Calculus Made Clear, 2nd Edition 2019-5 – Download

Change and Motion Course: Calculus Made Clear, 2nd Edition. One of the greatest accomplishments of the human mind is computation. It deserves a place in the pantheon of our achievements alongside Shakespeare’s plays, Beethoven’s symphonies, and Einstein’s theory of relativity. In fact, most of the differences between the way we experience life now and the way we experienced it in the early 17th century have emerged because of technological 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 useful strategies ever devised for analyzing our world. Calculus has made it possible to build bridges over rivers spanning miles, travel to the moon, and predict patterns of population change. For all its computational power, calculus is merely the exploration of two ideas—the derivative and the integral—both of which derive from the common-sense analysis of motion. Professor Michael Starbird says that a complete calculus textbook is 1,300 pages of basic ideas and 1,298 pages of examples, variations, and applications. Many of us keep ourselves from delving deeper into calculus because we can’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 all. Professor Starbird is committed to correcting the confusing way in which the beauty of calculus was hidden from many of us in school. He firmly believes that understanding calculus does not require complex vocabulary or notation. In fact, the purpose of these lectures is to clearly explain arithmetic and the concepts of the book and help you see that “arithmetic is the highest achievement of human intelligence 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 added. “This completely misses the true importance of the subject.” In this course, the concepts and insights at the core of calculus are brought into focus. The main ideas are completely meaningful and understandable to all intelligent people – regardless of their level of previous mathematical experience or age. Historical events and everyday activities form the basis of this journey through calculus.

Two Simple Ideas: After an introduction, the course begins with a discussion of a car driving on the road. As Professor Starbird discusses velocity and position, two fundamental concepts of calculus arise naturally and their connection to one another becomes clear and compelling. Professor Starbird introduces and reviews the basic ideas, then shows how they can be understood and applied in a number of settings.
Expanding Insights: Calculus arises from our desire to understand motion, which is a change in position over time. Professor Starbird then explains how calculus has developed powerful insights into everything that changes over time. Thus, the fundamental insights of calculus unify the way we view 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 evolution of calculus, your understanding of its inner workings will deepen and your knack for seeing how calculus can solve problems will grow. You will explore the connections between algebra, geometry, trigonometry, and calculus. You will go from considering the linear motion of a car on a straight road to considering the motion of a 2D plane or even the motion of a flying object in 3D space.