Scaling of Differential Equations by Hans Petter Langtangen
Scaling of Differential Equations - Table of Contents
1. Dimensions and Units
2. Ordinary Differential Equation Models
3. Basic Partial Differential Equation Models
4. Advanced Partial Differential Equation Models
What You Will Learn in Scaling of Differential Equations
"Scaling of Differential Equations" by Hans Petter Langtangen and Geir K. Pedersen is a practical guide for understanding how to simplify and analyze "differential equations" through "scaling" techniques. Scaling, also known as "non-dimensionalization", helps remove units, reduce parameters, and reveal the relationships between physical processes. The book is especially useful for applied mathematicians, engineers, and students who want to connect theoretical equations with real-world modeling.
The book covers both "ordinary differential equations (ODEs)" and "partial differential equations (PDEs)", offering step-by-step examples to show how to choose appropriate scales based on the underlying physics. Early chapters focus on basic concepts like "dimensions and units", making it accessible for beginners. Later sections explore complex systems from physics and engineering, including fluid dynamics, heat transfer, and gas flow. Each chapter emphasizes reasoning behind scale choices, making it easier to set up "numerical simulations" effectively.
Langtangen’s approach combines clear explanations with practical examples, showing how scaled equations simplify computations and highlight important dimensionless numbers. The concise presentation ensures students and professionals can quickly grasp the principles of scaling and apply them to modeling real-world systems. This book is a valuable reference for anyone seeking to improve problem-solving skills in mathematical modeling and computational science.
Book Details & Specifications
Title:
Scaling of Differential Equations by Hans Petter Langtangen
Publisher:
Springer
Year:
2016
Pages:
151
Type:
PDF
Language:
English
ISBN-10 #:
3319327259
ISBN-13 #:
978-3319327259
License:
CC BY-NC 4.0
Amazon:
Amazon
About the Author: Hans Petter Langtangen
The author Hans Petter Langtangen
was a renowned mathematician and computational scientist, widely recognized for his work in "differential equations", "numerical methods", and "scientific computing". He specialized in applying mathematical techniques to solve real-world problems in "engineering" and "physics", bridging theory with practical computation. His work, including "Scaling of Differential Equations", guide students and professionals in understanding "scaling principles", "modeling", and "simulation techniques", making complex mathematical concepts accessible and applicable in real-world scenarios.
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