INTEGRAL CALCULUS

 

MATH 262, FALL 2007

 

Instructor:  Dr. R. P. Webber

 

Office location and hours:  E. Ruffner 332, MWF 10:00-10:50, TR 1:10-2:00, and by appointment or coincidence

 

Telephone:  395-2192

 

Email:  webberrp@longwood.edu

 

 

Course description:  A unified course dealing with the basic ideas of calculus and analytic geometry.

 

Text:  Stweart, Single Variable Calculus Concepts and Context 3rd edition.  Thompson, 2005.  ISBN 0-534-41022-7.

 

Course objectives:

 

  1. Integrate elementary functions.
  2. Numerically approximate definite integrals.
  3. Evaluate improper integrals.
  4. Find areas and volumes of regions bounded by curves.
  5. Approximate functions with polynomials.
  6. Use a computer algebra system to solve computationally difficult integration problems.
  7. Determine when infinite series converge.
  8. Approximate functions with series.

 

Computer algebra system:  We will use Derive and Maple, which are on the computers in the lab.  Derive and Maple are commercial products.  Derive comes with TI-89 and TI-92 calculators.  You may purchase either system for your PC if you like, although it is not required.  See the teacher for details.

 

Course requirements and grading:

 

Three tests, class participation (drop lowest)...…………...50%

Labs…………………………………………………….25%

Exam……………………………………………………25%

 

90-100 A; 80-90 B;  70-80 C;  60-70 D;  below 60 F

 

Homework:  Problems will be assigned regularly, and everyone is expected to do them.  You should ask questions in or out of class about exercises you could not solve.   Homework is your responsibility to do, and it will not be collected or graded.  However, many test questions will be homework problems that have been assigned.

 

Labs:  These problems will be done in groups.  They will be computationally challenging (and thus best done on a computer) or intellectually challenging (and thus best done in cooperation with others), or occasionally both.  You will be expected to begin work on these problems in the Tuesday computer lab sessions and to complete them out of class.  You will hand in one solution to each problem from the group, and every member of the group will receive the same grade.  Each lab assignment will have a due date, and failure to hand it in by the start of class on the due date will result in a penalty of 25% per class day late.

 

Class participation:  Often you will be asked to work in groups in class.  Working in small groups of three or four (which need not be the same groups as in the lab), you will be asked to solve a problem and present your results to the class.

 

Tentative Schedule:

 

Week

Dates

Sections and topics

 

 

 

1

Aug 27 – 31

5.4 - 5.7:  Substitution, parts, trig integrals

2

Sep 4 – 7

5.7:  Trig substitution, partial fractions

3

Sep 10 – 14

5.8 – 5.9:  Approximating integrals

4

Sep 17 – 21

5.9:  Error bounds, complete work on integration

5

Sep 24 – 28

5.10:  TEST; Improper integrals

6

Oct 1 – 5

6.1 – 6.3:  Areas, volumes, arc length

7

Oct 8 -12

6.4 – 6.6:  Selected applications

 

 

Fall break

8

Oct 17 – 19

7.1, 7.2:  Introduction to differential equations

9

Oct 22 – 26

7.3, 7.4:  Separable differential equations

10

Oct 29 – Nov 2

8.1, 8.2:  TEST; Sequences and infinite series

11

Nov 5 – 9

8.3:  Integral and comparison tests; estimating sums

12

Nov 12 – 16

8.4, 8.5:  Alternating series, ratio test, power series

13

Nov 19 – 20

8.6:  Power series

 

 

Thanksgiving break

14

Nov 26 - 30

8.6, 8.7:  Taylor series

15

Dec 3 - 7

TEST; 8.9:  Taylor polynomials

 

 

Final exam Dec 13, 3:00 p.m. – 5:30 p.m. in the lab

 

 

  Attendance Policy: Your attendance is expected at all classes.  Makeup tests will be given reluctantly, and then only upon presentation of a doctor’s excuse.  Makeup tests are always more difficult than regular tests, regardless of the reason of absences.

 

  Honor Code:  The teacher subscribes to the Longwood College Honor System, which, among other things, assumes you to not cheat and that you take responsibility to see that others do not.  Infractions will be dealt with harshly.  A student who is convicted of an Honor Code offense involving this class will receive a course grade of F, in addition to penalties imposed by the Honor Board.