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Analytic Geometry & Calculus A (Math 243 sections 016, 017 & 018) Fall 2002
KRB 204 - Monday, Wednesday, & Friday 1115-1205
PRN 227 - Tuesday & Thursday 0800-0850 (discussion section 016 only)
SHL 116 - Tuesday & Thursday 1200-1250 (discussion section 017 only)
PRN 325 - Tuesday & Thursday 1300-1350 (discussion section 018 only)
©2002 L. F. Rossi All rights reserved.

Prof. L. F. Rossi
Office: Ewing 524
Telephone: x1880
Email: rossi@math.udel.edu
WWW: http://math.udel.edu/ $\sim$ rossi

Course description: The main topics of Calculus A involve the differentiation and integration of functions of one variable. Calculus forms the foundation for most, if not all, of the physical sciences in addition to most social sciences.

Prerequisites: There are no prerequisites for this course, but all students should have had the equivalent of two years of high school algebra, one year of geometry and one year of trigonometry.

Your objectives:

I hope everyone will hone their mathematical abilities to reason quantitatively, logically, confidently and eventually correctly. By the end of this course, every passing student should ...

... understand limits of representative functions ³ and be able to compute them where they exist.
... be able to determine whether or not a representative function is continuous or not.
... know the difference between a tangent and secant line, and compute the tangent and secant line.
... know the relationship between the derivative of a function and the tangent line to the function at a given point. Students should master this relationship to a point where if given an incomplete set of information about a function or its tangent line, students should be able to complete the set.
... be able to interpret the derivative of a function describing a quantity in an application.
... be able to compute the derivatives of representative functions by judicious use of the power rule, product rule, quotient rule and chain rule.
... understand the first and second derivative test.
... compute the local and global extrema, and inflection points of representative functions.
... form connections between a function to its graph using information about its derivatives, extrema, concavity and inflection points.
... be able to approximate the root of a function using Newton's method.
... be able to antidifferentiate representative functions with the judicious use of substitution, if necessary.
... understand the Fundamental Theorem of Calculus.
... be able to find the area between two curves.
... be able to compute volumes of solids of revolution through the judicious use of cylindrical shells or disks.

Your resources: All of the following will help you achieve your objectives.

$\bullet$: Time: The best way to learn mathematics is to spend time with it. It is your responsibility to come to class each day, and it is unlikely that you will pass if you miss more than a day or two, regardless of the reason. Attendance is crucial to success in this course.
$\bullet$: Textbook: Calculus, 4 $^{\rm th}$ ed. by James Stewart.
$\bullet$: Office hours: Monday 1000-1100, Thursday 1530-1630, Friday 0900-1000 or by appointment. This is time that I have set aside especially for you. Office hours are one of the most valuable and least used resources at the University, and I hope you will take advantage of them. I want to help you learn this material, so do not be shy about seeing me outside of class. Your exams will only be distributed during office hours. If you need to see me at a time other than an office hour, feel free to ``drop in'' or make an appointment.
$\bullet$: Calculator: I expect everyone to have at least a scientific calculator. You will not be allowed to use calculators on exams.
$\bullet$: Your classmates: Math is not a competitive sport. There are many obvious reasons to work together. Even if you end up helping others most of the time, teaching is one of the best ways to gain a deeper understanding of a subject.

Grading policy: Your grade is determined solely by your understanding of mathematics and your ability to communicate this knowledge to me on exams and other assignments.

Homework & quizzes 16%

Report problem 4 %

Exams (20% each) 60%

Final exam 20%

Final letter grades will be assigned strictly based on the following percentages of your total point score:
100 $\leftarrow$ A $\rightarrow$ 93 $\leftarrow$ A- $\rightarrow$ 90 $\leftarrow$ B+ $\rightarrow$ 87 $\leftarrow$ B $\rightarrow$ 83 $\leftarrow$ B- $\rightarrow$ 80 $\leftarrow$ C+ $\rightarrow$ 77 $\leftarrow$ C
C $\rightarrow$ 73 $\leftarrow$ C- $\rightarrow$ 70 $\leftarrow$ D+ $\rightarrow$ 67 $\leftarrow$ D $\rightarrow$ 63 $\leftarrow$ D- $\rightarrow$ 60 $\leftarrow$ F $\rightarrow$ 0

I reserve the right to adjust this scale to improve grades if the course material proves to be unreasonably demanding.

Exams: All exams will occur in class on the days listed on the syllabus. There are no makeup exams without prior notification and a valid, documented reason.

Homework and quizzes: Homework will be collected in your discussion section, and graded homework will be returned in your discussion section. Your discussion instructor may or may not give quizzes at his discretion. I will drop your lowest three homework or quiz scores during the semester. I do not accept late homework, so do not squander these three assignments. You might be sick sometime and not be able to do your homework on time. Each assignment is worth 10 points, 5 for completeness and 5 for the accuracy of several randomly selected problems.

Student conduct: To provide the best learning environment for all my students, I expect all my students to conduct all their scholarly activities with honesty and integrity. Students should note that in certain situations doing nothing can be dishonest. Though I hope there will never be a need to address academic dishonesty, I will strongly enforce all provisions noted in the Academic Regulations for Undergraduates. See The University of Delaware Undergraduate and Graduate Catalog

http://www.udel.edu/catalog/current/ugacadregs.html#acadhonesty

for further discussion on basic responsibilities.

Tentative schedule:

Week of Section(s) Topic(s)

Sep 4 Appendices A-D Why we do it, precalculus review

Sep 9 App. D, 2.1-2.2 Review (cont'd), limits.

Sep 16 2.3, 2.5, 2.6 Limits (cont'd), tangents.

Sep 23 3.1-3.3 Derivatives and differentiation.

Sep 30 3.5 Derivatives of trig. functions. Review. Exam 1.

Oct 7 3.6-3.8 The chain rule, implicit differentiation and higher derivatives.

Oct 14 3.9, 3.10, 4.1 Related rates, linear approximation, differentials, and extreme values.

Oct 21 4.2-4.4 The Mean Value Theorem, curves and to $\infty$ and beyond.

Oct 28 4.5 Curve sketching. Review. Exam 2.

Nov 4¹ 4.7, 4.9, 4.10 Optimization, Newton's Method, antiderivatives,

Nov 11 5.1, 5.2, 8.7 Areas, definite integrals and numerical integration.

Nov 18 5.3-5.5 The Fundamental Theorem of Calculus, indefinite integrals and substitution.

Nov 25² 6.1 Areas. Review. Exam 3.

Dec 2 6.2-6.3 Volumes of revolution: disks and shells.

Dec 9 6.4 Work. Review.

Important dates:

Sep 17 Last day to drop without record.

Oct 4 Exam 1.

Oct 29 Last day to drop with a ``W''.

Nov 1 Exam 2.

Nov 27 Exam 3.

TBA Final exam.

Problem sets: The best way to learn and understand mathematics is by trying problems. An excellent way to prepare for an exam is to make sure you can solve these and other non-assigned problems without referring to your book or notes. To receive credit, you must show your work. Below are problem assignments from the book that you must hand in.

Assignment Problems

1 A: 26, 37, 38, 42, 55, 56, 59, 60. B: 13, 14, 21, 24, 27, 32, 36, 49, 51, 56, 62.

C: 4, 7, 9, 19, 22, 25.

2 D: 1-3, 7-9, 30, 45, 48, 59, 60, 67-70. 2.1: 1, 5, 6, 8. 2.2: 1, 2, 7, 10.

3 2.2: 21, 24, 31, 36. 2.3: 1, 2, 5, 10, 21, 22, 23. 2.5: 7, 13, 14, 16-18, 23, 24.

2.6: 1, 2, 7, 8, 16, 19.

4 2.3: 46, 57, 58. 2.5: 38, 39, 41, 42. 2.6: 26. 3.1: 4-6, 13, 15, 16 18, 25, 26.

3.2: 4, 14, 17, 18, 20, 21, 23. 3.3: 1, 2, 5, 11-13, 16, 23, 26, 27, 35, 39.

5 3.1: 31-33. 3.2: 30, 32, 42. 3.3: 61, 62, 75, 78, 81. 3.5: 1, 2, 6, 9, 15, 17, 20, 35.

6 3.5: 36, 43, 46, 47. 3.6: 1-3, 6, 7, 13, 14, 27, 42, 45. 3.7: 2-4, 7, 13, 14, 28, 29, 35.

3.8: 1, 2, 5, 8, 15, 20, 26-28, 36, 39.

7 3.6: 47, 49, 53. 3.7: 45, 47, 49, 53. 3.8: 40, 43, 45, 46, 63. 3.9: 3, 4, 7, 19, 21, 25, 30-32, 34.

3.10: 1, 3, 6, 7, 17, 18, 23, 24, 39. 4.1: 3, 4, 7, 10, 32, 33, 44, 45, 49.

8 3.10: 42, 44, 48. 4.1: 52, 55, 66, 70. 4.2: 1, 2, 5, 6, 12, 14, 19, 20.

4.3: 1, 2, 5, 6, 9, 11, 13, 14, 17-19, 32. 4.4: 7-9, 12, 15, 16, 28, 39, 40.

9 4.2: 28, 32, 33. 4.3: 34, 46, 53, 58, 59. 4.4: 42, 48, 49, 56. 4.5: 1, 4, 7, 19, 26.

10 4.5: 50-52. 4.7: 9, 11, 28, 31, 35, 40. 4.9: 6, 7, 12, 15, 24. 4.10: 1, 2, 5, 6, 12, 19, 25, 26, 34.

11 4.7: 47, 50, 52, 54. 4.9: 30-32, 35, 37. 4.10: 37, 43, 54, 65, 70. 5.1: 1, 3, 4, 11, 12, 15, 16, 24.

5.2: 1, 7, 8, 15, 16, 19, 23, 29, 32, 43, 44, 51, 52. 8.7: 7-9, 11, 12, 18, 24, 27, 38, 45, 46.

12 5.2: 56, 63, 64. 5.3: 5, 6, 11, 17, 18, 22, 25, 26, 28, 42, 46, 51, 52, 57.

5.4: 1, 2, 3, 7, 8, 25, 36, 41, 45, 47, 49. 5.5: 1, 2, 4-6, 11, 16, 21, 30, 38.

13 5.4: 50, 60, 63. 5.5: 41, 54, 66, 68, 73, 74, 81.

6.1: 3, 4, 6, 13, 20, 23, 25, 27, 29, 40, 45, 47, 49-51.

14 6.2: 1, 3, 6, 10, 14, 15, 18, 20, 21, 32, 40, 48, 59, 61, 66, 67, 69.

6.3: 3, 4, 6, 7, 10, 11, 13, 15-17, 20, 22, 23, 35, 40, 43, 44.

15 (optional) 6.4: 2, 3, 8, 9, 18, 19, 22, 23, 25, 26.

Report problems: A special component of this course called report problems are designed to augment the textbook's approach. They will focus on problem solving, abstract reasoning and applications. The guidelines for reports are:

$\bullet$: Reports must be handed in by the due date.
$\bullet$: The intended audience of the report is your fellow classmates. You must explain each step you take clearly, neatly and accurately. A report should not exceed five pages.
$\bullet$: A single report may be submitted by teams of up to three people. Each team member must contribute roughly one third to the content of the report.
$\bullet$: Reports either receive full credit or a ``REDO.'' Full credit is awarded for a clear, concise and correct solution. REDO's are awarded otherwise.
$\bullet$: One can resubmit a corrected REDO for full credit for up to two weeks after reports are returned.
$\bullet$: Periodically, you may be asked to submit a progress report to help to make steady progress toward completing your reports. To receive credit for a report problem, you must hand in all the progress reports.

I have excellent examples of report problems available in my office for you to look at if you are unsure of what I expect.

About this document ...

Next: About this document ...

Louis F Rossi
2002-08-30

Homework & quizzes	16%
Report problem	4 %
Exams (20% each)	60%
Final exam	20%

Week of	Section(s)	Topic(s)
Sep 4	Appendices A-D	Why we do it, precalculus review
Sep 9	App. D, 2.1-2.2	Review (cont'd), limits.
Sep 16	2.3, 2.5, 2.6	Limits (cont'd), tangents.
Sep 23	3.1-3.3	Derivatives and differentiation.
Sep 30	3.5	Derivatives of trig. functions. Review. Exam 1.
Oct 7	3.6-3.8	The chain rule, implicit differentiation and higher derivatives.
Oct 14	3.9, 3.10, 4.1	Related rates, linear approximation, differentials, and extreme values.
Oct 21	4.2-4.4	The Mean Value Theorem, curves and to $\infty$ and beyond.
Oct 28	4.5	Curve sketching. Review. Exam 2.
Nov 4¹	4.7, 4.9, 4.10	Optimization, Newton's Method, antiderivatives,
Nov 11	5.1, 5.2, 8.7	Areas, definite integrals and numerical integration.
Nov 18	5.3-5.5	The Fundamental Theorem of Calculus, indefinite integrals and substitution.
Nov 25²	6.1	Areas. Review. Exam 3.
Dec 2	6.2-6.3	Volumes of revolution: disks and shells.
Dec 9	6.4	Work. Review.

Sep 17	Last day to drop without record.
Oct 4	Exam 1.
Oct 29	Last day to drop with a ``W''.
Nov 1	Exam 2.
Nov 27	Exam 3.
TBA	Final exam.

Assignment	Problems
1	A: 26, 37, 38, 42, 55, 56, 59, 60. B: 13, 14, 21, 24, 27, 32, 36, 49, 51, 56, 62.
	C: 4, 7, 9, 19, 22, 25.
2	D: 1-3, 7-9, 30, 45, 48, 59, 60, 67-70. 2.1: 1, 5, 6, 8. 2.2: 1, 2, 7, 10.
3	2.2: 21, 24, 31, 36. 2.3: 1, 2, 5, 10, 21, 22, 23. 2.5: 7, 13, 14, 16-18, 23, 24.
	2.6: 1, 2, 7, 8, 16, 19.
4	2.3: 46, 57, 58. 2.5: 38, 39, 41, 42. 2.6: 26. 3.1: 4-6, 13, 15, 16 18, 25, 26.
	3.2: 4, 14, 17, 18, 20, 21, 23. 3.3: 1, 2, 5, 11-13, 16, 23, 26, 27, 35, 39.
5	3.1: 31-33. 3.2: 30, 32, 42. 3.3: 61, 62, 75, 78, 81. 3.5: 1, 2, 6, 9, 15, 17, 20, 35.
6	3.5: 36, 43, 46, 47. 3.6: 1-3, 6, 7, 13, 14, 27, 42, 45. 3.7: 2-4, 7, 13, 14, 28, 29, 35.
	3.8: 1, 2, 5, 8, 15, 20, 26-28, 36, 39.
7	3.6: 47, 49, 53. 3.7: 45, 47, 49, 53. 3.8: 40, 43, 45, 46, 63. 3.9: 3, 4, 7, 19, 21, 25, 30-32, 34.
	3.10: 1, 3, 6, 7, 17, 18, 23, 24, 39. 4.1: 3, 4, 7, 10, 32, 33, 44, 45, 49.
8	3.10: 42, 44, 48. 4.1: 52, 55, 66, 70. 4.2: 1, 2, 5, 6, 12, 14, 19, 20.
	4.3: 1, 2, 5, 6, 9, 11, 13, 14, 17-19, 32. 4.4: 7-9, 12, 15, 16, 28, 39, 40.
9	4.2: 28, 32, 33. 4.3: 34, 46, 53, 58, 59. 4.4: 42, 48, 49, 56. 4.5: 1, 4, 7, 19, 26.
10	4.5: 50-52. 4.7: 9, 11, 28, 31, 35, 40. 4.9: 6, 7, 12, 15, 24. 4.10: 1, 2, 5, 6, 12, 19, 25, 26, 34.
11	4.7: 47, 50, 52, 54. 4.9: 30-32, 35, 37. 4.10: 37, 43, 54, 65, 70. 5.1: 1, 3, 4, 11, 12, 15, 16, 24.
	5.2: 1, 7, 8, 15, 16, 19, 23, 29, 32, 43, 44, 51, 52. 8.7: 7-9, 11, 12, 18, 24, 27, 38, 45, 46.
12	5.2: 56, 63, 64. 5.3: 5, 6, 11, 17, 18, 22, 25, 26, 28, 42, 46, 51, 52, 57.
	5.4: 1, 2, 3, 7, 8, 25, 36, 41, 45, 47, 49. 5.5: 1, 2, 4-6, 11, 16, 21, 30, 38.
13	5.4: 50, 60, 63. 5.5: 41, 54, 66, 68, 73, 74, 81.
	6.1: 3, 4, 6, 13, 20, 23, 25, 27, 29, 40, 45, 47, 49-51.
14	6.2: 1, 3, 6, 10, 14, 15, 18, 20, 21, 32, 40, 48, 59, 61, 66, 67, 69.
	6.3: 3, 4, 6, 7, 10, 11, 13, 15-17, 20, 22, 23, 35, 40, 43, 44.
15 (optional)	6.4: 2, 3, 8, 9, 18, 19, 22, 23, 25, 26.