Math 121 Calculus II

Spring 2007
Clark University
Department of Mathematics and Computer Science

This course page is obsolete.  I'll prepare a new page next time I teach the course.

Instructors:
- H. Servatius
- D. Joyce

Sections

Number   Section Instructor   Day     Time         Place
33639    1       Joyce        M W F   9:00-9:50    BOP 326
33640    2       Joyce        M W F   11:00-11:50  BOP 326
33641    3       Servatius    T R     9:00-10:15   KC 102
34595    4       Servatius    T R     10:25-11:40  KC 102

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 fulfill the Formal Analysis requirement. Math 122 is a prerequisite for Math 131 for students who have taken Math 120-121. Prerequisite for Math 120: appropriate score on the mathematics placement test, or appropriate grade in Math 119. / Offered every fall (120, 122) and spring (121).
Course administration. There will be quizzes, three evening midterms, and a final exam.
Homework and Quizzes. Practice problems will be assigned daily from the text to help you master the concepts discussed in class. Although the problems will not be collected regularly, it is expected that you will keep up to date on the problems. Math is not a spectator sport. You learn by doing; therefore, it is only to your advantage to keep abreast of the current work. Don't wait until the night before the exam to begin doing the problems. Periodically I will assign a few specific problems to be collected and graded. Homework is due in class on the assigned day. No late assignments will be accepted. Short 15-20 minute quizzes will be given periodically throughout the semester. No makeups for quizzes will be given for any reason. In computing the final Homework/Quiz average, the lowest homework or quiz grade will be dropped.
Exams will be given in a three-hour block in the evening on the above dates. The exams will be common for all students taking Math 121 and will be based on material discussed in the lecture or presented in the text prior to the date of the exam. Exams will be closed book, closed notebook. The use of calculators will not be allowed. In the event that a student has a legitimate, documented excuse for missing an exam, the student must contact me prior to the scheduled exam time. A makeup may be rescheduled at the instructor's convenience.
The final will be a two-hour, comprehensive exam, given during the final exam period. All students will be required to take the final exam at that time. Therefore do not make plans to leave campus before Tuesday, May 8.
The course grade is computed as follows
```
   15%, Homework/Quizzes 
   20%, Exam 1     - Monday Feb 5
   20%, Exam 2     - Monday Feb 26 
   20%, Exam 3     - Monday Apr 2 
   25%, Final Exam - Tuesday May 8
```
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.
Textbook. Salas, Hillie, & Et gen. Calculus: One and Several Variables, 9th edition, Wiley, 2003. ISBN 0-471-23120-7. Other editions are virtually identical, but the page and exercise numbers will be off in other editions.
This is the same textbook used last semester in Math 120, and it will be used next semester in Math 122.
Syllabus
Chapter 5 Integration
5.1 - The Definite Integral of a Continuous Function
5.2 - The Function F(x)
5.3 - The Fundamental Theorem of Integral Calculus
5.4 - Some Area Problems
5.5 - Indefinite Integrals
5.6 - The u-Substitution; Change of Variables
5.7 - Additional Properties of the Definite Integral
5.8 - Mean-Value Theorems for Integrals; Average Values Thur distance traveled
Chapter 6 Applications of the Integral
6.1 - More On Area
6.2 - Volume By Parallel Cross Sections; Discs and Washers
6.3 - Volume By the Shell Method
6.4 - Center of Mass
Chapter 7 The Transcendental Functions
7.1 - One-to-One Functions; Inverses
7.2 - The Logarithm Function, Part I
7.3 - The Logarithm Function, Part II
7.4 - The Exponential Function
7.5 - Arbitrary Powers; Other Bases
7.6 - Exponential Growth and Decay
7.7 - The Inverse Trigonometric Functions
Chapter 8 Techniques of Integration
8.1 - Integral Tables and Review (Quick Reference)
8.2 - Integration By Parts
8.3 - Powers and Products of Trigonometric Functions
8.4 - Trigonometric Substitutions
8.5 - Partial Fractions (only through page 473)

Practice Problems

Sec. 5.2 - p.273  #1,3,7,9,11,19,21,27-32
Sec. 5.3 - p.282  #1-17 odd
Sec. 5.4 - p.290  #1-25 odd, 26,29,39,45,55
           p.283  #21
Sec. 5.5 - p.297  #1,3,7,9,11,13,15,19,21,25,27,35
Sec. 5.6 - p.304  #1-11 odd, 19,23,25,29,35,37,39
Sec. 5.7 - p.313  #1,3,7,9,13,15,17,21,23,25,31,33,35,39,42,43,45,47,49,51,53,55,59
Sec. 5.8 - p.318  #1-5,7-10,16,17,19,21,23
           p.283  #23,25
Sec. 5.9 - p.323  #1,3,5,9,11,13

Sec. 6.1 - p.330  #1-11 odd, 17,23 
Sec. 6.2 - p.341  #1,3,5,9,17,19,21,23
Sec. 6.3 - p.349  #1-9 odd, 13,15,17,19,21
Sec. 6.4 - p.355  #7, 9, 15, 25

Sec. 7.1 - p.378  #1,3,7,9,19,23,25,28-31,35,39
Sec. 7.2 - p.387  #13,17,19,21,23 
Sec. 7.3 - p.395  #1-31 odd, 37-45 odd, 49,51,55,69 
Sec. 7.4 - p.404  #1-51 odd, 57,61
Sec. 7.5 - p.412  #1-8, 19,21,23,29,31,33,35,43-51 odd, 59, 61
Sec. 7.6 - p.420  #1,3,5,7,10-12,16,17,22,26,29
Sec. 7.7 - p.432  #1-11 odd,15-25 odd, 39,41,43,45, 49-61 odd 

Sec. 8.1 - p.449  #1-5, 9-13,15,17,19, 21-24,27,31,35,37 
Sec. 8.2 - p.457  #1-11 odd, 19,23,25,29,39
Sec. 8.3 - p.467  #1,3,4,5-11 odd, 17,24,33,37,41,43
Sec. 8.4 - p.472  #2-6,8,10,11,15,22,23
Sec. 8.5 - p.481  #1,3,5,9,11,12,14,15,21,31

Old Exams
Interesting Web Sites
Class notes.
- Summary of the foundations of integration.
- Basic rules of integration.
- Technique of substitution.
- 5 Feb, Monday. First midterm 6:00-9:00 Johnson Auditorium.
  First midterm. Answers.
- 26 Feb, Monday. Second midterm 6:00-9:00 Johnson Auditorium.
  Answers.
- The natural logarithm ln x.
- The natural exponential function. e^x
- Dave's short trig course
- How to evaluate an integral
This page is located at http://aleph0.clarku.edu/~djoyce/ma121/