Change and Motion: Calculus Made Clear (Audiobook) | Date: 13 April 2011, 12:44
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"Mathematics, rightly viewed, possesses not only truth, but supreme beauty ... such as only the greatest art can show." — Bertrand Russell
[b]Why Understand Calculus?[/b]
One of the greatest achievements of the human mind is calculus. It justly deserves a place in the pantheon of our accomplishments with Shakespeare's plays, Beethoven's symphonies, and Einstein's theory of relativity.
In fact, most of the differences in the way we experience life now and the way we experienced it at the beginning of the 17th century emerged because of technical advances that rely on calculus. Calculus is a beautiful idea exposing the rational workings of the world; it is part of our intellectual heritage.
[b]The True Genius of Calculus Is Simple[/b]
Calculus, separately invented by Newton and Leibniz, is one of the most fruitful strategies 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.
Yet for all its computational power, calculus 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, variations, and applications.
Many of us exclude ourselves from the profound insights of calculus because we didn't continue in mathematics. This great achievement remains a closed door. But Professor Starbird can open that door and make calculus accessible to all.
[b]Why You Didn't Get It the First Time[/b]
Professor Starbird is committed to correcting the bewildering way that the beauty of calculus was hidden from many of us in school.
He firmly believes that calculus does not require a complicated vocabulary or notation to understand it. Indeed, the purpose of these lectures is to explain clearly the concepts of calculus and to help you see that "calculus is a crowning intellectual achievement of humanity that all intelligent people can appreciate, enjoy, and understand."
He adds: "The deep concepts of calculus can be understood without the technical background traditionally required in calculus courses. Indeed, frequently the technicalities in calculus courses completely submerge the striking, salient insights that compose the true significance of the subject.
"In this course, the concepts and insights at the heart of calculus take center stage. The central ideas are absolutely meaningful and understandable to all intelligent people—regardless of the level or age of their previous mathematical experience. Historical events and everyday action form the foundation for this excursion through calculus."
[hide=Course Lecture Titles][list][*]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—The Integral
[*]4. The Fundamental Theorem of Calculus
[*]5. Visualizing the Derivative—Slopes
[*]6. Derivatives the Easy Way—Symbol Pushing
[*]7. Abstracting the Derivative—Circles and Belts
[*]8. Circles, Pyramids, Cones, and Spheres
[*]9. Archimedes and the Tractrix
[*]10. The Integral and the Fundamental Theorem
[*]11. Abstracting the Integral—Pyramids and Dams
[*]12. Buffon’s Needle or ? from Breadsticks
[*]13. Achilles, Tortoises, Limits, and Continuity
[*]14. Calculators and Approximations
[*]15. The Best of All Possible Worlds—Optimization
[*]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
[/list][/hide]
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