### Homework assignments for Math 213: Calculus III

From William G. McCallum, Deborah Hughes-Hallett, Andrew M. Gleason, et al., Multivariable Calculus, Wiley 1997, New York. Section numbers are links to solutions (in .pdf format), posted after an assignment is turned in.

Chapter 11:

• Sec 11.1, p 7: #3, 4, 6, 12, 15. You may find the answer to #15 surprising.
• Sec 11.2, p 13: #4, 6, 7, 8, 10, 12, 19, 20.
• Sec 11.3, p 19: #2, 3abc, 4abc, 5, 7, 8, 14 (omit the "reasonable units" part in (b)).
• Sec 11.4, p 31: #2, 4, 8 (in all of these, omit the "Describe in words ..." sentence), 23, 29, 30abcfgh.
• Sec 11.5, p 41: #3, 4, 6, 10, 15, 16, 18, 19.
• Sec 11.6, p 49: #13-19.
• Sec 11.7, p 55: #1, 3, 4. It might be wise to ask Winplot to draw you a better figure for #4 than Figure 11.104 in the text. And, though I am not assigning any of the problems #5-9, I must insist that we add something to the instructions: "... that polynomial, exponential, lograrithmic and trigonometric functions are continuous where they are defined."
[To the course syllabus]

Chapter 12:

• Sec 12.1, p 66: #3, 4, 6, 8, 17, 18, 19, 20, 30.
• Sec 12.2, p 74: #1, 2, 3, 4, 5, 11, 13, 14.
• Sec 12.3, p 82: #4, 5, 6, 11, 12, 14, 15, 16, 18, 22, 24, 28.
• Sec 12.4, p 90: #1, 2, 3, 6, 7, 10, 12, 14, 15.
[To the course syllabus]

Chapter 13:

• Sec 13.1, p 102: #2, 6, 8, 10, 11.
• Sec 13.2, p 108: #3, 4, 5, 14, 21, 22, 26, 30, 31, 34, 35bc, 36.
• Sec 13.3, p 115: #2, 4, 8, 11, 14, 15, 16, 22. (For #22(a), temporarily denote the constant mass of the liquid by m, so that the density p = m/V; the m should cancel out in your result.)
• Sec 13.4, p 124: #7, 8, 9, 12, 14, 26, 28, 31, 36, 37.
• Sec 13.5, p 133: #2, 4, 6, 7, 11(bc only, at (1,1,1) only), 12, 13, 14, 15.
• Sec 13.6, p 140: #2, 3, 4, 6, 10, 11, 14.
• Sec 13.7, p 145: #3, 6, 7, 9, 10.
• Sec 13.9, p 159: #2, 3, 7, 17. Wherever possible, use the standard Taylor series rather than computing from scratch. You should know that, although #7 and #17 require a lot of reasoning and computation, the answers given by the Taylor polynomials are surprisingly accurate: In #7, even the linear Taylor polynomial gives the value for f(1.1,1.1) correct to 12 decimal places (according to my calculator). And in #17, the actual errors are identical for the linear and quadratic polynomials, and much smaller than the error bounds you are asked to compute.
[To the course syllabus]

Chapter 14:

[To the course syllabus]

Chapter 15:

• Sec 15.2, p 233: #6, 7, 8, 10, 11, 13, 14, 16, 20, 21.
• Sec 15.3, p 238: #2, 5, 7, 8, 9, 10, 12, 13, 14, 16 (on #16, set up integrals only; do not evaluate).
• Sec 15.5, p 246: #2, 3, 4, 6, 7, 9, 11, 12, 15, 16, 19, 21. (Note: The integrand in #21(a) should just be delta of r and theta; you'll decide its value in (b) and evaluate the integral in (c).)
• Sec 15.6, p 254: #2, 3, 6, 7, 8, 9, 11, 12, 17, 22.
[To the course syllabus]

Chapter 16:

• Sec 16.1, p 281: #2, 3, 11, 12, 13, 14, 16, 17, 24, 25, 26, 30, 31, 32, 33.
• Sec 16.2, p 291: #3, 9, 12, 13, 16 (don't "Explain"), 18, 23, 24, 28.
• Sec 16.3, p 303: #3, 4, 5, 8, 9, 12, 17, 18, 30.
[To the course syllabus]

Chapter 17:

[To the course syllabus]

Chapter 18:

[To the course syllabus]

Revised: May 2, 2001. Questions to: dlantz@mail.colgate.edu