Home' Technology Review : July August 2010 Contents One of the greatest achievements of
the mind is calculus. It belongs in
the pantheon of our accomplish-
ments with Shakespeare’s plays, Beethoven’s
symphonies, and Einstein’s theory of relativ-
ity. Calculus is a beautiful idea exposing the
rational workings of the world.
Calculus, separately invented by Newton
and Leibniz, is one of the most fruitful strat-
egies for analyzing our world ever devised.
Calculus has made it possible to build bridges
that span miles of river, travel to the moon,
and predict patterns of population change.
The fundamental insight of calculus unites
the way we see economics, astronomy, popu-
lation growth, engineering, and even baseball.
Calculus is the mathematical structure that
lies at the core of a world of seemingly unre-
Expanding the Insight
Yet for all its computational power, calcu-
lus is the exploration of just two ideas—the
derivative and the integral—both of which
arise from a commonsense analysis of motion.
All a 1,300-page calculus textbook holds,
Professor Michael Starbird asserts, are those
two basic ideas and 1,298 pages of examples,
applications, and variations.
Professor Starbird teaches that calculus
does not require a complicated vocabulary
or notation to understand it. “Calculus is a
crowning intellectual achievement of human-
ity that all intelligent people can appreciate,
enjoy, and understand.”
This series is not designed as a college cal-
culus course; rather, it will help you see calcu-
lus around you in the everyday world. Every
step is in English rather than “mathese.” The
course takes the approach that every equation
is also a sentence that can be understood, and
solved, in English.
About Your Professor
Professor Michael Starbird is a distin-
guished and highly popular teacher with
an uncommon talent for making the won-
ders of mathematics clear to nonmathemati-
cians. He is Professor of Mathematics and
a Distinguished Teaching Professor at The
University of Texas at Austin. Professor
Starbird has won several teaching awards, most
recently the 2007 Mathematical Association of
America Deborah and Franklin Tepper Haimo
National Award for Distinguished College or
University Teaching of Mathematics, which is
limited to three recipients annually from the
27,000 members of the MAA.
About The Teaching Company®
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We’ve been doing this since 1990, pro-
ducing more than 3,000 hours of material in
modern and ancient history, philosophy, liter-
ature, fine arts, the sciences, and mathematics
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ers. If a course is ever less than completely
satisfying, you may exchange it for another, or
we will refund your money promptly.
1. Two Ideas, Vast Implications
2. Stop Sign Crime—The First Idea
of Calculus—The Derivative
3. Another Car, Another Crime—
The Second Idea of Calculus—
4. The Fundamental Theorem of Calculus
5. Visualizing the Derivative—Slopes
6. Derivatives the Easy Way—
7. Abstracting the Derivative—
Circles and Belts
8. Circles, Pyramids, Cones, and Spheres
9. Archimedes and the Tractrix
10. The Integral and the
11. Abstracting the Integral—
Pyramids and Dams
12. Buffon’s Needle or p from Breadsticks
13. Achilles, Tortoises, Limits,
14. Calculators and Approximations
15. The Best of All Possible
16. Economics and Architecture
17. Galileo, Newton, and Baseball
18. Getting off the Line—Motion in Space
19. Mountain Slopes and Tangent Planes
20. Several Variables—Volumes Galore
21. The Fundamental Theorem Extended
22. Fields of Arrows—Differential Equations
23. Owls, Rats, Waves, and Guitars
24. Calculus Everywhere
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Calculus Is the Exploration of Two Basic Ideas.
Master Them and Open a New World for Yourself !
Change and Motion: Calculus Made Clear, 2
Edition, on DVD
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