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Standard-Slope Integration: A New Approach to Numerical Integration
Paperback
Publisher Price: $29.99
Publisher: Peter J. Italia
Published: May 30 2013
Pages: 84
Weight: 0.64
Height: 0.22 Width: 8.50 Depth: 11.00
Language: English
A New Approach to Numerical Integration
A new numerical integration method rarely appears in applied mathematics. Combining accuracy and stability, Standard-Slope Integration introduces one. This book presents a computational approach to solving ordinary differential equations that begins with a simple observation: the slope information already present in an initial value problem can be used more directly than traditional schemes allow. From that starting point, the method takes shape almost intuitively and performs reliably.
Rather than extending existing families of numerical integrators, SSI offers a distinct pathway to numerical integration. The method is built from first principles, with an emphasis on clarity, geometric insight, and the practical demands of real-world computation. Examples throughout the book illustrate how the approach behaves across a range of differential equations, highlighting both its strengths and limitations with equal transparency. When traditional antiderivatives are difficult to obtain or unavailable, Standard-Slope Integration provides a fast, direct way to approximate the area under a curve using only the derivative itself.
Standard-Slope Integration is written for readers who work with differential equations in applied settings - researchers, computational scientists, engineers, and students - and introduces a method that is easy to use, easy to understand, and based on solid mathematics.
For those interested in numerical methods, algorithmic thinking, or the ongoing evolution of ODE solvers, this book offers a clear introduction to a new option in the computational toolbox.
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