Автор: Michael Starbird \ Майкл Старберд
Издательство: The Teaching Company
Продолжительность: 24 лекции по 30 минут
Описание: Величайшее достижение человеческтва - это создание исчисления. По мнению автора, оно достойно стоять рядом с поэмами Шекспира и симфониями Бетховена.
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 π 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
"Mathematics, rightly viewed, possesses not only truth, but supreme beauty ... such as only the greatest art can show."
Why Understand Calculus?
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.
The True Genius of Calculus Is Simple
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.
Why You Didn't Get It the First Time
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."
Two Simple Ideas
After the introduction, the course begins with a discussion of a car driving down a road. As Professor Starbird discusses speed and position, the two foundational concepts of calculus arise naturally, and their relationship to each other becomes clear and convincing.
Professor Starbird presents and explores the fundamental ideas, then shows how they can be understood and applied in many settings.
Expanding the Insight
Calculus originated in our desire to understand motion, which is change in position over time. Professor Starbird then explains how calculus has created powerful insight into everything that changes over time. Thus, the fundamental insight of calculus unites the way we see economics, astronomy, population growth, engineering, and even baseball. Calculus is the mathematical structure that lies at the core of a world of seemingly unrelated issues.
As you follow the intellectual development of calculus, your appreciation of its inner workings will deepen, and your skill in seeing how calculus can solve problems will increase. You will examine the relationships between algebra, geometry, trigonometry, and calculus. You will graduate from considering the linear motion of a car on a straight road to motion on a two-dimensional plane or even the motion of a flying object in three-dimensional space.
Designed for Nonmathematicians
Every step is in English rather than "mathese." Formulas are important, certainly, but the course takes the approach that every equation is in fact also a sentence that can be understood, and solved, in English.
This course is crafted to make the key concepts and triumphs of calculus accessible to nonmathematicians. It requires only a basic acquaintance with beginning high-school level algebra and geometry. This series is not designed as a college calculus course; rather, it will help you see calculus around you in the everyday world.
The Teaching Company was founded in 1990 by Thomas M. Rollins, former Chief Counsel of the United States Senate Committee on Labor and Human Resources.
Years earlier, as a Harvard Law School student, Rollins had an unforgettable experience that opened his eyes to the extraordinary power of a great lecturer captured on tape.
Rollins was facing an important exam in the Federal Rules of Evidence but was not well prepared. He managed to obtain videotapes of 10 one-hour lectures by a noted authority on the subject, Professor Irving Younger.
"I dreaded what seemed certain to be boring," Rollins says. "I thought that few subjects could be as dull as the Federal Rules of Evidence. But I had no other way out."
Rollins planted himself in front of the TV and played all 10 hours nearly non-stop. The lectures, he says, "were outrageously insightful, funny, and thorough." Watching Professor Younger's lectures was one of Rollins's best experiences as a student.
Rollins made an "A" in the course. And he never forgot the unique power of recorded lectures by a great teacher.
After many years of government service, Rollins founded The Teaching Company in 1990 to ignite people's passion for lifelong learning by offering great courses taught by great professors.
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