
Mastering Differential Equations The Visual Method 

Mastering Differential Equations The Visual Method
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EBook Description: 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.

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MathTutor Differential Equations Vol. 1 First Order Equations
Differential equations is used in all branches of engineering and science. In essence, once a student begins to study more complex problems, nature usually obeys a differential equation which means that the equation involves one or more derivatives of the unknown variable. In other words, a differential equation involves the rate of change of a variable rather than the variable itself. The simplest example of this is F=ma. The "a" is acceleration which is the second derivative of the position of the object. Although differential equations may look simple to solve by just integration, they frequently require complex solution methods with many steps. This 10 hour DVD course teaches how to solve first order differential equations using fully worked example problems. All intermediate steps are shown along with graphing methods and applications of differential equations in science and engineering.
Mastering Differential Equations:The Visual Method
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 easytograsp 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 halfhour 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.
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