## Math 20C: Fundamentals of Calculus II

### Fall 2008

**Course Info:**

**Course:**Fundamentals of Calculus II**Lectures:**Monday, Wednesday, Friday, 12:20 p.m. - 01:10 p.m.**Dates:**Wednesday, 3 September - Wednesday, 10 December 2008**Room:**Perkins 107**Instructor:**John Voight**Office:**16 Colchester Ave, Room 207C**Phone:**(802) 656-2271**E-mail:**jvoight@gmail.com**Office hours:**Mondays, 11:00 a.m. - 12 noon, 2:30 p.m. - 3:30 p.m.; Wednesdays, 11:00 a.m. - 12 noon; or please make an appointment!**Course Web Page:**http://www.cems.uvm.edu/~voight/20/**Instructor's Web Page:**http://www.cems.uvm.edu/~voight/**Prerequisites:**Math 19 or permission.**Required Text:**Stefan Waner and Steven Costenoble, Applied Calculus, 4th edition, and website.**Grading:**Weekly homework will count for 10% of the grade, weekly quizzes will count for 20%, three exams will count for 45%, and a comprehensive final exam will count for 25%.**Final Exam:**Thursday, 18 December 2008, 3:30 - 6:30 p.m.

**Syllabus:**

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**Syllabus**

According to the course catalogue, the course will cover an "introduction to integral calculus with a wide variety of applications."

More specifically, Fundamentals of Calculus II is the second course in a two course sequence. The underlying applications of integral calculus will be investigated along with some methods for doing multivariable calculus (chapters 6-9 and P). The topics will include, but not be limited to, basic integration, *u*-substitution, integration by parts, improper integrals, probability, differential equations, and multivariable functions with multivariable calculus. This understanding will be discovered and shown via mathematical modeling of real world situations. An emphasis will be made to understand these new concepts graphically, numerically, verbally, and algebraically. The course work will involve some fairly intense computations and mathematical modeling, and it is required that students purchase or obtain an appropriate calculator. A TI-83/84 Graphing calculator is highly recommended. Students will be allowed to use a calculator on all assignments and tests, but please be aware that the instructor may ask for all work to be shown in order to receive credit.

**Computational Tools:**

Open a Sage worksheet by connecting to chaka.uvm.edu (link will only work on campus or on a machine with a VPN client installed); or just go to the Sage notebook, which is hosted by William Stein at the University of Washington.

Sage is free software. See the download instructions to install it on your machine.

Mathematica can be download and installed here. Here is a Mathematica worksheet for plotting 3D surfaces.

There is also a numerical integrator available.

**Homework:**

Homework is due on Wednesdays. The homework will only be graded "for completeness"--I will rarely grade individual problems. It is *extremely* important that you attempt all of the problems listed and seek help for those which you are unable to finish: the only way to learn mathematics is to practice, make mistakes, and correct them!

Cooperation on homework is permitted (and encouraged), but if you work together, do not take any paper away with you--in other words, you can share your thoughts (say on a blackboard), but you have to walk away with only your understanding. In particular, write the solution up on your own.

**HW #1**, due 10 Sep:

Section 6.1: 1-45 (odd), 49, 63**HW #2**, due 17 Sep:

Section 6.2: 1-17 (odd), 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 69, 73

Section 6.3: 1, 3, 5, 9, 13, 17**HW #3**, due 24 Sep:

Section 6.3: 19, 25, 27, 29, 33, 35, 37, 63-69 (odd)

Section 6.4: 1-17 (odd), 21, 25, 29, 33, 37, 39, 51, 53, 57

See the computational resources above for Problems 35 and 37.**HW #4**, due 1 Oct:

Section 7.1: 1, 5, 7, 13, 15, 17, 19, 23, 27, 35, 39, 45**HW #5**, due 8 Oct:

Section 9.3: 1-23 (odd), 41, 43, 45, 51

Section 7.2: 1, 5, 9, 13, 17, 21, 23, 25, 27**HW #6**, due 15 Oct:

Section 7.3: 1, 3, 5, 6, 25, 27, 35

Section 7.4: 25, 27, 29, 31, 33, 35, 49 Section 7.5: 1, 3, 5, 7, 9**HW #7**, due 22 Oct:

Section 7.5: 11, 27, 29, 31, 35

Section 7.6: 1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 31, 34**HW #8**, due 29 Oct:

Section 8.1: 1, 3, 9-21 (odd), 25, 31-41 (odd)**HW #9**, due 5 Nov:

Section 8.2: 3-9 (odd), 11-19, 23, 27, 29, 31, 33, 39, 41, 45

Section 8.3: 1-11 (odd)

See the computational resources above for a sample Mathematica worksheet.**HW #10**, due 12 Nov:

Section 8.3: 19, 23, 25, 29, 31, 43, 45

Section 8.4: 1-11, 13, 15, 21, 25, 33, 35, 39**HW #11**, due 19 Nov:

Section 8.5: 1, 3, 5, 7, 9, 11, 19, 23, 29

~~Section 8.6: 1, 3, 7, 11, 17, 19, 21, 23, 25, 27, 37~~**HW #12**, due 10 Dec:

Section P.2: 1, 3, 7, 9, 11, 13, 15, 17-27, 29-39 (odd)

Section P.3: 1, 3, 7, 9, 11, 15, 21-37 (odd), 38, 63, 65, 67, 69

**Worksheets:**

When there are worksheets from group work in class, they will be posted here.

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**Worksheet, Day #3 (September 8)**

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**Worksheet, Day #5 (September 12)**

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**Worksheet, Day #9 (September 22)**

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**Worksheet, Day #12 (September 29)** ...
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**Solutions**

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**Worksheet, Day #14 (October 3)** ...
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**Solutions**

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**Worksheet, Day #17 (October 10)** ...
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**Solutions**

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**Worksheet, Day #19 (October 15)** ...
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**Solutions**

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**Worksheet, Day #21 (October 20)**

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**Worksheet, Day #34 (November 19)**

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**Worksheet, Day #40 (December 10)** ...
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**Solutions**

**Quizzes:**

Every Wednesday there will be a 15 minute quiz. The problem(s) on the quiz will be taken directly from the homework, possibly with a few numerical changes. Your lowest two scores will be dropped. No make-up quizzes will be permitted.

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**Quiz #1 (September 10)** ...
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**Solutions**

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**Quiz #2 (September 17)** ...
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**Solutions**

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**Quiz #3 (October 1)** ...
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**Solutions**

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**Quiz #4 (October 8)** ...
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**Solutions**

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**Quiz #5 (October 15)** ...
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**Solutions**

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**Quiz #6 (October 29)** ...
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**Solutions**

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**Quiz #7 (November 2)** ...
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**Solutions**

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**Quiz #8 (November 14)** ...
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**Solutions**

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**Quiz #8 (Repeat) (November 17)** ...
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**Solutions**

**Exams:**

There will be three exams, on these dates:

**Exam #1**: Wednesday, September 24 (covering Sections 6.1-6.4)**Exam #2**: Wednesday, October 22 (covering Sections 7.1-7.6, 9.3)**Exam #3**: Friday, November 21 (covering Sections 8.1-8.5)

You are permitted to bring to each exam one 8x11-sheet of paper upon which you may write anything that you like on one side. Photocopies and word-processed text are forbidden.

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**Exam #1 (September 24)** ...
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**Solutions**

There were 6 scores <= 25, 5 scores in the range 26-30, 8 in the range 31-35, 9 in the range 36-40, and 5 scores >= 41.

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**Exam #2 (October 22)** ...
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**Solutions**

There were 6 scores <= 19, 10 scores in the range 20-22, 6 in the range 23-25, and 11 scores >= 26.

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**Exam #3 (November 21)** ...
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**Solutions**

There were 5 scores <= 29, 13 scores in the range 30-33, and 12 scores >= 34.

Combining the weighted three exams, there are 5 totals <= 30, 10 in the range 30-35, 13 in the range 35-40, and 2 in the range >= 40.

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**Final Exam (December 18)** ...
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**Solutions**

**Online Sections:**

- Numerical Integration (Section 6.5)
- Applied Probability and Statistics (Sections P.1-P.3)

**Links:**

- Having trouble? Check out the Academic Support Programs (ASP) here at UVM!
- Textbook resources
- Vince Koehler's 20 Sections