General Quantum Variational Calculus by Svetlin G. Georgiev Paperback Book

Description: General Quantum Variational Calculus by Svetlin G. Georgiev, Khaled Zennir Quantum calculus is the modern name for the investigation of calculus without limits. The quantum calculus or q-calculus began with FH Jackson in the early twentieth century, but this kind of calculus had already been worked out by Euler and Jacobi. FORMAT Paperback CONDITION Brand New Publisher Description Quantum calculus is the modern name for the investigation of calculus without limits. Quantum calculus, or q-calculus, began with F.H. Jackson in the early twentieth century, but this kind of calculus had already been worked out by renowned mathematicians Euler and Jacobi.Lately, quantum calculus has aroused a great amount of interest due to the high demand of mathematics that model quantum computing. The q-calculus appeared as a connection between mathematics and physics. It has a lot of applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hypergeometric functions and other quantum theory sciences, mechanics, and the theory of relativity. Recently, the concept of general quantum difference operators that generalize quantum calculus has been defined. General Quantum Variational Calculus is specially designed for those who wish to understand this important mathematical concept, as the text encompasses recent developments of general quantum variational calculus. The material is presented in a highly readable, mathematically solid format. Many practical problems are illustrated, displaying a wide variety of solution techniques.This book is addressed to a wide audience of specialists such as mathematicians, physicists, engineers, and biologists. It can be used as a textbook at the graduate level and as a reference for several disciplines. Author Biography Svetlin G. Georgiev is a mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales.Khaled Zennir earned his PhD in mathematics in 2013 from Sidi Bel Abbès University, Algeria. In 2015, he received his highest diploma in Habilitation in mathematics from Constantine University, Algeria. He is currently an assistant professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and longtime behavior. Table of Contents 1. Elements of the Multimensional General Quantum Calculus1.1 The Multidimensional General Quantum Calculus1.2 Line Integrals1.3 The Green Formula1.4 Advanced Practical Problems2. β-Differential Systems2.1 Structure of β-Differential Systems2.2 β-Matrix Exponential Function2.3 The β-Liouville Theorem2.4 Constant Coefficients2.5 Nonlinear Systems2.6 Advanced Practical Problems3. Functionals3.1 Definition for Functionals3.2 Self-Adjoint Second Order Matrix Equations3.3 The Jacobi Condition3.4 Sturmian Theory4. Linear Hamiltonian Dynamic Systems4.1 Linear Symplectic Dynamic Systems4.2 Hamiltonian Systems4.3 Conjoined Bases4.4 Riccati Equations4.5 The Picone Identity4.6 "Big" Linear Hamiltonian Systems4.7 Positivity of Quadratic Functionals 5. The First Variation5.1 The Dubois-Reymond Lemma5.2 The Variational Problem5.3 The Euler-Lagrange Equation5.4 The Legendre Condition5.5 The Jacobi Condition5.6 Advanced Practical Problems6. Higher Order Calculus of Variations6.1 Statement of the Variational Problem6.2 The Euler Equation6.3 Advanced Practical Problems7. Double Integral Calculus of Variations7.1 Statement of the Variational Problem7.2 First and Second Variation7.3 The Euler Condition7.4 Advanced Practical Problems 8. The Noether Second Theorem8.1 Invariance under Transformations8.2 The Noether Second Theorem without Transformations of Time8.3 The Noether Second Theorem with Transformations of Time8.4 The Noether Second Theorem-Double Delta Integral CaseReferencesIndex Details ISBN1032900695 Author Khaled Zennir Publisher Taylor & Francis Ltd Year 2024 ISBN-13 9781032900698 Format Paperback Imprint Chapman & Hall/CRC Country of Publication United Kingdom Alternative 9781032899732 Audience Tertiary & Higher Education ISBN-10 1032900695 Publication Date 2024-12-19 UK Release Date 2024-12-19 Series Advances in Applied Mathematics DEWEY 515.64 Pages 258 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:168580979;

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