Discrete Hilbert-type inequalities including Hilbert's inequality are important in mathematical analysis and its applications. In 1998, the author presented an extension of Hilbert's integral inequality with an independent parameter. In 2004, some new extensions of Hilbert's inequality were presented by introducing two pairs of conjugate exponents and additional independent parameters. Since then, a number of new discrete Hilbert-type inequalities have arisen. In this book, the author explains how to use the way of weight coefficients and introduce specific parameters to build new discrete Hilbert-type inequalities and consider some applications. The book is intended to augment the reader's understanding of Hilbert-type inequalities.

This e-book presents several research areas of elliptical problems solved by differential equations. The mathematical models explained in this e-book have been contributed by experts in the field and can be applied to a wide range of real life examples. Methods explained include pre-conditioned conjugate grid models, higher order discretization and finite element mesh generation. This e-book should be a useful reference for scholars and professionals interested in elliptical partial differential equations.

Exterior calculus is a branch of mathematics which involves differential geometry. In Exterior calculus the concept of differentiations is generalized to antisymmetric exterior derivatives and the notions of ordinary integration to differentiable manifolds of arbitrary dimensions. It therefore generalizes the fundamental theorem of calculus to Stokes' theorem. This textbook covers the fundamental requirements of exterior calculus in curricula for college students in mathematics and engineering programs. Chapters start from Heaviside-Gibbs algebra, and progress to different concepts in Grassman algebra. The final section of the book covers applications of exterior calculus with solutions. Readers will find a concise and clear study of vector calculus and differential geometry, along with several examples and exercises. The solutions to the exercises are also included at the end of the book. This is an ideal book for students with a basic background in mathematics who wish to learn about exterior calculus as part of their college curriculum and equip themselves with the knowledge to apply relevant theoretical concepts in practical situations.

This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics and applications. The information in the book is presented in four parts: 1. Fractional Diffusion Equations: (i) solutions of fractional diffusion equations using wavelet methods, (ii) the maximum principle for time fractional diffusion equations, (iii) nonlinear sub-diffusion equations. 2. Mathematical Analysis: (i) shifted Jacobi polynomials for solving and identifying coupled fractional delay differential equations, (ii) the monotone iteration principle in the theory of Hadamard fractional delay differential equations, (iii) dynamics of fractional order modified Bhalekar-Gejji System, (iv) Grunwald-Letnikov derivatives. 3. Computational Techniques: GPU computing of special mathematical functions used in fractional calculus. 4. Reviews: (i) the popular iterative method NIM, (ii) fractional derivative with non-singular kernels, (iii) some open problems in fractional order nonlinear system This is a useful reference for researchers and graduate level mathematics students seeking knowledge about of fractional calculus and applied mathematics.

The knowledge of quantitative turbulence mechanics relies heavily upon the definition of the concept of a vortex in mathematical terms. This reference work introduces the reader to Liutex, which is an accepted, accurate and mathematical definition of a vortex. The core of this book is a compilation of several papers on the subject. presented in the 13th World Congress of Computational Mechanics (WCCM2018), Symposium 704, Mathematics and Computations for Multiscale Structures of Turbulent and Other Complex Flows, New York, United States on July 27, 2018. This compilation also includes other research papers which explain the work done on the vortex definition, vortex identification and turbulence structure from different insight angles including mathematics, computational physics and experiments. The thirteen chapters in this volume will be informative to scientists and engineers who are interested in advanced theories about fluid dynamics, vortex science and turbulence research.

Higher Mathematics for Science, Technology and Engineering is a textbook for undergraduate and postgraduate students undertaking science, technology, engineering and mathematics (STEM) courses. The book begins with an introduction to one variable functions, followed by chapters covering functional derivatives, partial differentiation, integrals, matrices and determinant theory, partial fractions and much more. Key features of this textbook include: -simple, easy-to-understand explanations of relevant concepts -a wide range of simple and complex examples -several figures where appropriate

Hilbert-type integral inequalities, including the well known Hilbert’s integral inequality published in 1908, are important in analysis and its applications. This well organized handbook covers the newest methods of weight functions and most important recent results of Hilbert-type integral inequalities and applications in three classes of normal spaces. It is clear and well written, suitable for researchers, mathematicians and advanced students who wish to increase their familiarity with different topics of modern and classical mathematical inequalities related to Real Analysis and Operator Theory. Both basic and applied aspects are presented in this book. The many illustrative worked-out examples given in several chapters should help readers acquire expertise in this field.

This Ebook is concerned with both the theory of the Kurzweil-Henstock integral and the basic facts on Riesz spaces. Moreover, even the so-called Šipoš integral, which has several applications in economy, is illustrated. The aim of this Ebook is two-fold. First, it can be understood as an introductory textbook to the Kurzweil-Henstock integral as well as to some algebraic structures which are important from the viewpoint of applications to integration and probability theory. Second, it discusses some possibilities of further developments including recent results and open problems.

Numberama: Recreational Number Theory in the School System presents number patterns and mathematical formulas that can be taught to children in schools. The number theories and problems are reinforced by enjoyable games that children can play to enhance their learning in a fun-loving way. Key features of the book include: • information about a number of well-known number theory problems such as Fibonaccci numbers, triangular numbers, perfect numbers, sums of squares, and Diophantine equations • organized presentation based on skill level for easy understanding • all basic mathematical operations for elementary school children • a range of algebraic formulae for middle school students • descriptions of positive feedback and testimonials where recreational number theory has been effective in schools and education programs This book is a useful handbook for elementary and middle-school teachers, students, and parents who will be able to experience the inherent joys brought by teaching number theory to children in a recreational way.

“ Lecture Notes in Numerical Analysis with Mathematica” highlights most of the important algorithms and their solved examples by Mathematica. The contents of this book include chapters on floating point computer arithmetic, natural and generalized interpolating polynomials, uniform approximation, numerical integration, polynomial splines and many more. This book is intended for undergraduate and graduate students in institutes, colleges, universities and academies who want to specialize in this field. The readers will develop a solid understanding of the concepts of numerical methods and their application. The inclusion of Lagrane and Hermite approximation by polynomials, Trapezian rule, Simpsons rule, Gauss methods and Romberg`s methods with illustrative examples is a valuable resource for the readers. Each chapter ends with examples and test questions.