The Great Courses – Change and Motion: Calculus Made Clear, 2nd Edition 2019-5

Change and Motion Course: Calculus Made Clear, 2nd Edition. One of the greatest achievements of the human mind is calculation. It justly deserves a place in our pantheon of achievements 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 that reveals the rational workings of the universe. It is part of our intellectual heritage. Calculus, invented separately 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 spanning miles of rivers, travel to the moon, and predict patterns of population change. For all its computational power, calculus is only an exploration of two ideas—the derivative and the integral—both of which derive from the common-sense analysis of motion. Professor Michael Starbird states that all a calculus textbook is 1,300 pages of basic ideas and 1,298 pages of examples, variations, and applications. Many of us exclude ourselves from deep insight into calculus because we didn’t keep up with the math. This great achievement is still a closed door. But Professor Starbird can open that door and make calculus accessible to everyone. Professor Starbird is committed to correcting the confusing way in which the beauty of calculus was hidden from many of us in school. He strongly believes that calculus does not require complex vocabulary or notation to understand. In fact, the purpose of these lectures is to clearly explain the concepts of arithmetic and books and help you see that “arithmetic is the crowning achievement of human intellect that all intelligent people can appreciate, enjoy and understand.” “The deep concepts of calculus can be understood without the technical background traditionally required in calculus courses,” he adds. completely drowns out what constitutes the true significance of the subject.” In this course, the concepts and insights at the heart of calculus are brought into focus. The main ideas are completely meaningful and understandable to all intelligent people – regardless of their level or age of previous mathematical experience. Historical events and everyday actions form the basis of this journey through calculus.”

Two simple ideas: After the introduction, the course begins with a discussion of driving a car on the road. As Professor Starbird discusses velocity and position, the two fundamental concepts of calculus arise naturally and their relationship to each other becomes clear and compelling. Professor Starbird presents and reviews basic ideas, then shows how they can be understood and applied in many settings.
Expanding Insights: Calculus originates in our desire to understand motion, which is the change of position over time. Professor Starbird then explains how calculus has developed powerful insights into everything that changes over time. Thus, the fundamental insight of calculus unifies the way we see economics, astronomy, population growth, engineering, and even baseball. Calculus is a mathematical structure that lies at the core of a world of seemingly unrelated problems. As you follow the intellectual development of calculus, your understanding of its inner workings will deepen and your skill at seeing how calculus can solve problems will increase. You will explore the relationships between algebra, geometry, trigonometry, and calculus. You will go from considering the linear motion of a car on a straight road to the motion of a 2D plane or even the motion of a flying object in 3D space.