Mastering Differential Equations: The Visual Method
by Robert L. Devaney /
2011 / English / PDF
3.4 MB Download
For centuries, differential equations have been the key to unlocking nature's deepest secrets. Over 300 years ago, Isaac Newton invented differential equations to understand the problem of motion, and he developed calculus in order to solve differential equations. Since then, differential equations have been the essential tool for analyzing the process of change, whether in physics, engineering, biology, or any other field where it's important to predict how something behaves over time. 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. Even then, most problems involving differential equations had to be simplified, often in unrealistic ways; and a huge number of equations defied solution at all using these techniques. But that was before computers revolutionized the field, extending the reach of differential equations into previously unexplored areas and allowing solutions to be approximated and displayed in easy-to-grasp computer graphics. For the first time, a method exists 2000that can start a committed learner on the road to mastering this beautiful application of the ideas and techniques of calculus. Mastering Differential Equations: The Visual Method takes you on this amazing mathematical journey in 24 intellectually stimulating and visually engaging half-hour lectures taught by a pioneer of the visual approach, Professor Robert L. Devaney of Boston University, coauthor of one of the most widely used textbooks on ordinary differential equations.
