Georgiev S.G., Zennir K. General Quantum Numerical Analysis

CRC Press, 2024. - 370 p. - (Advances in Applied Mathematics). - ISBN 1032741503.This book is focused on the qualitative theory of general quantum calculus, the modern name for the investigation of calculus without limits. It centers on designing, analysing and applying computational techniques for general quantum differential equations. The 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 Euler and Jacobi. Recently, it has aroused interest due to high demand of mathematics that models quantum computing and the connection between mathematics and physics. Quantum calculus has many applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hyper-geometric functions and other sciences such as quantum theory, mechanics and the theory of relativity. The authors summarize the most recent contributions in this area. General Quantum Numerical Analysis is intended for senior undergraduate students and beginning graduate students of engineering and science courses. The twelve chapters in this book are pedagogically organized, each concluding with a section of practical problems.Preface.
General Quantum Differentiation.
General Quantum Integration.
β-Elementary Functions.
General Quantum Polynomial Interpolation.
Numerical β-Integration.
Piecewise Polynomial Approximation.
The Euler Method.
The Order-Two Taylor Series Method-TS(2).
The Order-p Taylor Series Method-TS(p).
Linear Multistep Methods-LMMs.
Runge-Kutta Methods-RMMs.
The Adomian Polynomials Method.
Bibliography.
Index.True PDF