, Solution to Test 3