Math 121 Calculus II

Math 121 Calculus II
Spring 2013
Prof. D. Joyce, BP 322, 793-7421
Department of Mathematics and Computer Science
Clark University

Please bookmark this page, http://aleph0.clarku.edu/~djoyce/ma121/, so you can readily access it.

General description from Clark's Academic Catalog
Math 120 and 121 (Calculus I and II) / Lecture
Calculus is essential for majors in biology, chemistry, computer science, mathematics, physics, and environmental science and policy. Part I includes functions, limits, continuity, differentiation of algebraic and trigonometric functions, mean value theorem, and various applications. Part II includes Riemann sums and integrals, techniques and applications of integration, improper integrals, transcendental functions (logarithms, exponential functions, and inverse trigonometric functions), sequences, and series. Though not all results are derived rigorously, care is taken to distinguish intuitive arguments from rigorous proofs. Math 120 and 121 each fulfill the Formal Analysis requirement.
Prerequisite for Math 120: appropriate score on the mathematics placement test, or appropriate grade in Math 119. Prerequisite for Math 121: Math 120, or Math 124, or AP credit in Calculus. Offered every fall (120) and spring (121).
Course hours MWF 11:00–11:50, BP316
Office hours My office hours are MWF 10-11 and others to be determined.
My office is right across the hall from the classroom. My phone extension is 7421. Email me at djoyce.
Description for the course. This is the second course in a three-semester calculus sequence designed for students majoring in a field that requires the tools of calculus. Besides the computational aspects of calculus, we will develop the concepts of calculus with some rigor. Prerequisite: Math 120, Math 124, or AP credit for a semester of calculus.
Web pages for related courses
Text. Our text for this course is University Calculus by Hass, Weir and Thomas, second edition. This same book is used in Math 120.
Assignments. The course will use the software MyMathLab for the homework assignments To start using it, you must register to your section online at http://pearsonmylabandmastering.com/ using the Course ID and access code to be given in class.
Course administration. There will be two tests during the semester and a final examination during finals week in May. The final is cumulative, but post-midterm material will be emphasized. Short 15-20 minute quizzes will be given periodically throughout the semester.
Class attendance and class participation are obligatory. During the class meeting the text will be supplemented with more rigorous theory and special topics.
The course grade will be based on 30% for homework assignments and quizzes, 20% for each of the two midterms, and 30% for the final.
Work expectation. You will work on average about six to eight hours each week outside of class. This will include studying from your notes and the textbook, doing the homework assignments, and studying for quizzes and exams. See About studying mathematics in general, and Calculus in particular for more details.
Tutoring/mentoring. Experienced upperclass mentors will be available in the evenings, 7:00 to 9:00, on Sundays through Thursdays with extended days on Mon and Wed 6:00 to 10:00 (but not Fridays or Saturdays) in the seminar room BP312.
Syllabus Additional topics not in the text are displayed in blue. Some of the other listed topics are optional.

Chapter 5. Introduction to integration.
- 5.1. Area and estimating with finite sums
  Exercises: 1, 5, 11, 15.
- 5.2. Sigma notation and limits of finite sums
  Exercises: 1, 7, 8, 11, 14, 17, 21, 29.
- 5.3. The definite integral
  Exercises: 1, 7, 9, 11, 13, 15, 17, 75.
  See also Handout on the origin of the FTC at http://math.clarku.edu/~djoyce/ma121/FTC.pdf
  Handout on the Definition of integrals at http://math.clarku.edu/~djoyce/ma121/integral.pdf
  Handout on the Summary of foundations of integration at http://math.clarku.edu/~djoyce/ma121/foundations.pdf
- 5.4. The fundamental theorem of calculus. FTC
  Exercises: 1, 4, 7, 8, 9, 17, 21, 29, 30, 45, 50, 61, 71.
  Handout on proofs of FTC^–1 and FTC at http://math.clarku.edu/~djoyce/ma121/FTCproof.pdf
- 5.5. Indefinite integrals and the substitution method
  Exercises: 1, 3, 4, 7, 9, 11, 17, 18, 19, 21, 22, 27, 29, 47, 55, 69.
- 5.6. Substitution and area between curves
  Exercises: 2, 5 7, 11, 15, 19, 27, 29, 39.
  More exercises: 47, 51, 53, 54, 55, 57, 63, 65, 97, 113.
Chapter 6. Applications of definite integrals.
- 6.1. Volumes using cross-sections
  Exercises: 1, 9, 13, 17, 19, 23, 25, 37, 39.
- 6.2. Volumes using cylindrical shells
  Exercises: 1, 3, 5, 35
- 6.3. Arc length
  Exercises: 1, 2, 3, 5, 26, 29
- 6.4. Areas of surfaces of revolution
  Exercises: 9, 13, 15, 21, 28, 29
- Handouts on continuous probabilities: part I and part II at http://math.clarku.edu/~djoyce/ma121/prob1.pdf and http://math.clarku.edu/~djoyce/ma121/prob2.pdf
Chapter 7. Integrals and transcendental functions.
- 7.1. The logarithm defined as an integral
  Handout on logarithms at http://math.clarku.edu/~djoyce/ma121/logs.pdf
  Exercises: 1, 3, 5, 9, 10, 19, 27, 31
- 7.2. Exponential change and separable differential equations
  Exercises: 3, 5, 9, 11, 17
  More exercises: 25, 31, 33, 39, 43, 44
Chapter 8. Techniques of integration.
- 8.1. Integration by parts
  Handout on integration by parts at http://math.clarku.edu/~djoyce/ma121/parts.pdf and
  Handout summarizing Rules and methods of integration at http://math.clarku.edu/~djoyce/ma121/rules.pdf
  Exercises: 4, 5, 7, 8, 11, 21, 29, 33
- 8.2. Trigonometric integrals
  See also Dave's Short Trig Course at http://www.clarku.edu/~djoyce/trig
  Exercises: 3, 5, 33
- 8.3. Trigonometric substitutions
  Handout on Trigonometric Substitutions at http://math.clarku.edu/~djoyce/ma121/trigsubs.pdf
  Exercises: 15, 17, 19, 21
- 8.4. Integration of rational functions by partial fractions
  Handout on The Method of Partial Fractions to Integrate Rational Functions at http://math.clarku.edu/~djoyce/ma121/parfrac.pdf
  Handout on the Logistic population model at http://math.clarku.edu/~djoyce/ma121/logistic.pdf and
  Exercises: 1, 6, 10, 11, 17, 22
- 8.7. Improper integrals
  Exercises: 2, 10, 21, 25, 65
Chapter 9. Infinite sequences and series.
- Handout on Survey of sequences and series at http://math.clarku.edu/~djoyce/ma121/seqser.pdf
- 9.1. Infinite sequences
  Handout on Summary of limits of sequences at http://math.clarku.edu/~djoyce/ma121/limits.pdf
  Handout on (1 + 1/n)ⁿ → e at http://math.clarku.edu/~djoyce/ma121/elimit.pdf
  Exercises: 3, 13, 15, 27, 31, 35, 37, 41, 53, 65
- 9.2. Infinite series
  Exercises: 1, 3, 19, 21, 31, 61, 63, 88, 94
- 9.3. The integral test for convergence
  Exercises: 3, 4, 6, 13, 15, 19, 21, 25
- 9.4. Comparison tests for convergence
  Exercises: 1, 9, 15, 21, 25, 31, 34, 37
- 9.5. The ratio test for convergence
  Handout on Various tests for convergence for series with positive terms at at http://math.clarku.edu/~djoyce/ma121/posseries.pdf
  Exercises: 1, 9, 15, 21, 25, 31, 34, 37
- 9.6. Alternating series, absolute and conditional convergence
  Handout on Alternating series, Absolute and conditional convergence, Leibniz' alternating series test at http://math.clarku.edu/~djoyce/ma121/altseries.pdf
  Exercises: 3, 5, 7, 15, 21, 31
- 9.7. Power series
  Handout on Power series, interval and radius of convergence at http://math.clarku.edu/~djoyce/ma121/powerseries.pdf
  Exercises: 1, 5, 15, 25
- 9.8. Taylor's formula for the n^th coefficient in a power series
  Exercises: 1, 4, 15, 32
Quizzes and tests
- Quiz 1 . Friday, Feb 8, on sections 5.4–5.6. Answers.
- Test 1. Monday Feb 18 on chapter 5 and section 6.1. Answers.
- Test 2. Wednesday Mar 27 on sections 6.3, 6.4, 7.1, 7.2, and 8.1. Answers.
- Quiz 2. Friday, April 19, on sections 9.1-9.3. Answers.
- Final Exam. Thursday, May 2, 6:30-8:30. Sample exam.
Some past tests
- 2012 Test 1 on chapter 5. Answers.
- 2012 Test 2 on chapters 6 and 7. answers
- 2012 Final exam. answers

This page is located at http://aleph0.clarku.edu/~djoyce/ma121/