Teaching Assistants:

- Gergely Bana,
room 3C15 in DRL: office hours Monday 5-6 p.m., Tuesday 4-5 p.m.,
*bana@math.upenn.edu* - Marcus Khuri,
room 3C15 in DRL: office hours Monday 8-9 a.m., Wednesday 10-11 a.m.,
*khuri@math.upenn.edu*

**
Course grades are available
on-line
from a secure file that
requires your full eight-digit Penn ID for access to your grades.
**

- 60% midterm exam average (lowest grade eliminated)
- 30% final exam
- 10% computer assignments plus recitation participation.

**EXAM 1 Wednesday, January 27**covers the course through Ch 9[C] and Ch 6[F]. We are going to skip Section 9.4[C] (Approximate Solutions).**EXAM 2 Wednesday, February 10**covers the course from the beginning through Ch 7[F] with emphasis on material since the last exam.**EXAM 3 Wednesday, March 3**covers the course from the beginning through Ch 10[C] and Ch 8[F] with emphasis on material since the last exam.**EXAM 4 Tuesday, March 30 (*****NOTE this one is TUESDAY*****)**covers the course from the beginning through Ch 11[C] and Ch 8[C] Sections 1-3 with emphasis on material since the last exam. We are going to skip Section 11.6[C] (Newton's Method).**EXAM 5 Wednesday, April 14**covers the course from the beginning through Ch 8[C] sections 4-8 and Ch 2[F] sections 1-4 with emphasis on material since the last exam. We are going to skip Section 8.6[C] (Total Differentials).

- No calculators or computing devices will be allowed on the exams.
- Your lowest midterm exam grade will be dropped.
- There will be a make-up exam for the final.
- There will be no make-up exams for the five midterms. If you miss a midterm exam, then that will be the exam for which the grade is dropped. If you have valid reasons (explained, for example, in a letter from the Advising Dean of your School) for missing more than one midterm exam, then the final exam will count more heavily in determining your course grade.
**VERY IMPORTANT:**You may bring only one page (8 1/2" x 11") of notes with you to the exam. Otherwise the exam is closed book.- Please be in your seats by 6:20, so that we may start on time.

The assigned homework represents the MINIMUM amount of material that you must master for success in this course.

- Tuesday, January 12: C 9.1, C 9.2
- Thursday, January 14: C 9.3, F 6.1
- Tuesday, January 19: F 6.2, F 6.3
- Thursday, January 21: F 6.3, F 6.4
- Tuesday, January 26: F 7.1, F 7.2, F 7.3
- Thursday, January 28: F 7.4, F 7.5
- Tuesday, February 2: F 7.6, Review
- Thursday, February 4: Review of F 7, New material F 8.1, F 8.2
- Tuesday, February 9: Review of F 7, New material F 8.2, F 8.3
- Thursday, February 11: F 8.4
- Tuesday, February 16: F 8.4, C 10.1, C 10.2
- Thursday, February 18: C 10.3, F 8.5
- Tuesday, February 23: Review F 8, C 10
- Thursday, February 25: C 11.1, C 11.2
- Tuesday, March 2: C 11.3, C 11.4
- Thursday, March 4: C 11.4, C 11.5
- Tuesday, March 16: C 11.5, C 8.1, C 8.2
- Thursday, March 18: C 8.4, C 8.5
- Tuesday, March 23: Review
- Thursday, March 25: C 8.7, C 8.8
- Tuesday, March 30: F 2.1, F 2.2
- Thursday, April 1: F 2.3, F 2.4
- Tuesday, April 6: F 2.5, F 2.6
- Thursday, April 8: F 2.6, F 2.7
- Tuesday, April 13: F 9.1, Review
- Thursday, April 15: F 9.2, F 9.3
- Tuesday, April 20: F 9.3, Review
- Thursday, April 22: Review

I suggest that you try each homework assignment on your own at first, then get together with a small study group -- at least two but no more than four -- to review your solutions and to work out parts that you did not get on your own. A study group is right for you if you are sometimes a giver and sometimes a taker, but not always one or the other. If you have difficulty finding an appropriate study group, please ask your TA for help in forming one.

After working with the study group, finish your homework by writing up your
own version of the solutions. This last
step is *very important*. Do not neglect it as it is precisely what you
will be required to do on the exams. Keep in
mind that the exams will primarily be based on the homework, so if you have
done the homework well, you should
do well on the exams.

Homework will generally consist of
core problems
and from the old final exam questions.
Old final exam questions are included
at the back of the Maple Calculus
Lab Manual.
**It is VERY IMPORTANT that you work through these exams
as they give you a very
good indication of the type and level of material that we will expect you to
know on the final exam this year. I will
assign problems from previous finals as we go through the semester.
As with all of the homework, these problems
may serve as models for mid-semester exam questions.**

**Homework #1 to be discussed in recitations January 11, 13, 18, and 20:**

- All core problems from sections: C 9.1, C 9.2, C 9.3. Use Maple when it seems appropriate. In particular, try DEplot. See Maple Demonstrations #2 and #3.
- Old finals problems: Fall 94 #1, Spring 95 #1, 2, Fall 95 #14, Spring 96 #1, 2, 3, 24, Fall 96 #3, 5, Spring 97 #1, 2, 3, Fall 97 #1, 2, Spring 98 #7, 14.

- All core problems from chapter F 6.
- Old finals problems: Spring 95 #4, Spring 96 #5, 11, Fall 96 #1, Fall 97 #3, Spring 98 #4, 11.

- All core problems from chapter F 7, Sections 1 through 5. Note that the answer in the text to part d of problem 27 from section 7.1 is incorrect. It should be 9 rather than 6.
- Old finals problems: Fall 94 #3, Spring 95 #3, 5, Fall 95 #5, 6, 14, Spring 96 #4, 6, Fall 96 #2, 4, 9, Spring 97 #4, 5, 6, 8, Fall 97 #5, 7, Spring 98 #1, 8, 18, 21.
- MAPLE: Read and work through the Probability portion of the Probability and Statistics section of the Lab Manual. Work through Maple demonstrations #4 and #6. Go through the worked Math 151 Sample Problems in the Lab Manual Chapter 7. I suggest that you first do the problems using MAPLE on your own. Then compare your solutions with those in the Lab Manual.

- All core problems from chapter F 7 Section 6.
- Old finals problems: Fall 95 #8, Spring 96 #9, Fall 96 #8, Spring 97 #9, 10, Fall 97 #6, Spring 98 #22.

- All core problems from chapter F 8 Sections 1 through 4.
- Old finals problems: Spring 95 #20, Fall 95 #11, Spring 96 #10, Fall 96 #11, Fall 97 #4.
- MAPLE: Read pages 109 to 114 of the Lab Manual. This material is on statistical distributions, through the binomial distribution. Work through MAPLE Demonstrations #5 on the binomial distribution. Study the worked Math 151 Sample Problems in the Lab Manual through Chapter 8 Section 4 (pages 149 - 155). I suggest that you first do the problems using MAPLE on your own. Then compare your solutions with those in the Lab Manual.

- All core problems from Chapter F 8 Sections 4 and 5, and from Chapter C 10 Section 1, 2, and 3.
- Old finals problems: Fall 94 #8, Spring 95 #6, 7, 19, Fall 95 #10, 16, 20, Spring 96 #6, 7, 8, 23, Fall 96 #6, 7, 9, 10, 12, Spring 97 #7, 11, Fall 97 #8, 9, Spring 98 #5, 12, 15. Corrections to assigned Old Final Exam problems: Answer C for problem 20 of the Fall 1995 Final Exam should be .53, not .5. There is no correct answer for problem 5 on the Spring 1998 Final Exam. The mean is 2/3 and the standard deviation is 1/sqrt(18).
- MAPLE: Read pages 114 to 116 of the
Lab Manual. This material is on continuous distributions.
Study the worked Math 151 Sample Problems in the
Lab Manual through Chapter C 10 Section 3 (page
155). I suggest that you first do the problems using MAPLE on your own.
Then compare your solutions with those in the Lab Manual.
**In addition, you should be working on the MAPLE assignment due in recitations March 15 and 17: Problem #12 on Samples and Polls, page 209 in the Probability section of the Lab Manual.**

- All core problems from Chapter C 11 Sections 1 and 2.
**Correction:**The claimed values for a_{2}and a_{3}in part (a) of problem 47 of section 11.2 are nonsense. Because this is an annuity, an additional $100 is deposited each month. Thus a_{2}=100(1.01)^2+100(1.01), and a_{3}=100(1.01)^3+100(1.01)^2+100(1.01). You can use a geometric series to determine that the value of this annuity after 24 months is $2724.32. For comparison, you should also do this problem by the integral technique for income streams of Chapter 6 Section 7. There it is assumed that the interest is compounded continuously. For that calculation you will get $2712.49. Can you see why this amount is slightly smaller even though the interest here is compounded continuously? - Old finals problems: Fall 95 # 15, Fall 96 # 13.
- MAPLE: Read pages 117 - 120 of the
Lab Manual. This material is on Taylor polynomials.
Study the worked Math 151 Sample Problem in the
Lab Manual on Taylor polynomials (page
156). I suggest that you first do the problems using MAPLE on your own.
Then compare your solutions with those in the Lab Manual.
**In addition, you should be working on the MAPLE assignment due in recitations March 15 and 17: Problem #12 on Samples and Polls, page 209 in the Probability section of the Lab Manual.**

- All core problems from Chapter C 11 Sections 3 - 5.
**Correction:**The answer in the text and the solutions manual for C 11.4 #27 is incorrect. The terms before the summation sign should be 1 + (1/2)(x-1) - ... Furthermore, the answer in the text and the solutions manual for C 11.4 # 31 is off by a factor of -1. You can check your answer for #31 of section C 11.5 quickly by using the tables of the normal distribution. - Old finals problems: Fall 94 #4, 7, Spring 95 #12, 14, 15, Fall 95 #17, 19, Spring 96 #17, 18, 19, Fall 96 #14, 19, Spring 97 #17, 19, 23, Fall 97 #10, 11, 12, Spring 98 #3, 6, 13, 23.
- MAPLE assignment due in recitations March 15 and 17: Problem #12 on Samples and Polls, page 209 in the Probability section of the Lab Manual.
**Supplementary Material on Series:**The text coverage of infinite series is particularly skimpy. We will cover additional material in the lectures. Even more material than we will cover may be found at the web site of supplementary material produced by the author of our textbook. Also included are supplementary exercises and answers. However, the only supplementary material you are responsible for is the material on infinite series covered in the lectures or on the old final exams. The web sites mentioned above contain much more material than that.

- All core problems from Chapter C 8 Sections 1-4.
- Old finals problems: Fall 94 #9, Spring 95 #10, Fall 95 #12, Spring 96 #14, Fall 96 #15, Spring 97 #13, 14, 16, Spring 98 #19.
- MAPLE: Read pages 91 - 92 and pages 121 - 130 of the Lab Manual. This material is on partial derivatives and on plot3d, implicitplot and implicitplot3d. Study the worked Math 151 Sample Problem in the Lab Manual on critical points (pages 158 - 159). I suggest that you first do the problems using MAPLE on your own. Then compare your solutions with those in the Lab Manual.

- All core problems from Chapter C 8 Sections 5, 7, and 8. Skip Section 6.
- Old finals problems: Fall 94 #5, Spring 95 #8, 9, Fall 95 #13, 18, Spring 96 #12, 13, 15, 16, Fall 96 #18, Spring 97 #12, 15, 18, Fall 97 #13, 14, Spring 98 #9, 16, 20.
- MAPLE: Read pages 91 - 92 and pages 121 - 130 of the Lab Manual. This material is on partial derivatives and on plot3d, implicitplot and implicitplot3d. Study the worked Math 151 Sample Problem in the Lab Manual (pages 158 - 160). I suggest that you first do the problems using MAPLE on your own. Then compare your solutions with those in the Lab Manual. After that work through MAPLE Demonstrations #10, 11, 12, and 13. These demonstrations are quite good and very useful. Once you have done this, modify demonstrations #12 and #13 to solve some of the core problems. Notice how easy it is to do these problems with MAPLE.

- All core problems from Chapter F 2 Section 1 - 4.
- Old finals problems: Fall 94 #10, Spring 95 #17, Fall 95 #1, 4, Spring 96 #21, Fall 96 #17, Spring 97 #21, Fall 97 # 15, 16, Spring 98 #10.
- MAPLE: Study pages 131 - 133 of the Lab Manual. This material is on linear algebra. Study the worked Math 151 Sample Problem in the Lab Manual for Chapter F 2 Sections 1 and 3 (page 161). I suggest that you first do the problems using MAPLE on your own. Then compare your solutions with those in the Lab Manual. After that work through MAPLE Demonstration #14. This demonstration is especially useful. You will find MAPLE to be a big time saver in solving systems of linear equations.

- All core problems from Chapter F 2 Sections 5 - 7.
- Old finals problems: Fall 94 #6, Spring 95 #16, 18, Fall 95 #2, 9, Spring 96 #20, Fall 96 #16, Spring 97 #20, 22, Fall 97 #17, Spring 98 #24. Please note that no correct answer is given for final exam problem #9, Fall 95. To fix answer F (which is claimed to be the answer) change the upper right entry of the 2 x 2 matrix from 1 to 0, and the lower left entry from 0.98 to -0.02. In the Spring 97 final exam problem # 22, the smudge in the upper entry of matrix D should be an 8.
- MAPLE: Study the worked Math 151 Sample Problem in the Lab Manual for Chapter F 2 Sections 5-7 (pages 162 - 164). I suggest that you first do the problems using MAPLE on your own. Then compare your solution with the one in the Lab Manual.

- All core problems from Chapter F 9 Sections 1,2.
- Old finals problems: Spring 95 #11, Fall 95 #7, Spring 96 #22, Fall 97 #18, Spring 98 #17.