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Topic: Seeking Beautiful Single-Variable Calculus Problems
Replies: 8   Last Post: Jul 16, 2006 2:35 PM

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Karl M. Bunday

Posts: 127
Registered: 12/6/04
Seeking Beautiful Single-Variable Calculus Problems
Posted: Jul 12, 2006 12:02 AM
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Hi, everyone,

I'm a math team coach and homeschooling parent looking for some extra depth for
the math learners in my care. Most of the young people on my math team get their
main math instruction from the U. of MN Talented Youth Mathematics Program,
using the Stewart Early Transcendentals textbook with an excellent supplementary
materials. Even though they've got some good instruction already, I'm looking
for suggestions of calculus problems that really make a learner THINK about
calculus concepts and go beyond the usual school homework exercise. That's the
best way to help those kids thrive in their main program and go on to higher
mathematics study. What I especially need, as someone largely clueless about
calculus myself, is to find exercises that have numerical or symbolic answers,
or better still full solutions, so that I can check them even if I can't (as is
likely) work through them myself from first principles. My students work beyond
my own level of ability, and they are eager to learn more.

Here's a list of calculus books I own, from which it would be especially easy to
find problems that you suggest are good, challenging problems. The list is
ordered by publication date.

Burington, Richard Stevens & Torrance, Charles Chapman, Higher Mathematics: With
Applications to Science and Engineering (New York: McGraw-Hill, 1939).

Randolph, John F., Analytic Geometry and Calculus (New York: Macmillan, 1949).

Hart, William, Calculus (Boston: D.C. Heath, 1955).

Thomas, George B., Calculus and Analytic Geometry (Reading, MA: Addison-Wesley,
4th ed. 1968).

Kline, Morris, Calculus: An Intuitive and Physical Approach (Mineola, NY: Dover
c. 1977).

Thomas, George B. & Finney, Ross L., Elements of Calculus and Analytic Geometry
(Menlo Park, CA: Addison-Wesley, 1981) (and separate solution manual for this
title).

Marsden, Jerrold & Weinstein, Alan, Calculus I Second Edition (New York:
Springer-Verlag, 1985).

Marsden, Jerrold & Weinstein, Alan, Calculus II Second Edition (New York:
Springer-Verlag, 1985).

Purcell, Edwin J & Varberg, Dale, Calculus with Analytic Geometry (Englewood
Cliffs, NJ: Prentice Hall, 5th ed. 1987) (and separate solution manual for this
title).

Spivak, Michael, Calculus (Houston, TX: Publish or Perish, 3rd ed. 1994).

Finney, Ross L., Thomas, George B., Demana, Franklin & Waits, Bert K., Calculus:
Graphical, Numerical, Algebraic: Single Variable Version (Reading, MA:
Addison-Wesley, 1995).

Ostebee, Arnold & Zorn, Paul, Calculus from Graphical, Numerical, and Symbolic
Points of View Volume 1 (Fort Worth, TX: Saunders College Publishing,
preliminary ed. 1995) (and separate selected answers volume for this title).

Priestley, William McGowen, Calculus: A Liberal Art (New York: Springer-Verlag,
2nd ed. 1998).

Anton, Howard, Calculus: A New Horizon (New York: John Wiley, 6th ed. 1999).

Stewart, James, Calculus: Early Transcendentals (Belmont, CA: Brooks/Cole, 5th
ed. 2003).

Hughes-Hallett, Deborah, et al., Calculus (New York: Wiley, 4th ed. 2005).


I have had some other really good books out of libraries, such as Apostol,
Strang, and Courant. And if you know of great problems with solutions from
online sources, I'm sure that would be of interest to many of us. Please let me
know about your favorite problems for the student who wants to go beyond the
usual syllabus.

--
Karl M. Bunday P.O. Box 1456, Minnetonka MN 55345
Learn in Freedom (TM) http://learninfreedom.org/
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