Math 121 Calculus II
Spring 2014 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) / LectureCalculus 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).**Description for the course.**This is the second course in a two-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. Topics in Math 121 include techniques of integration, applications of integration, a short introduction to differential equations, sequences, series, and power series. See below for a detailed syllabus of the course. Prerequisite: Math 120, Math 124, or AP credit for a semester of calculus.**Goals.**See goals for an outline of the course goals including knowledge, intellectual and practical skills, skepticism and the mathematical mind, and integrating knowledge and skills**Text.**Our text for this course is*University Calculus*by Hass, Weir and Thomas, second edition. This same book is used in Math 120. Our text for this course is*University Calculus*by Hass, Weir and Thomas,*early transcendentals*, second edition. See http://www.pearsonhighered.com/educator/product/University-Calculus-Early-Transcendentals-Plus-NEW-MyMathLab-with-Pearson-eText-Access-Card-Package-2E/9780321759900.page. Note that you’ll need the version that gives you access to MyMathLab, which you already have if you used this book in Math 120. The book without access to MyMathLab is not enough. The Clark University Bookstore has it.**Accessing MyMathLab.**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/. You will need:- The Course ID.
- An Access Code. This comes with the book that you purchased. (It can be purchased separately. Note also that there is an option to grant you temporary access to your course for 14 days even if you don’t have an access code yet.) Keep a record of your purchase.

To get precise registration instructions, go to MyMathLab, http://pearsonmylabandmastering.com, and, on the right, click on

*Student*under*Register*. There you will give your course ID and follow the steps given. Be careful to put in your name precisely as it appears in the university records.At the end of the registration process you will have a login name and password. Each time you want to access MyMathLab, click on

*Sign in*(under*sign in*, and then put in your data. On the left of the resulting screen you will see*Math 120-...*. Click on that.On the web page that comes up you’ll see buttons on the left that are used to give the various options of the software. From here you can do an assignment, take a test, etc. There’s a button

*Study Plan*, which allows you to practice problem solving, with help from the program if requested. You also have a*Multimedia Library*which contains useful material.By the way, you can access MyMathLab from any computer on the internet. There are computers in Goddard Library if you don’t have one or if yours breaks down.

As a final note, remember that aside from online support, Pearson offers tech support for MyMathLab, so you can call them if anything goes wrong. The Pearson 24/7 Technical Support web page is at http://247pearsoned.custhelp.com/. (In the past the web site has sometimes been down for short periods of time, but it came back up fairly quickly.)

**Assignments.**The course will use the software MyMathLab for the homework assignments.

If you get an exercise wrong, you’ll be able to try it a second time. If you’re ill or otherwise need an extension, an extension can be arranged. Otherwise, late exercises will by reduced by 25%, and they’ll only be available for a few days after the due date.

The assignments are all on line, but if for any reason you can’t access them, here’s a corresponding list of exercises from the text. They’ll be assigned as the course progresses.

**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.- First test: Thursday Feb 20 on chapters 5 and 6
- Second test: Thursday Mar 27 on chapters 7 and 8
- Final exam: Either May 2 or May 6, your choice, 6:30–8:30 in Johnson Auditorium, S120

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 20% for homework assignments and quizzes, 25% for each of the two midterms, and 30% for the final. The final will be cumulative, and the final will be weighted more than 30% if you do better on it than the midterms.

**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. Times are yet to be determined.**Syllabus.**Some of the listed topics are optional.We've already covered sections 5.1 through 5.4 in Math 120, Calculus I, so we'll only review them briefly at the beginning of the course. There will be, however, a homework assignment from section 5.4.

Chapter 5.**Introduction to integration.**- 5.1. Area and estimating with finite sums
- 5.2. Sigma notation and limits of finite sums

Fermat computes an integral - 5.3. The definite integral

The origin of the FTC

Definition of integrals

Summary of foundations of integration - 5.4. The fundamental theorem of calculus. FTC

Antiderivatives

Proofs of FTC^{–1}and FTC

Exercises: 3, 19, 22, 31, 35, 75, 81. - 5.5. Indefinite integrals and the substitution method

Substitution for integrals

Exercises: 1, 3, 4, 7, 9, 11, 17, 18, 19, 21, 22, 27, 29, 47, 55. - 5.6. Substitution and area between curves

Exercises: 2, 5, 7, 11, 15, 19, 21, 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. Optional topic: Volumes using cylindrical shells
- 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 - Optional topic: Continuous probabilities part I and part II

Chapter 7.**Integrals and transcendental functions.**- 7.1. The logarithm defined as an integral

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

Rules and methods of integration

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

Exercises: 15, 17, 19, 21 - 8.4. Integration of rational functions by partial fractions

The Method of Partial Fractions to Integrate Rational Functions

Summary on integration

The Logistic population model

Exercises: 1, 6, 10, 11, 17, 22 - 8.7. Improper integrals

Exercises: 2, 10, 21, 25, 65

Chapter 9.**Infinite sequences and series.**- Survey of sequences and series
- 9.1. Infinite sequences

Summary of limits of sequences

On the limit (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. Various tests for convergence for series with positive terms

Exercises: 1, 9, 15, 21, 25, 31, 34, 37 - 9.6. Alternating series, Absolute and conditional convergence, Leibniz’ alternating series test

Exercises: 3, 5, 7, 15, 21, 31 - 9.7. Power series, interval and radius of convergence

Exercises: 1, 5, 15, 25 - 9.8. Taylor’s formula for the
*n*^{th}coefficient in a power series

Exercises: 1, 4, 15, 32

- Practice sheets and tests
- Practice your integration. Basic integration.
- Test 1. Answers.
- Test 2. Answers.
- Useful formulas and theorems attached to the final exam

**Some past tests****Web pages for related courses**

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