Calculus II
Math 250 - 5
Spring
2002
Instructor: Prof. Dr. rer. nat. Henri Schurz
Time: MTWF 1:00 - 1:50 p.m., Location: LSII 450
Office Hours: MWF 12:00-12:50, 15:10-16:00 pm
Office Location: Neckers 265
(Last Update: 04/30/02)
Sample final exams are available before the exam dates
from Copies and More! Overall grades and final exam results can be seen in
my office between Wednesday, May 8, 4pm and Friday, May 10, 3pm. You
must personally come to my office to find out about your grades. After
that time slot I will turn in the overall grades to the university recording
center and I will be off campus after May 11!
Textbook:
Calculus: Early Transcendentals, 4th Edition.
by J. Stewart, Brooks/Cole Publishing Company, Pacific Grove, 1999.
Read this
Without Tears:
WHAT IS EXPECTED OF YOU
(From "Teaching at the University Level" by Stephen Zucker, Notices Amer.
Math. Soc. 43 (1996), p. 863):
1. You are no longer in high school. The great majority of you, not having
done so already, will
have to discard high school notions of teaching and learning and replace
them by university-level
notions. This may be difficult, but it must happen sooner or later, so
sooner is better. Our goal is
more than just getting you to reproduce what was told you in the classroom.
2. Expect to have material covered at two to three time the pace of high
school. Above that, we
aim for greater command of the material, especially the ability to apply
what you have learned to
new situations (when relevant).
3. Lecture time is at a premium, so it must be used efficiently. You cannot
be "taught" everything
in the classroom. It is YOUR responsibility to learn the material. Most of
this learning must
take place outside the classroom. You should be willing to put in two hours
outside the classroom
for each hour of class.
4. The instructor's job is primarily to provide a framework, with some of
the particulars, to guide
you in doing your learning of the concepts and methods that comprise the
material of the course. It
is not to "program" you with isolated facts and problem types nor to monitor
your progress.
5. You are expected to read the textbook for comprehension. It gives the
detailed account of the
material of the course. It also contains many examples of problems worked
out, and these should
be used to supplement those you see in the lecture. The textbook is not a
novel, so the reading
must often be slow-going and careful. However, there is the clear advantage
that you can read it
at your own pace. Use pencil and paper to work through the material and to
fill in omitted steps.
(till here: extracted from Joe Mashburn (Uni Dayton)/
joe.mashburn@udayton.edu)
6. Do not expect that exam problems are exactly the same as in homework
problems. Homework problems should be understood to strengthen and to
improve
your knowledge on subject related issues.
7. Work with your tutors and / or TA's as much as you can and form study groups if
necessary, ask subject related questions, and be active.
8. Read further additional literature (Do not stick to course material
completely!). The professors can always give you more literature hints.
9. Make always written notices what the instructor tells you about the
subject, work through your course notes after the lectures continuously.
10. We all expect mutual respect, polite, correct, honest and
sincere personal behaviour on student's and instructor's side as it
should be common among human beings.
(These are my main 10 principles for success in academic studies!)
Course
Description: This course is the second part of a two
semester course on Calculus, meant to be an introduction to basic
aspects of functions, series, limits, differentiation and integration.
Calculus II especially deals with techniques of integration, its
applications (volumes, surface areas, arc length), parametric curves
(polar coordinates) and series (summation rules, convergence test
criteria, Taylor MacLaurin and Binomial series).
Calculus is a very large field, and we will certainly
not be able to cover all of the important techniques in a
one or two-semester course. A preliminary list of topics covered
includes l'Hospital's rule, basic techniques of integration,
integration by parts, trig integrals, trig substitution, volumes by
revolution, surface areas, arclength, polar coordinates, parametric
curves, series, convergence tests (comparison, ratio, root, integral
tests), absolute convergence, alternating series, Binomial and
Taylor - MacLaurin series and approximate integration.
(I am afraid of skipping any other very important issues).
Prerequisites
and Development of Contents:
This course should be accessible to any student with a $C-$ in Math
150 or replacement exam. However, I strongly advice you to review
your knowledge which you should know from high school math in your
previous carrier. I will always assume that you profoundly know the
facts from that part, including standard trigonometric formulas.
The content of this course itself should very nearly coincide with that of
Stewart's book, running from chapter 7.1 until 11.12.
I am not perfect. However, be sure that I
will do my very best to please you and your expectations.
Readings,
Problem Sets, Exams:
Readings and problem sets will be from the text and my manuscript, and
it will be assigned in classes and perhaps additionally published at
my homepage. Exams will cover all material covered in the lectures,
recitation classes and/or the readings. James Stewart seems to
have put a fair effort into his presentation from very practically
oriented point of view, and their approach is probably quite different
from what you've seen before (hopefully not). Thus, I really encourage
you to read the book as lectures advances.
Exam
Dates:
- Midterm I: Tuesday, February 19, 2002 (in class)
- Midterm II: Tuesday, March 26, 2002 (in class)
- Midterm III: Tuesday, April 23, 2002 (in class)
- Final: Monday, May 6, 2002
(QUIGLEY 203, 10:10 am - 12:10 pm)
Grading Strategies - Grade Distribution:
- 20 (15) % Homeworks & Quizzes, 60 % Midterms (20 % each exam), 20 (25) % Final Exam
- 90 % <= A-class, 75 % <= B-class, 60 % <= C-class, 45 % <= D-class
- Deviation departmental guideline: Except for very well-documented cases,
under normal circumstances, there is only such an overall grade possible
which differs from the grade result of final exam at most about one grade.
- Your scores from 15 homeworks & 2 quizzes are recorded in my office,
taking individually the best 12 homeworks. Work for the two extra credit
problems must be turned in before May 8. The score of the final exam is
also evaluated according to the gradeline meeting on total grade
distribution of all students after
the final date. Thus, your results in the midterms and final exams will
rule over the remaining portion of quizzes and homeworks.
- Grading and evaluation will be completed by the afternoon of May 8.
Course
Syllabus (Last Update: 01/10/02) - You will need an utility
like ghostview to read it!
Please, note you need ghostview to read the postscript files after
downloading! See http://www.cs.wisc.edu/~ghost/index.html for more software
product information.
Remarks for Withdrawal:
The last day to withdraw from the course without a grade is Friday, January
25. The last day to withdraw from the course with a grade of W is
Monday, March 18. You should be aware that the grade INC (incomplete) cannot
be used as a withdrawal and can only be assigned to students who
are passing the course and for reasons beyond their control cannot complete
all class assignments. See the undergraduate catalog for more details.
Remarks for the Prerequisites and First Week:
Please, review problems from sections 1 to 6. You should know the
fundamental theorem of calculus, standard differentiation and integration rules,
and a strong grasp what is a function. In particular, recall the table of
standard antiderivatives.
Remarks for the 1st Midterm Exam:
Please, review your notes and sections 7.1. - 8.2. The midterm exams are
not of multiple choice. Midterm I will contain 6 problems (no word
problems). The main goal is to check your capability of learnt calculus
techniques. In particular, you should be sure in substitution techniques,
integration by parts, integration by partial fractions, rationalizing
substitution, trigonometric substitution, arc length and surface area
computations, approximate integration and Riemann sum techniques.
No books, no notes, no
tables, no calculators at all, no notebooks are permitted (pocket
calculators wouldn't help you much anyway).
I don't expect that you know all formulas, but you should be able to
understand and work with them. Do the sample midterm exam I which I will
release shortly before the exam and you will discover all formulas you
need to solve the midterm problems.
Remarks for the 2nd Midterm Exam:
Please, review your notes and sections 7.1. - 10.5. The midterm exams are
not of multiple choice. Midterm II will contain 6 problems (no word
problems). The main goal is to check your capability of learnt calculus
techniques. In particular, you should be sure in substitution techniques,
integration by parts, integration by partial fractions, rationalizing
substitution, trigonometric substitution, improper integrals, rule of
L'Hospital, arc length and surface area
computations in general from sections 7.1. - 8.2. There will be no
Riemann sum and no approximate integral on the test this time.
In addition to that, you must know parametric curves, area, arc-length and
surface area computations for parametric curves, Polar coordinates,
area and arc-length computation for curves in polar coordinates from
section 10.1. - 10.5.
No books, no notes, no
tables, no calculators at all, no notebooks are permitted (pocket
calculators wouldn't help you much anyway).
I don't expect that you know all formulas, but you should be able to
understand and work with them. Do the sample midterm exam II which I will
release shortly before the exam and you will discover all formulas you
need to solve the midterm problems.
Remarks for the 3rd Midterm Exam:
Please, review your notes and sections 11.1. - 11.10. The midterm exams are
not of multiple choice. Midterm III will contain 10 problems (no word problems,
each 10 points). The main goal is to check your capability of learnt calculus
techniques for series computations. In particular, you should be sure in
convergence concepts (absolute, conditional), alternating series test,
ratio and root test, integral test, comparison and limit comparison test,
Abel's p-series test, geometric series, intervals of convergence,
absolute convergence radius, power series, Taylor series, McLaurin series,
binomial series and related topics. Best to review your problems from
homeworks and class notes too. No books, no notes, no
tables, no calculators at all, no notebooks are permitted (pocket
calculators wouldn't help you much anyway).
I don't expect that you know all formulas, but you should be able to
understand and work with them. Do the sample midterm exam III which I will
release shortly before the exam and you will discover all formulas you
need to solve the midterm problems.
Remarks for the Final Exam:
The final exam is a fairly comprehensive exam for 2 hours.
The topics run from chapter 7 till 11.
The final involves problems on rule of L'Hospital, basic
integration techniques, tangents and derivatives of parametric curves,
polar coordinates and related areas, arc-length and surface area computations,
Taylor and MacLaurin series, convergence of series, estimates of series
remainder terms, power series, interval and radius of convergence, and
improper integrals. Compare it with Copies & More handout of old finals
edited by math department. Old final exams are discussed within the last
classes before the exam week.
Scientific calculators are probably allowed (but better check the
department policy on it now). Other calculators,
notebooks, notes, cheating sheets and books are not permitted.
Bring your I.D. with photo with you. Only photo I.D. checked
exams will be accepted!
Current Course Outline (Last Update:
04/20/02):
Week 1 : Introduction, 4.4., 7.1.-7.2
Week 3 : 7.4.-7.5., 7.7. (7.6 omitted)
Week 6 : Review, Exam I, 10.1. (8.4.-8.5, 9 omitted)
Week 8 : 10.3.-10.5 (10.6.-10.7 omitted), 11.1
Week 9 : Spring Break (Hurra!)
Week 10 : Review Week & Sample Exam II
Week 11: 11.1., Exam II, 11.2-11.3
Week 15: 11.11.-11.12, Sample Exam & Review, Exam III
Week 16: Selected Optional Topics, Review for Final Exam
Thus, sections 7.6, 8.4.-8.5, 9.1.-9.7, 10.6.-10.7 are omitted.
If some time is left we will address issues of multivariate
calculus, i.e. topics out of 14.1, 14.3, 15.1.-15.3 in the
section titled ``Selected Optional Topics''.
Remarks for Homeworks, Quizzes and Recitation Classes:
The homeworks and quizzes are assigned in FRIDAY classes and are due by
the next FRIDAY thereafter. The recitation takes place during class hours.
The recitation discussion is meant to strengthen your knowledge in related
areas touched in lectures. Thus, your active participation is required.
Random quizzes results are counted as extra credit added to your weakest
part of grading sections. We rarely anticipate to arrange quizzes, basicly
to rise the attention to continuous class participation.
The homeworks and quizzes play an essential role in forming your grade
according to the presented grade distribution.
Homework Assignments (Collected & Graded)
(due on Fridays):
Week 16: 11.10.: no. 6, 8, 15, 16, 22, 28, 30, 44, 38, 58 (due on 05/03/02)
Week 15: 11.8.: no. 4, 14, 25, 26, 31, 34a | 11.9.: no. 9, 14, 26, 28 (due on 04/26/02)
Week 14: 11.5.: no. 24, 30, 36 | 11.6.: no. 4, 12, 14, 20, 26, 30 | 11.7.:
no. 38 (due on 04/19/02)
Week 13: 11.3.: no. 7, 8, 26 | 11.4.: no. 5, 6, 12, 34 | 11.5.: no. 3, 4, 14
(due on 04/12/02)
Week 12: 11.1.: no. 17, 18, 29, 30 | 11.2.: no. 11, 12, 44, 66 | 11.3.: no.
4, 28 (due on 04/05/02)
Week 11: 10.4.: no. 19, 20, 24 | 10.5.: no. 8 | 11.1.: no. 8, 12, 34,
37, 56, 58 (due on 03/29/02)
Week 10: 10.4.: no. 14, 48, 60, 62, 68 | 10.5.: no. 4, 6, 20, 28, 46 (due on 03/22/02)
Week 8: 10.3.: no. 6, 16, 17, 18, 25, 29 | 10.4.: no. 4, 12, 26, 50 (due on 03/08/02)
Week 7: 10.1.: no. 20, 22, 28 | 10.2.: 4, 8, 10, 22, 29, 30, 34 (due on 03/01/02)
Week 6: 8.2.: no. 14, 20, 31 | 8.3.: no. 20, 21, 22, 25, 26 | 10.1.: no. 6,
12
Week 5: 7.8.: 40, 54, 58, 71 | 8.1.: 5, 7, 8, 22 | 8.2.: 4, 8
Week 4: 7.5.: 2, 6, 18, 24, 50, 52 | 7.7.: 11, 16 | 7.8.: 2, 14
Week 3: 7.4.: 2, 8, 12, 18, 26, 32, 52, 60 | 7.5.: 34, 46
Week 2: 7.2.: 2, 6, 20, 26, 64 | 7.3.: 2, 4, 10, 20, 28
Week 1: 4.4.: 6, 8, 10, 20, 73 | 7.1.: 10, 24, 32, 48, 54
On-line Exercises To Check Prerequisites From Calculus I:
For those who like to work with internet access and check their
preknowledge electronically, there are on-line exercises related to Calculus I
available. See
On-line Web-Drill