Math 253: Calculus III, Fall 2007

Course information

CRN:	13171
Location:	185 Lillis
Time:	Monday–Wednesday, Friday
	8:00–8:50 a.m.
Office hours:	See schedule
Text:	Calculus, 5th ed., by James Stewart
Prerequisites:	Math 252 and a graphing calculator (such as the TI-84)
Supervisor:	Wendy Sullivan, assistant department head

Class log

Some online versions of handouts are in the Portable Document File format and require a special reader. You probably already have a PDF viewer installed on your system. If not, some PDF viewers include GSView and Adobe Reader (previously known as Acrobat Reader). These programs are included on the Duckware CD.

Sunday, 2 December:

• Redacted version of the final

Wednesday, 21 November

• Homework (due Wednesday, 28 November):
  • Section 10.2: 57, 58, 60.
  • Section 10.3: 2, 4, 10, 16, 20, 32, 36, 40, 56, 60, 66.

Monday, 12 November

• Homework (due Wednesday, 14 November):
  • Read Section 8.2. Then do exercises 1, 2, 3, 4, 5, 8, 12, 14. (Pay attention to the instructions!)
  • Read Section 10.1. Then do exercises 1, 3, 6, 8, 14, 24, 40.
• Homework (due Friday, 16 November): Read Section 10.2. Then do exercises 4, 6, 8, 12, 14, 18, 20, 26, 34, 38, 39, 40, 44, 52.
• The Famous Curves Index at The MacTutor History of Mathematics archive lists some interesting curves.

Monday, 5 November

• Homework (due Friday, 9 November): Read Section 8.1. Then do exercises 1, 6, 8, 10, 12, 14, 16, 17, 18, 19, 20, 31, 33. (Pay attention to the instructions for exercises 17–20!)
• Illustrations from the lecture (linked to full-sized versions):
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• Here’s another illustration of the concept of a surface of revolution I created (linked to full version):
  

Friday, 2 November

• Redacted version of Midterm II

Wednesday, 31 October

• Homework (due Monday, 5 November): Read Section 11.10. Then do exercises 2, 4, 6, 8, 10, 12, 14, 14, 16, 24, 26, 28, 30 (Hint: Use cos² x = (1 + cos 2x)/2), 40, 42, 47 (Hint: Follow example 9), 57 (Hint: This is some Maclaurin series evaluated at π/4), 60 (Hint: What is e^{-ln 2}?)

Monday, 29 October

• Homework (due Wednesday, 31 October): Read Section 11.9. Then do exercises 4, 6, 8, 10, 12, 14, 16, 18, 24, 26, 38.

Friday, 26 October

• Taylor series are named after the English mathematician Brook Taylor (1685–1731), but they were actually first discovered by the Indian mathematician Madhava of Sangamagramma (1350–1425).

Wednesday, 24 October

• Homework (due Monday, 29 October): Read Section 11.8. Then do exercises 4, 6, 8, 10, 12, 14, 16, 18, 20, 28, 34(a), 35.

Friday, 19 October

• Homework (due Wednesday, 24 October): Read Sections 11.6–11.7. Then do: Section 11.6, exercises 2, 4, 6, 8, 10, 12, 14, 16, 18, 22, 26, 30.

Tuesday, 16 October

• Homework (due Friday, 19 October): Read Section 11.5. Then do exercises 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 32, 34.

Wednesday, 10 October

• Midterm I information
• Homework (due Monday, 15 October): Read Sections 11.3 and 11.4. Then do:
  • Section 11.3: 4, 6, 8, 10, 12, 14, 20, 26, 34, 35.
  • Section 11.4: 2, 4, 6, 8, 10.
• I will not be here on Friday. James Wilson will be my substitute.

Monday, 8 October

• Approximations of Apéry’s constant (Σ(1/n^3) (the table I displayed briefly on the document viewer).
• You might find this handout on sigma notation useful, as it includes instructions on how to evaluate finite sums on a calculator.

Thursday, 4 October

• Homework (due Tuesday, 9 October):
  • Read Section 11.3.
  • Section 11.2 (p. 720–722): 58, 62, 63, 65, 68.
  • Also, consider this analogue of the Koch snowflake¹:
    
    We start with a square with area 1. To each edge, we add a square of area 1/9. To the edge of the resulting shape, we add a square of area (1/9)². Continue this process indefinitely. What is the area of the resulting shape?
• If you are interested: More information on Apéry’s constant.

1. This problem was suggested by Jonny Comes.

Tuesday, 2 October

• Construction of the Koch snowflake.
• Construction after several iterations.
• You can find more information about the Koch snowflake on MathWorld.

Monday, 1 October

• Homework (due Wednesday, 3 October): Section 11.2 (p. 720–722): 12, 14, 16, 18, 20, 28, 29, 32, 36, 40, 42.

Friday, 28 September

• Quiz #1.
• The department is starting an undergraduate math seminar, to be held Tuesdays at noon in the Hilbert Space (the undergraduate math lounge). The first talk will be on 2 October.

Monday, 24 September

• Syllabus
• Homework standards
• Getting to know you (Please fill this out and return to me within the next day or so.)
• Quiz Friday on Section 11.1.
• Homework (due Wednesday, 26 September Friday, 28 Sept.):
  • Read Sections 11.1 and 11.2.
  • Section 11.1 (pp. 710–712): 1, 3, 4, 5, 6, 9, 10, 12, 15, 18, 23, 24, 26, 28, 33, 35, 37, 41, 44, 51.

Last updated: 21 November 2007