Stieltjes Differential Calculus With Applications
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A01=Sanket Tikare
A01=Svetlin G Georgiev
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Author_Sanket Tikare
Author_Svetlin G Georgiev
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Category1=Non-Fiction
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First-Order Stieltjes Differential Equations
Language_English
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Second-order Stieltjes Differential Equations
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Stieltjes Derivative
Stieltjes Differential Systems
Stieltjes Elementary Functions
Stieltjes Homogeneous and Nonhomogeneous Initial Value Problems
Stieltjes Integral
Stieltjes Laplace Transform
Stieltjes Linear Boundary Value Problems
StieltjesAcAEURA"EulerAcAEURA"Cauchy Equations
The Helly Principle of Choice
Product details
- ISBN 9789811294228
- Publication Date: 10 Jan 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
- Language: English
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The Stieltjes derivative is a modification of the usual derivative through a nondecreasing and left-continuous map. This change in the definition allows us to study several differential problems under the same framework.This monograph is the first published book that offers a comprehensive view of the fundamentals of Stieltjes calculus and its applications, making it approachable to newcomers and experts. It aims to provide an integrated approach to the foundations and recent developments in the area of the Stieltjes derivatives and the qualitative theory of the Stieltjes differential equations. Through 10 pedagogically organized chapters, the authors examine a wide scope of the concept of the Stieltjes derivative and its applications. Each chapter focuses on theory, and proofs, and contains sufficient examples to enrich the reader's understanding.The Stieltjes derivative contains the Hilger delta derivative on time scales. Thus, offering a new unification and extension of continuous and discrete calculus. Further, a study of differential equations in the sense of the Stieltjes derivative allows the study of many classical problems in a unique framework. This theory has the advantage that ordinary differential equations, ordinary difference equations, quantum difference equations, impulsive differential equations, dynamic equations on time scales, and generalized differential equations can be treated as particular instances of the Stieltjes differential equations. Hence, this book serves as a basic reference for researchers to harness this powerful technique further to unlock new insights and embrace the intricacies of natural processes. Researchers and graduate students at various levels interested in learning about the Stieltjes differential calculus and related fields will find this text a valuable resource of both introductory and advanced material.
