INTEGRAL CALCULUS

 

MATH 262         SPRING 2012

 

Instructor:  Dr. R. P. Webber

 

Office location and hours:  E. Ruffner 332, MTF 2 - 3:30 mand by appointment or coincidence. I am in class practically all day on Wednesday, and  I am not normally on campus on Thursday.

 

Telephone:  395-2192

 

Email:  webberrp@longwood.edu

 

 

Course description:  Integrals and their applications; sequences and series

 

Text:  Rogawski, Single Variable Calculus Early Transcendentals, second edition.  W.H.Freeman, 2012.

 

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 Mathematica.  You have already paid for this program in your course fee, and you will need to download this program to your computer.  Go to https://user.wolfram.com/portal/requestAK/e6c1656c6d1912f417ae3fb7964296047862bdb1 .  Follow the link to request an Activation Key.  Then download the installation file from the User Portal.  Dr. Shoenthal (the department chair) will be notified automatically and will approve you as a new user.  When he has done that, you will get an email and will be able to install the system on your computer.

 

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

 

Jan 18 – 20

5.1 - 5.3:  Areas; the Fundamental Theorem of Calculus

2

 

Jan 23 - 27

5.4 – 5.6:  The Fundamental Theorem; substitution

3

 

Jan 30 – Feb 3

5.6 – 5.8:  Substitution; log and trig integrals

4

 

Feb 6 – 10

6.1:  Areas between curves; catch up; TEST

5

 

Feb 13 – 17

6.2, 6.3: Volumes; 7.1, 7.2: parts, trig integrals

6

 

Feb 20 – 24

7.3, 7.5:  Trig substitution; partial fractions

7

 

Feb 27 – Mar 2

7.6, 7.8:  numerical integration; improper integrals

8

 

Mar 5 - 9

Catch up, review, TEST

 

 

Spring break

9

 

Mar 19 - 23

8.1 – 8.4:  Applications

10

 

Mar 26 - 30

10.1 – 10.3:  Sequences; series; convergence tests

11

 

Apr 2 - 6

10.4 – 10.5:  Convergence tests; estimating sums

12

 

Apr 9 – 13

10.5, 10.6:  Power series

13

 

Apr 16 – 20

10.7:  Taylor series; catch up

14

 

Apr 23 - 27

Review, TEST, review

 

Tuesday, May 1

3:00 – 5:30 Final exam

 

 

  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.