Homework

Homework will be announced here as the term progresses. (For solutions, see Coursework.)
  1. Due Thursday, October 1st, in discussion section.
    From the textbook :
    section 5.1 : questions 4, 14, 20, 22
    section 5.2 : questions 2, 12, 32, 42.
    Additional question : (based on question 50, section 5.2)
    Suppose that f is a piecewise continuous function defined on the interval [0,1], with absolute minimum m and absolute maximum M. Between what two values must the integral of f from 0 to 1 lie? What property of the integral allows you to say this? Give an example of a piecewise continuous function for which the integral equals the lower bound you just found, give an example for which the integral achieves the upper bound, and give an example for which the integral achieves some value in between. (You may provide your example by sketching the graph of the curve, but be careful to indicate clearly what the function does at its jump discontinuities, if it has any.)
  2. Due Thursday, October 8th, in discussion section.
    From the textbook :
    section 5.3 : 30, 32
    section 5.4 : 14, 18, 20
    section 5.5 : 6, 8, 36, 64, 68
    This assignment was changed on October 1st, at 11:30 AM.
  3. Due Tuesday, October 13th, in discussion section
    From the textbook :
    Section 5.6 : 18, 30, 36, 44
    Section 5.7 : 8, 18
  4. Due Thursday, October 22nd, in discussion section.
    Section 5.9 : 2, 6, 20, 28, 36, 38, 40 (for #40, do not use the error formula, but show it follows from the definition in Simpson's rule).
    Also, think about 37, but do not hand it in.
  5. Due Thursday, October 29th, in discussion section.
    Section 5.10 : 6, 8, 14, 32, 34, 46, 48, 50, 62, 64.
  6. Due Tuesday November 3rd, in discussion section.
    Section 6.1 : 16, 24, 34
    Section 6.2 : 4, 16, 46 (note the deleted problem!)
  7. Due Thursday, November 12th, in discussion section.
    section 6.2 : 44, 54
    section 6.3 : 18, 30, 32, 38
    section 6.4 : 28, 30, 34b (you can do (a) too, but don't hand it in)
    section 6.5 : 18
  8. Due Thursday, November 19th, in discussion section.
    Section 6.6 : 12, 18, 44, 46, 48, 50, 52 (this question is easier if you look at 51 first)
  9. Due Thursday, December 3rd, in discussion section.
    Homework assignment 9 [PDF format]

Suggested problems

Here are some suggested problems from some of the sections we have covered :
section 5.3 : 29, 67, 69
section 5.4 : 13, 17, 19, 29
section 5.5 : 3, 7, 21, 31, 35, 61, 63, 67

section 5.7 : 21, 27, 31, 33, 35, 36.
section 5.10 : 2, 26, 54, 57, 61, all the calculation of improper integrals problems, all the questions involving use of the comparison theorem.
section 6.1 : 17, 31, 37, 41.
section 6.2 : 31, 45, 46, 47, 52, 53.
section 6.3 : 3, 7, 9, 13, 17, 19, 23.
Section 6.6 : 15, 17, 21, 27, 51
Chapter 6 review : 5, 6, 12, 20, 23, 27, 29

Guidelines

Homework is due on Thursday, in your discussion section. An exception will be the weeks of the two midterms, when (a shorter) homework will be due on Tuesday. Late homework will not be accepted. The lowest homework grade will be dropped.

The TAs and I will be happy to discuss all problems with you, even ones not assigned as homework.

You are encouraged to discuss the homework problems, and potential methods of solution, with other students. You must, however, write up your homework solution on your own. If the distinction is unclear to you, please do not hesitate to ask for clarification.