General Quantum Numerical Analysis

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 FH Jackson in the early twentieth century, but this kind of calculus had already been worked out by Euler and Jacobi. Recently it arose interest due to high demand of mathematics that models quantum computing and in 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 quantum theory, mechanics and the theory of relativity. The authors summarize the most recent contributions in this area. The book is intended for senior undergraduate students and beginning graduate students of engineering and science courses. There are twelve chapters in this book. The chapters in the book are pedagogically organized. Each chapter concludes with a section with practical problems.