TTC Video - Mastering Differential Equations: The Visual Method

TTC Video - Mastering Differential Equations: The Visual Method: "
TTC Video - Mastering Differential Equations: The Visual Method
TTC Video - Mastering Differential Equations: The Visual Method
English | 640x480 | H264 | 29.97fps 1536kbps | AAC 128kbps | 7.74GB
Taught By Professor Robert L. Devaney | 24 Lectures | 30 minutes/lecture

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 that 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.

Differential Equations without Drudgery
A firm believer that there is no excuse for drudgery in a subject as fascinating as 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.

Beautiful Ideas plus Amazing Applications
Differential equations involve velocity, acceleration, growth rates, and other quantities that can be interpreted by derivatives, which are a fundamental concept of calculus. Often expressed with utmost simplicity and mathematical elegance, differential equations underlie some of nature's most intriguing phenomena

A Taste of 21st-Century Mathematics
Each of the four sections of Mastering Differential Equations begins with a phenomenon that can be modeled with differential equations. As you probe deeper, fundamental ideas (the derivative, integral, and vector field) and other relevant tools from calculus are introduced, along with new mathematics, including four lectures on linear algebra and five lectures on chaos theory.

More info:
_http://www.thegreatcourses.com/tgc/courses/course_detail.aspx?cid=1452

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TTC Video - Mastering Differential Equations: The Visual Method



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