Math 121 Calculus II

Math 121 Calculus II
Spring 2012
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, 121 and 122 (Calculus I, II, and III) / 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). Part III includes further topics from calculus proper (sequences, series, polar coordinates) and introduces linear algebra (vectors, matrices, and linear systems). Though not all results are derived rigorously, care is taken to distinguish intuitive arguments from rigorous proofs. Math 120, 121, and 122 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. Prerequisite for Math 122: Math 121. / Offered every fall (120, 122) and spring (121).

Sections

Section	Instructor	Meeting time	Location
§ 1.	D. Joyce	M W F 11:00-11:50	BP 316
§ 2.	G. Bahir-Maschler	T R 9:00-10:15	BP 326
§ 3.	D. Joyce	M W F 12:00-12:50	BP 316
§ 4.	M. Satz	T R 2:50-4:05	BP 326

Office hours My office hours are MWF 10-11 and 1-2, subject to change.
My office is right across the hall from the classroom. My phone extension is 7421. Email me at djoyce.
Registrar's Office with course listings and the semester schedule.
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 and Math 122.
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 given to you by your instructor and your access code.
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 25% for homework assignments and quizzes, 20% for each of the two midterms, and 35% 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, 8:00 to 10:00, on Sundays through Thursdays (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. Due Wednesday, Jan 25.
- 5.2. Sigma notation and limits of finite sums
  Exercises: 1, 7, 8, 11, 14, 17, 21, 29. Due Friday, Jan 27.
- 5.3. The definite integral
  Exercises: 1, 7, 9, 11, 13, 15, 17, 75, 77. Due Monday, Jan 30.
  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. Due Wednesday, Feb 1.
  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. Due Friday, Feb 3.
- 5.6. Substitution and area between curves
  Exercises: 2, 5 7, 11, 15, 19, 27, 29, 39. Due Monday, Feb 6.
  More exercises: 47, 51, 53, 54, 55, 57, 63, 65, 97, 113. Due Wednesday, Feb 8.
- Quiz Friday, Feb 10, on using the FTC.
- Test on chapter 5, Wednesday Feb 15. Answers. Extra credit answers.
Chapter 6. Applications of definite integrals.
- 6.1. Volumes using cross-sections
  Exercises: 1, 7, 9, 13, 17, 21, 23, 35, 37. Due Monday, Feb 13.
- 6.2. Volumes using cylindrical shells
  Exercises: 1, 3, 5, 35 Due Wednesday, Feb 22.
- 6.3. Arc length
  Exercises: 1, 2, 3, 5, 26 Due Friday, Feb 24.
- 6.4. Areas of surfaces of revolution
  Exercises: 9, 13, 15, 19, 21, 28, 29 Due Monday, Feb 27.
- Quiz Wednesday, Feb 29, on 6.1 and 6.2. Answers
- 6.6. Moments and centers of mass
- 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 Due Friday, Mar 16.
- 7.2. Exponential change and separable differential equations
  Exercises: 3, 5, 9, 11, 17 Due Monday, Mar 19.
  More exercises: 25, 31, 33, 39, 43, 44 Due Wednesday, Mar 21.
- Sample Test on chapters 6 and 7.
- Second test version a, answers
- Second test version b, answers
- Second test extra credit problems, answers
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: 3, 5, 9, 11, 17 Due Monday, Mar 26. 4, 5, 7, 8, 11, 21, 25, 29, 33, 35
- Quiz on integration by parts, Answers
- 8.2. Trigonometric integrals
  See also Dave's Short Trig Course at http://www.clarku.edu/~djoyce/trig
  Exercises: 3, 5, 13, 33, 35 Due Monday, Apr 9.
- 8.3. Trigonometric substitutions
  Handout on Trigonometric Substitutions at http://math.clarku.edu/~djoyce/ma121/trigsubs.pdf
  Exercises: 5, 13, 15, 17, 19, 21 Due Friday, Apr 13.
- 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, 19, 22, 25 Due Monday, Apr 16.
- 8.7. Improper integrals
  Exercises: 2, 9, 10, 21, 25, 65, 67 Due Wednesday, Apr 25.
Some past tests with answers
This page is located at http://aleph0.clarku.edu/~djoyce/ma121/