Spring 1999
Math 151 - Lecture 003, TTh 12-1:30 DRL A1
Office: Room 4E6 in David Rittenhouse Laboratory
Telephone: eight five nine eight three
( Math. Dept. Office: eight eight one seven eight )
Fax: three four zero six three
E-mail: lastname at math
Office Hours: By appointment
Teaching Assistants:
FINAL EXAM is on Friday, May 7
from 11 a.m. to 1 p.m. in the
Chemistry Building Auditorium 102. Please familiarize
yourself with the final exam site a few days before the exam.
On the day of the exam
please be in your seats by 10:50 a.m., so that we may start on time.
This exam covers the entire course.
Course grades are available
on-line
from a secure file that
requires your full eight-digit Penn ID for access to your grades.
Math 151 Resources
Grades
Your course grade will be computed as follows:
- 60% midterm exam average (lowest grade eliminated)
- 30% final exam
- 10% computer assignments plus recitation participation.
You will have access to your own grades during the semester through the link
GRADES.
This is a secure grade file that
requires your full eight-digit Penn ID for access to your grades.
Exams
We will have five exams during the semester, approximately 60 to 90 minutes in
length. The exams will be
common with all sections of Math 151 and will be given in the evenings
beginning at 6:30 sharp.
The dates and the
material to be covered are as follows:
- 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).
Exam rules:
- 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.
**********************************************
FINAL EXAM. The final exam is also common with all sections of
Math 151. It will take place on Friday, May 7,
from 11 to 1. This exam will cover the entire course with extra emphasis on
Chapters 2[F] and 9[F]. We are going
to skip Chapters 3&4[F] (Linear Programming).
**********************************************
Level of difficulty
CAUTION: Math 151 is significantly more difficult than Math 150. In part
the difficulty is due to the fact
that there are many new topics. These are interesting and useful subjects,
most of which you have not
seen before. In my opinion, the minimum amount of time that will be required
for an average performance
in this course is 12 hours every week. It is very important that you establish
good study habits at the
beginning of the semester.
The assigned homework represents the MINIMUM amount of material that you must
master for success in this course.
Upcoming lectures
Please note that Math 151 syllabus can be found on page 10 of the Maple
Calculus Lab Manual or in Math 151 Resources on this web page.
- 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
Homework
The homework assignments are designed to help you master the course and prepare
for the
exams. Homework assignments -- with the exception of two Maple assignments --
will NOT be collected.
However, you should write up your solutions in full and come to recitation to
join other students in presenting
solutions and discussing any points that are not clear.
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.
Homework #2 to be discussed in recitations January 18, 20, 25, and 27:
- 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.
Homework #3 to be discussed in recitations February 1, 3:
- 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.
Homework #4 to be discussed in recitations February 8, 10:
- 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.
Homework #5 to be discussed in recitations February 15, 17:
- 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.
Homework #6 to be discussed in recitations February 22, 24:
- 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.
Homework #7 to be discussed in recitations March 1 and 3 is light
so that there is time for additional discussion of the problems from
old homework on topics covered on Exam #3, that is, topics from the
beginning of the course through Chapter F 8 and Chapter C 10.
The new homework problems, which will not
be included on Exam #3, are:
- All core problems from Chapter C 11 Sections 1 and 2.
Correction: The claimed values for a2 and a3
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 a2=100(1.01)^2+100(1.01), and
a3=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.
Homework #8 to be discussed in recitations March 15 and 17:
- 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.
Homework #9 to be discussed in recitations March 22 and 24:
- 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.
Homework #10 to be discussed in recitations March 29 and 31:
- 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.
Homework #11 to be discussed in recitations April 5 and 7:
- 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.
Homework #12 to be discussed in recitations April 12 and 14:
- 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.
Homework #13 (the last!) to be discussed in recitations April 19 and 21
is listed below. As I have explained in class, the text sets up the transition
matrices for Markov processes in a non-standard way. That peculiar usage has
been repeated in the old final exam problems Spring 96 #22 and Spring 98 #17.
In both of those problems, replace T by the transpose of T. Then solve TX = X
with the additional equation that the sum of the entries in X equals 1.
- 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.
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