# MATH 2163 - Calculus III - Fall 2006

• Instructor: Dr. Mathias Schulze
• Class Time and Location:
• Section 3: MWF 9:30-10:20 HES 303
• Section 4: MWF 11:30-12:20 HES 303
• Textbook: James Stewart, Calculus, 5th edition, Brooks/Cole (2003).
• Prerequisites: MATH 2153 - Calculus II
• Course Page:

# Quizzes

In general it is hard to catch up with the lecture once you fell behind. To avoid this problem and incite you to work continuously there will be occasional in-class quizzes throughout the semester. You will be asked to solve a short exercise similar to your homework problems or examples discussed in the lecture. No make-up quiz will be given for any reason, however your 3 lowest quiz scores will be dropped. This policy allows you legitimate absences such as medical emergencies or certain university-related activities. Books, notes, and electronic devices are not permitted during quizzes. The statistics section shows your quiz performance.

# Examinations

There will be 3 midterm in-class exams and a final exam. Dates will be announced at least one week in advance in class and on this page. It is very important that you take the examinations at the scheduled times. If you can not attend a scheduled exam, you must contact me before the exam. A make-up exam will be given only if you have a compelling reason like a family emergency or a severe illness. Books, notes, and electronic devices are not permitted during exams.

The following exam schedule is preliminary.

 Exam Date Midterm 1 Midterm 2 Midterm 3 Final Exam 9/22 10/23 11/20 Section 3: 12/11, 8:00-9:50amSection 4: 12/15, 10:00-11:50am

The statistics section shows your exam performance.

Your goal in this course is to understand abstract concepts and learn correct processes to solve certain types of problems. Therefore you may gain little credit for writing down the answer only. Your work must show clearly how you proceeded to find the answer or why your answer is correct. You will be given more credit for a correct procedure with a computational error as for the correct answer only. On tests it is important that you indicate clearly what is scratch work and what is to be graded. In particular the answer to a computational problem should be marked by the word solution or by drawing a rectangle around it.

The contributions to your total score are weighted as follows.

 Contribution Weight Homework Quizzes 3 Midterms Final Exam 10% 15% 3 x 15% 30%

Your total score will be truncated to an integer percentage and determines your final grade as follows.

 Total Score Final Grade 0-59% 60-69% 70-79% 80-89% 90-100% F D C B A

Curving may be applied in form of a linear adjustment to all scores on a particular exam. I reserve the right to decide borderline cases based on class attendance and subjective impressions such as effort and conscientiousness.

6 week grades are determined based on the above pattern where only one lowest quiz score is dropped and the 1st midterm counts for all 3 midterms and the final exam.

# Honors contracts

For students with honors contract there are X-tra homework problems. The due dates are the same as for the regular homework. However I ask you to hand in these problems separately.

# Free Tutoring Assistance

The Mathematics Learning Resource Center (MLRC) can provide tutoring and other services for this and other mathematics courses. It is located in the lower level of South Murray Hall, across from Theta Pond. Please remember that the tutor's task is to help you to learn, not to do your homework.

# Course schedule

The following course schedule is preliminary. It contains homework with due dates as well as additional course material like Maple worksheets.

Lesson Date Section: Subject Homework [Honors Contract] Due Date Appendix
18/2113.2: Vectors3,4cd,5cd,6df,8,12,14,16,20,22,25,26,31,398/28Maple worksheet (PDF-version)
28/2313.3: The Dot Product1,5,6,8,10,11,16,20,22,24,26,28,38,39,41,448/28
38/2513.4: The Cross Product1,7,9,11,14,16,22,28,30,34,39,458/28
48/2813.5: Equations of Lines and Planes1,4,5,8,10,13,14,15,18,21,25,269/6
58/3013.5: Equations of Lines and Planes27,30,32,34,36,39,47,54,65,689/6Maple worksheet (PDF-version)
69/115.1: Functions of Several Variables2,4,6,8,9,16,20,26,29,309/6Maple worksheet (PDF-version)
-9/4Labor Day
79/615.1: Functions of Several Variables31,32,34,35,38,39,47,51,53,58,[X1]9/11Maple worksheet (PDF-version)
89/815.2: Limits and Continuity1,6,7,9,12,15,18,24,31,369/11
99/1115.3: Partial Derivatives6,17,19,29,30,39,41,51,54,70a9/20
109/1315.4: Tangent Planes and Linear Approximation3,4,5,10,13,16,17,19,[X2]9/20Maple worksheet (PDF-version)
119/1515.4: Tangent Planes and Linear Approximation23-28,30,31,34,409/20
129/1815.5: The Chain Rule3,6,8,9,22,239/20
139/20Review for Midterm 1
149/22Midterm 1: 13.2-5, 15.1-5Solutions
159/2515.6: Directional Derivatives and the Gradient Vector5,6,8,10,13,14,19,209/27Maple worksheet (PDF-version)
169/2715.6: Directional Derivatives and the Gradient Vector26,28,30,40,48,49,[X3]10/4
179/2915.7: Minimum and Maximum Values2,4,8,10,20,3010/4
1810/215.7: Minimum and Maximum Values28,30,39,42,49,5110/4
1910/415.8: Lagrange Multipliers4,8,10,24,[X4]10/11
2010/616.1: Double Integrals over Rectangles1,5,9,1210/11
-10/9Fall Break
2110/1116.2: Iterated Integrals3,5,6,9,14,1610/18
2210/1316.3: Double Integrals over General Regions2,6,9,1110/18
2310/1616.3: Double Integrals over General Regions14,15,19,2310/18
2510/20Review for Midterm 2
2610/23Midterm 2: 15.6-8, 16.1-3Solutions
2810/2713.7: Cylindrical and Spherical Coordinates3,9,13,23,27,54,56,[X5]11/01
2910/3016.4: Double Integrals in Polar Coordinates1-1011/1
3011/116.4: Double Integrals in Polar Coordinates12,17,21,3311/8
3111/316.5: Applications of Double Integrals3,7,9,12,24,[X6]11/8Maple worksheet (PDF-version)
3211/616.6: Surface Area1,2,6,1011/8
3311/8Example sessionMaple worksheet (PDF-version)
3411/1016.7: Triple Integrals2,7,11,1411/15
3511/1316.8: Triple Integrals in Cylindrical Coordinates8,12,15,3411/15
3611/1516.8: Triple Integrals in Spherical Coordinates18,20,22,28,3611/22
3711/17Review for Midterm 3
3811/20Midterm 3: 13.7, 16.4-8Solutions
3911/2216.9: Change of Variables in Multiple Integrals3,5,8,11,14,1511/29
-11/24Thanksgiving Break
4011/2717.1: Vector Fields3,6,24,25,29-32,[X7]11/29
4111/2917.2: Line Integrals2,4,8,10,1412/6
4212/1Snow
4312/417.2: Line Integrals of vector fields
17.3: The Fundamental Theorem for Line Integrals
17.2: 17,18,21,40
17.3: 3,11,22,23
12/6
4412/617.3: The Fundamental Theorem for Line Integrals5,8,9,15,18,29-32,33-
4512/8Review for Final Exam
4612/11
12/15
Final Exam, Section 3: 8:00-9:50am, HES 303.
Final Exam, Section 4: 10:00-11:50am, HES 303.
Solutions

# X-tra Homework Problems

The following X-tra homework problems are intended for students with honors contract. For due dates see the course schedule.

X1)
Find a function of two variables with level curves similar to 15.1.32,35,31,36.
X2)
Write a Maple procedure L(f,a,b) that computes the linearization of the function f(x,y) at the point (a,b). Hint: Look up the keyword "procedure" in the Maple help system and use the Maple worksheet of lecture 10.
X3)
Solve 15.5.53-55. Formulate an analog of 15.5.53.(b) for a function f that satisfies f(t2x,t3y)=tnf(x,y). Can such a function be homogeneous? Explain your answer. Download Solutions.
X4)
Discovery Project on page 1000: Solve problems 1, 3.(a), 3.(b), and 4. Hint for problem 4: Remember what I explained about coordinate changes in the lecture. Download Solutions.
X5)
Solve 13.7.68. Hint: Change from spherical to rectangular coordinates and use the dot product to compute the angle.
X6)
Compute the volume of the intersection of the three cylinders in the discovery project on page 1076. Download Solutions.
X7)
Use Newton's Law of Gravitation to estimate the gravitational force between the earth and the moon.

This section gives you an idea of how your performance relates to that of the other students.

## Homework

 Section 3 HW 1 HW 2 HW 3 HW 4 HW 5 HW 6 HW 7 HW 8 HW 9 HW 10 HW 11 HW 12 HW 13 HW 14 HW 15 Average raw % 84.2 85.4 89.2 89.3 92.6 76.6 87.7 87.1 96.7 94.6 83.6 82.3 76.3 89.2 89.4 Std. dev. raw % 19.8 16.1 10.5 15.1 9.3 22.2 13.5 16.0 10.2 9.2 13.2 16.0 19.9 16.4 13.0
 Section 4 HW 1 HW 2 HW 3 HW 4 HW 5 HW 6 HW 7 HW 8 HW 9 HW 10 HW 11 HW 12 HW 13 HW 14 HW 15 Average raw % 84.1 80.3 89.0 86.7 90.9 76.9 90.2 81.5 97.3 91.3 81.7 80.0 79.0 90.6 83.0 Std. dev. raw % 17.6 23.1 12.8 13.0 10.3 17.2 12.3 19.0 5.5 11.1 17.2 21.4 21.4 14.0 18.9

## Quizzes

 Section 3 Quiz 1 Quiz 2 Quiz 3 Quiz 4 Quiz 5 Quiz 6 Quiz 7 Average raw % 59.4 62.1 40.0 66.6 61.6 72.2 75.0 Std. dev. raw % 26.8 24.6 29.5 34.1 37.3 27.2 18.9
 Section 4 Quiz 1 Quiz 2 Quiz 3 Quiz 4 Quiz 5 Quiz 6 Quiz 7 Average raw % 60.5 64.1 54.5 74.7 75.7 70.9 74.6 Std. dev. raw % 27.3 25.6 29.2 27.1 34.3 28.0 16.2

## Exams

 Section 3 Midterm 1 Midterm 2 Midterm 3 Final Exam Average curved % 78.47 82.06 78.30 79.19 Std. dev. curved % 13.04 14.60 17.75 13.19
 Section 4 Midterm 1 Midterm 2 Midterm 3 Final Exam Average curved % 78.59 83.53 79.44 79.35 Std. dev. curved % 12.68 13.23 18.49 15.82