Mastering Differential Equations

The pinnacle of a mathematics education, differential equations assume a basic knowledge of calculus, and they have traditionally required the rote memorization of a vast "cookbook" of formulas and specialized tricks needed to find explicit solutions. But now, computers have allowed solutions to be approximated and displayed in easy-to-grasp computer graphics. For the first time, a method exists that can start a committed learner on the road to mastering this beautiful application of...
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The pinnacle of a mathematics education, differential equations assume a basic knowledge of calculus, and they have traditionally required the rote memorization of a vast "cookbook" of formulas and specialized tricks needed to find explicit solutions. But now, computers have allowed solutions to be approximated and displayed in easy-to-grasp computer graphics. For the first time, a method exists that can start a committed learner on the road to mastering this beautiful application of the ideas and techniques of calculus - without the need for all that memorization. This course takes you on an amazing mathematical journey in 24 intellectually stimulating and visually engaging half-hour lectures taught by a pioneer of the visual approach, Professor Robert Devaney, the coauthor of one of the most widely used textbooks on ordinary differential equations. Professor Devaney draws on the power of the computer to explore solutions visually. Throughout these graphics-intensive lectures, you investigate the geometric behavior of differential equations, seeing how the computer can calculate approximate solutions with as much precision as needed. And you may be surprised to learn how easily you can calculate and display approximate solutions yourself, even using nothing more than an ordinary spreadsheet. Best of all, the visual method means that unrealistic simplifications need not be applied to a problem. Mastering Differential Equations: The Visual Method guides you into the 21st century, showing how this deceptively simple tool - the differential equation - continues to give surprising and spectacular insights into both the world of mathematics and the workings of the universe