Böcker av Dingyu Xue

Fractional calculus and its applications are fascinating research areas in many engineering disciplines. This book is a comprehensive collection of research from the author's group, which is one of the most active in the fractional calculus community worldwide and is the birthplace of one of the four MATLAB toolboxes in fractional calculus, the FOTF Toolbox. The book presents high-precision solution algorithms for a variety of fractional-order differential equations, including nonlinear, delay, and boundary value equations. Currently, there are no other universal solvers available for the latter two types of equations. Through this book, readers can systematically study the mathematics and solution methods in the field of fractional calculus and apply these concepts to different engineering fields, particularly control systems engineering.This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.

The textbook is intended for teaching MATLAB language and its applications. The book is composed of three parts: MATLAB programming, scientific computing with MATLAB, and system simulation with Simulink. Since MATLAB is widely used in all fields of science and engineering, a good introduction to the language can not only help students learn how to use it to solve practical problems, but also provide them with the skills to use MATLAB independently in their later courses and research. The three parts of the book are well-balanced and tailored to the needs of engineering students, and the mathematical problems commonly encountered in engineering can be easily solved using MATLAB. This textbook is suitable for undergraduate and graduate students majoring in science and engineering.The study guide of this textbook could be accessed via: http://sn.pub/thGR7v. This website provides links to recorded teaching videos, MATLAB toolbox for the book, interactive slide decks files in Powerpoint documents, and solution manuals by the authors.

This book focuses the solutions of linear algebra and matrix analysis problems, with the exclusive use of MATLAB. The topics include representations, fundamental analysis, transformations of matrices, matrix equation solutions as well as matrix functions. Attempts on matrix and linear algebra applications are also explored.

This book focuses on solving optimization problems with MATLAB. Descriptions and solutions of nonlinear equations of any form are studied first. Focuses are made on the solutions of various types of optimization problems, including unconstrained and constrained optimizations, mixed integer, multiobjective and dynamic programming problems. Comparative studies and conclusions on intelligent global solvers are also provided.

This book focuses on solving practical problems in calculus with MATLAB. Descriptions and sketching of functions and sequences are introduced first, followed by the analytical solutions of limit, differentiation, integral and function approximation problems of univariate and multivariate functions. Advanced topics such as numerical differentiations and integrals, integral transforms as well as fractional calculus are also covered in the book.

This book presents fundamentals in MATLAB programming, including data and statement structures, control structures, function writing and bugging in MATLAB programming, followed by the presentations of algebraic computation, transcendental function evaluations and data processing. Advanced topics such as MATLAB interfacing, object-oriented programming and graphical user interface design are also addressed.

This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to find high-precision solutions to fractional-order differentiations and differential equations. Numerical algorithms and their implementations are proposed to analyze multivariable fractional-order control systems. Through high-quality MATLAB programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems. ContentsIntroduction to fractional calculus and fractional-order controlMathematical prerequisitesDefinitions and computation algorithms of fractional-order derivatives and IntegralsSolutions of linear fractional-order differential equationsApproximation of fractional-order operatorsModelling and analysis of multivariable fractional-order transfer function MatricesState space modelling and analysis of linear fractional-order SystemsNumerical solutions of nonlinear fractional-order differential EquationsDesign of fractional-order PID controllersFrequency domain controller design for multivariable fractional-order SystemsInverse Laplace transforms involving fractional and irrational OperationsFOTF Toolbox functions and modelsBenchmark problems for the assessment of fractional-order differential equation algorithms