KUWAIT UNIVERSITY Department of Mathematics MATH 102 Calculus II Spring Semester 2013 College of Science Prerequisite: MATH 101 Calculus I Textbook: J. Stewart, Calculus, Seventh Edition, Metric Version, Brooks/Cole, Cengage Learning, 2012 (ISBN-10: 0-538-49884-6, ISBN-13: 978-0-538-49884-5) Contents: 6. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions 6.1. Inverse Functions...........................................................384 6.2*. The Natural Logarithm Function (excluding Example 1 (b)).................................................. 421 6.3*. The Natural Exponential Function........................................ 429 6.4*. General Logarithmic and Exponential Functions (excluding the subsection The Number e as a Limit )...................... 437 6.6. Inverse Trigonometric Functions........................................... 453 6.7. Hyperbolic Functions (excluding the subsection Inverse Hyperbolic Functions )...................462 6.8. Indeterminate Forms and l Hospital s Rule (excluding Cauchy s Mean Value Theorem and the proof of l Hospital s Rule).................... 469 7. Techniques of Integration 7.1. Integration by Parts........................................................488 7.2. Trigonometric Integrals.....................................................495 7.3. Trigonometric Substitution (excluding Example 5 Solution 2)........................................... 502 7.4. Integration of Rational Functions by Partial Fractions...................... 508 The Weierstrass Substitution (Exercises 59 63)............................. 517 7.5. Strategy for Integration.................................................... 518 7.8. Improper Integrals (excluding the subsection A Comparison Test for Improper Integrals ).....743 8. Further Applications of Integration 8.1. Arc Length (excluding Example 3 (b)).................................................. 562 8.2. Area of a Surface of Revolution.............................................569 8.3. Applications to Physics and Engineering (excluding the subsection Hydrostatic Pressure and Force, and the Theorem of Pappus)............. 576 1
10. Parametric Equations and Polar Coordinates 10.1. Curves Defined by Parametric Equations.................................. 660 10.2. Calculus with Parametric Curves.......................................... 669 10.3. Polar Coordinates......................................................... 678 10.4. Areas and Lengths in Polar Coordinates...................................689 Recommended exercises: Section Supervised Unsupervised 6.1 10, 19, 27, 28, 36, 41, 46, 50 2, 3, 6, 11, 20, 32 6.2* 12, 32, 39, 50, 64, 71, 81 3, 5, 24, 51, 63, 70, 72, 86, 89 6.3* 7, 16, 27, 54 1, 4, 5, 11, 17, 30, 36, 43, 55, 60, 70, 85, 91, 102, 107 6.4* 12, 54, 66 1, 2, 6, 9, 18, 23, 25, 30, 42, 47, 49, 65 6.6 9, 13, 18, 32, 37 1, 3, 6, 7, 11, 21, 23, 34, 38, 44, 46, 52, 61, 64, 67, 74, 77, 80 6.7 3, 15, 17, 20, 35, 54, 56 4, 7, 9, 19, 23, 34, 36, 55, 57, 61, 63, 64 6.8 1, 25, 38, 45, 50 12, 21, 28, 52, 63, 65, 66 7.1 10, 30, 48, 51 2, 8, 17, 26, 33, 38, 47, 54, 68, 70, 72 7.2 3, 15, 26, 29, 40, 48, 67 10, 19, 20, 38, 47, 50, 55, 69 7.3 3, 15, 24, 30, 31 1, 5, 10, 26, 32, 33 7.4 5, 122, 37, 47, 54, 58 1, 2, 7, 9, 30, 31, 39, 43, 45, 59, 61, 63, 72 7.5 4, 22, 31, 45, 50, 63, 72, 80 1, 9, 19, 41, 58, 70, 71, 78, 83 7.8 1, 13, 35, 58, 77 7, 8, 14, 25, 26, 40, 49, 55, 59 8.1 1, 32 2, 13, 18, 19 8.2 2, 11, 16 1, 9 8.3 24, 27, 31 22, 26 10.1 4, 12, 21, 24, 28 1, 9, 15, 17, 22, 26 10.2 5, 10, 13, 20, 33, 39, 44, 53, 58 7, 16, 29, 37, 42, 45, 62, 65 10.3 20, 37, 39, 54 4, 6, 10, 12, 17, 19, 25, 42, 44, 56, 62, 65, 66 10.4 8, 21, 28, 31 2, 3, 7, 11, 19, 24, 33, 34, 35, 38, 41, 45 2
Schedule: Week Dates Sections 1 27 Jan 31 Jan 6.1, 6.2* 2 3 Feb 7 Feb 6.2*, 6.3* 3 10 Feb 14 Feb 6.4*, 6.6 4 17 Feb 21 Feb 6.7, 6.8 5 24 Feb 28 Feb (National and Liberation days) 6 3 Mar 7 Mar 7.1 7 10 Mar 14 Mar 7.2 8 17 Mar 21 Mar 7.3 9 24 Mar 28 Mar 7.4 10 31 Mar 4 Apr Weierstrass substitution, 7.5, 7.8 11 7 Apr 11 Apr 7.8, 8.1 12 14 Apr 18 Apr 8.2, 8.3 13 21 Apr 25 Apr 10.1, 10.2 14 28 Apr 2 May 10.3, 10.4 15 5 May 8 May reserve Assessment: The course will be graded based on quizzes (10%), two in-term tests (25% each), and, a comprehensive final examination (40%). The first in-term test will be held on Saturday 9 March at 09:00, last 90 minutes, and concern the material from Chapter 6 of the textbook. The second in-term test will be held on Saturday 27 April at 09:00, last 90 minutes, and concentrate on the material from Chapter 7 of the textbook. The final examination will be on Saturday 11 May 2013 at 17:00, last 120 minutes, and encompass the entire content of the course. Note: Students are expected to know how to prove the following: the laws of the natural logarithm function ( 3 page 422 ), the laws of the natural exponential function ( 7 page 431 ), and the derivatives of the inverse trigonometric functions ( 11 page 457 ). 3
Examination and test regulations: Calculators and electronic communication devices, such as mobile telephones or pagers, are strictly prohibited from rooms in which an examination or test is taking place. Students are not permitted to leave the test/examination room within the first 30 minutes, and students are not permitted to enter the test/examination room after the first 30 minutes. Supervisory staff will not answer queries regarding a question posed or its method of solution part of the objective is to assess the student s understanding and ability to solve the question. A student who misses a test or examination due to circumstances beyond their control may be permitted to sit a so-called incomplete test or examination. To be eligible for the incomplete, students must provide their instructor with documentary evidence, such as a medical certificate, justifying their absence from the normal test or examination at least one full working day beforehand. Permission to sit the incomplete is at the discretion of their instructor. Getting help: All instructors of this course are available to help students with any queries related to the course during designated office hours. If none of these is suitable, students are encouraged to make an appointment with their instructor at an alternative mutually agreeable time. Final notice: All of the above is subject to change. Dr. Brian H. Gilding, 28 January 2013 4
Recommended exercises from the 6th Edition of the textbook: Section Supervised Unsupervised 7.1 10, 19, 27, 28, 34, 39, 42, 46 2, 3, 5, 11, 20, 32 7.2* 10, 28, 30, 37, 48, 60, 69, 79 2, 7, 22, 49, 62, 68, 70, 84, 87 7.3* 7, 16, 27, 50 1, 4, 6, 11, 17, 30, 36, 39, 51, 56, 66, 77, 83, 92, 97 7.4* 12, 54, 66 1, 2, 6, 9, 18, 23, 25, 29, 42, 47, 49, 65 7.6 9, 13, 18, 32, 37 1, 3, 6, 7, 11, 21, 23, 34, 38, 44, 46, 52, 60, 64, 67, 74, 77, 80 7.7 3, 15, 17, 20, 35, 54, 56 4, 7, 9, 19, 23, 31, 34, 36, 53, 55, 59, 61, 62 7.8 1, 21, 36, 42, 48, 52, 93 8, 11, 13, 26, 50, 55, 63, 64, 94 8.1 10, 26, 44, 47 2, 8, 17, 22, 29, 34, 45, 50, 64, 66, 68 8.2 3, 15, 26, 29, 42, 48, 67 10, 19, 20, 40, 47, 50, 55, 69 8.3 3, 15, 24, 30, 31 1, 5, 10, 26, 32, 33 8.4 5, 18, 37, 47, 52, 56 1, 4, 8, 12, 30, 31, 39, 43, 45, 57, 59, 61, 70 8.5 4, 22, 31, 45, 50, 61, 70, 78 2, 9, 19, 41, 46, 58, 68, 69, 81 8.8 1, 13, 35, 58, 77 7, 8, 14, 25, 26, 40, 49, 55, 59 9.1 6, 34 2, 13, 18, 19 9.2 3, 11, 16 1, 9 9.3 24, 27, 31 22, 25 11.1 4, 12, 21, 24, 28 1, 9, 16, 17, 22, 26 11.2 5, 10, 14, 20, 33, 39, 44, 53, 58 8, 16, 29, 38, 42, 47, 60, 65 11.3 20, 34, 39, 56 4, 6, 9, 12, 17, 18, 25, 44, 46, 58, 64, 69, 70 11.4 8, 21, 28, 31 2, 4, 7, 11, 17, 24, 33, 34, 35, 38, 41, 45 5
Recommended exercises from the 5th Edition of the textbook: Section Supervised Unsupervised 7.1 10, 21, 29, 30, 36, 41, 44, 48 2, 3, 5, 12, 22, 33 7.2* 10, 24, 28, 33, 44, 56, 67, 75 2, 7, 20, 45, 58, 64, 66, 80, 83 7.3* 9, 18, 27, 46 1, 4, 6, 12, 19, 30, 34, 37, 47, 50, 62, 71, 75, 81, 82, 84, 87 7.4* 12, 50, 62 1, 2, 6, 9, 18, 21, 24, 27, 38, 43, 45, 61 7.5 9, 13, 18, 32, 37 1, 3, 6, 7, 11, 21, 23, 34, 38, 44, 46, 52, 63, 64, 67, 74, 77, 80 7.6 3, 15, 17, 21, 41, 52, 54 4, 7, 9, 19, 23, 33, 37, 38, 51, 53, 57, 69, 60 7.7 1, 21, 36, 40, 46, 50, 87 8, 10, 13, 26, 45, 53, 60, 62, 88 8.1 10, 28, 42, 45 2, 8, 15, 22, 29, 34, 43, 48, 62, 64, 66 8.2 3, 15, 26, 29, 40, 46, 65 9, 19, 20, 38, 45, 48, 53, 67 8.3 3, 15, 24, 30, 31 1, 5, 10, 26, 32, 33 8.4 5, 18, 37, 47, 50, 54 1, 4, 8, 12, 30, 31, 39, 43, 45, 55, 57, 59, 68 8.5 2, 14, 31, 45, 50, 63, 70, 78 1, 7, 20, 41, 46, 56, 59, 68, 81 8.8 1, 13, 36, 51, 58, 77 7, 8, 22, 25, 26, 40, 49, 54, 55, 59 9.1 8, 37 2, 11, 16, 20 9.2 3, 11, 16 1, 9 9.3 22, 25, 29 20, 23 11.1 4, 12, 21, 24, 28 1, 9, 16, 17, 22, 26 11.2 5, 6, 14, 20, 33, 39, 42, 53, 58 8, 16, 29, 38, 44, 47, 60, 65 11.3 20, 34, 39, 54 4, 6, 9, 12, 17, 18, 25, 42, 44, 56, 62, 67, 68 11.4 8, 21, 28, 31 2, 4, 7, 11, 12, 17, 24, 34, 35, 38, 41, 45 6