Written Homework Assignment 1
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Dear Students,
The following are additional questions for you to work on that cannot be easily implemented in the online homework
system. You need to submit a clearly written and legible solution (typed or handwritten is fine). You can use a
webcam, phone or a scanner to digitize your work and then upload your written solution as a pdf or doc file (a jpg
will not work for this assignment). You can also get a scan to pdf app for your smartphone (if you have one). Make
sure the pdf is submitted right side up, and that the pages are in order. Please make sure that your work is clearly
legible and that your name is on the paper.
NOTE: There are no extensions on written homework assignments.
Below are the questions for the first written assignment, covering chapter 15 and sections 16.1 + 16.2.
1) (Marsden/Tromba, Vector Calculus, 6th ed., page 305, Chapter 5 Review Exercises, #37 or in your E-Book,
Review Exercises for Chapter 15, Question 15.151) Write the iterated integral
an integral over a region in
as
and then rewrite it in a different order of integration.
2) (Marsden/Tromba, Vector Calculus, 6th ed., page 347, Chapter 6 Review Exercises, #1 or in your E-Book,
Review Exercises for Chapter 16, Question 16.117)
(a) Find a linear transformation taking the square
to the parallelogram
with vertices (0,0),
(2,0), (1,2) and (3,2).
(b) Write down a change of variables formula appropriate to the transformation you found in (a).
3) (Marsden/Tromba, Vector Calculus, 6th ed., page 328, Section 6.2 Exercises, #29 or in your E-Book, Exercises
for Section 16.2, Question 16.56)
Integrate
over the solid bounded by the two spheres
where
and
.
4) (Marsden/Tromba, Vector Calculus, 6th ed., page 328, Section 6.2 Exercises, #35 or in your E-Book, Exercises
for Section 16.2, Question 16.62)
The mapping
region
of the
(a) Show that
transforms the rectangle
of the
-plane into a
-plane.
is one-to-one.
(b) Find the area of
using the change of variables formula.
5) (Marsden/Tromba, Vector Calculus, 6th ed., page 348, Chapter 6 Review Exercises, #21 or in your E-Book,
Review Exercises for Chapter 16, Question 16.137)
Find the center of mass of the solid hemisphere
constant.
if the density is
6) (Marsden/Tromba, Vector Calculus, 6th ed., page 349, Chapter 6 Review Exercises, #33 or in your E-Book,
Review Exercises for Chapter 16, Question 16.149)
Evaluate
where
.
Hint: You may assume that changing variables and Fubini's theorem are valid for improper integrals.
Points
20
Submitting
a file upload
File Types
doc, pdf, and docx
Due
For
Available from
Until
Apr 28
Everyone
-
May 3 at 11:59pm
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