This book explores boundary value problems for Riemann-Liouville fractional dynamic equations on arbitrary time scales as well as the shifting problem on the whole time scale. The author includes an introductory overview of fractional dynamic calculus on time scales. The book also introduces the Laplace transform on arbitrary time scales, including the bilateral Laplace transform, the Laplace transform of power series, and a deduction of an inverse formula. The author then discusses the generalized convolutions of functions on arbitrary time scales and the shifting problem for existence of...
This book explores boundary value problems for Riemann-Liouville fractional dynamic equations on arbitrary time scales as well as the shifting prob...
This book addresses the description and analysis of occurrence data frequently encountered in epidemiological studies. With the occurrence of Covid-19, people have been exposed to the analysis and interpretation of epidemiological data. To be informed consumers of this information, people need to understand the nature and analysis of these data. Effort is made to emphasize concepts rather than mathematics. Subjects range from description of the frequencies of disease to the analysis of associations between the occurrence of disease and exposure. Those analyses begin with simple...
This book addresses the description and analysis of occurrence data frequently encountered in epidemiological studies. With the occurrence of Covi...
This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how to obtain frequencies that are present in numerical data and utilizes Mathematica to illustrate the calculations. This book also contains numerical solution of differential equation of driven damped oscillator using 4th order Runge-Kutta method. Numerical solutions are compared with analytical solutions, and the behaviors of mechanical system are also depicted by plotting velocity versus displacement rather than displaying displacement as a...
This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how t...
This book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q-functions. Classical multivariate discrete distributions are defined on a sequence of independent and identically distributed Bernoulli trials, with either being a success of a certain rank (level) or a failure. The author relaxes the assumption that the probability of success of a trial is constant by assuming that it varies geometrically with the number of trials and/or the number of successes. The latter is advantageous in the sense that it...
This book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q...
This book presents a short introduction to the main tools of optimization methodology including linear programming, steepest descent, conjugate gradients, and the Karush-Kuhn-Tucker-John conditions. Each topic is developed in terms of a specific physical model, so that the strategy behind every step is motivated by a logical, concrete, easily visualized objective. A quick perusal of the Fibonacci search algorithm provides a simple and tantalizing first encounter with optimization theory, and a review of the max-min exposition of one-dimensional calculus prepares readers for the more...
This book presents a short introduction to the main tools of optimization methodology including linear programming, steepest descent, conjugate g...
This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build a theory of generalized differentiation for convex functions and sets in finite dimensions. The book serves as a bridge for the readers who have just started using convex analysis to reach deeper topics in the field. Detailed proofs are presented for most of the results in the book and also included are many figures and...
This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible tech...
This book explores boundary value problems for fractional dynamic equations on arbitrary time scales, including Caputo fractional dynamic equations, impulsive Caputo fractional dynamic equations, and impulsive Riemann-Liouville fractional dynamic equations. The author provides an introduction to each fractional dynamic equation before delving into the problems. The book also covers initial value problems, boundary value problems, initial boundary value problems for each type of equation. The author provides integral representations of the solutions and proves the existence and uniqueness...
This book explores boundary value problems for fractional dynamic equations on arbitrary time scales, including Caputo fractional dynamic equations...
This book explores boundary value problems for Riemann-Liouville fractional dynamic equations on arbitrary time scales as well as the shifting problem on the whole time scale. The author includes an introductory overview of fractional dynamic calculus on time scales. The book also introduces the Laplace transform on arbitrary time scales, including the bilateral Laplace transform, the Laplace transform of power series, and a deduction of an inverse formula. The author then discusses the generalized convolutions of functions on arbitrary time scales and the shifting problem for existence of...
This book explores boundary value problems for Riemann-Liouville fractional dynamic equations on arbitrary time scales as well as the shifting prob...
This book is intended for a first-semester course in calculus, which begins by posing a question: how do we model an epidemic mathematically? The authors use this question as a natural motivation for the study of calculus and as a context through which central calculus notions can be understood intuitively. The book’s approach to calculus is contextual and based on the principle that calculus is motivated and elucidated by its relevance to the modeling of various natural phenomena. The authors also approach calculus from a computational perspective, explaining that many natural phenomena...
This book is intended for a first-semester course in calculus, which begins by posing a question: how do we model an epidemic mathematically? The auth...
This book describes how complex systems from a variety of fields can be modeled using quantum mechanical ideas; from biology and ecology, to sociology and decision-making. Quantum mechanics is traditionally associated with microscopic systems; however, quantum concepts have also been successfully applied to a wide range of macroscopic systems both within and outside physics. The mathematical basis of these models is covered in detail, providing a self-contained and consistent approach. This book provides unique insight into the dynamics of these macroscopic systems and opens new...
This book describes how complex systems from a variety of fields can be modeled using quantum mechanical ideas; from biology and ecology, to sociol...
