Simon Serovajsky - Böcker

Mathematical Modelling sets out the general principles of mathematical modelling as a means comprehending the world. Within the book, the problems of physics, engineering, chemistry, biology, medicine, economics, ecology, sociology, psychology, political science, etc. are all considered through this uniform lens. The author describes different classes of models, including lumped and distributed parameter systems, deterministic and stochastic models, continuous and discrete models, static and dynamical systems, and more. From a mathematical point of view, the considered models can be understood as equations and systems of equations of different nature and variational principles. In addition to this, mathematical features of mathematical models, applied control and optimization problems based on mathematical models, and identification of mathematical models are also presented.Features Each chapter includes four levels: a lecture (main chapter material), an appendix (additional information), notes (explanations, technical calculations, literature review) and tasks for independent work; this is suitable for undergraduates and graduate students and does not require the reader to take any prerequisite course, but may be useful for researchers as well Described mathematical models are grouped both by areas of application and by the types of obtained mathematical problems, which contributes to both the breadth of coverage of the material and the depth of its understanding Can be used as the main textbook on a mathematical modelling course, and is also recommended for special courses on mathematical models for physics, chemistry, biology, economics, etc.

Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject.Features All notions and properties are introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture.

The equations of mathematical physics are the mathematical models of the large class of phenomenon of physics, chemistry, biology, economics, etc. In Sequential Models of Mathematical Physics, the author considers the justification of the process of constructing mathematical models. The book seeks to determine the classic, generalized and sequential solutions, the relationship between these solutions, its direct physical sense, the methods of its practical finding, and its existence.Features Describes a sequential method based on the construction of space completion, as well as its applications in number theory, the theory of distributions, the theory of extremum, and mathematical physics Presentation of the material is carried out on the simplest example of a one-dimensional stationary heat transfer process; all necessary concepts and constructions are introduced and illustrated with elementary examples, which makes the material accessible to a wide area of readers The solution of a specific mathematical problem is obtained as a result of the joint application of methods and concepts from completely different mathematical directions

Mathematical Modelling sets out the general principles of mathematical modelling as a means comprehending the world. Within the book, the problems of physics, engineering, chemistry, biology, medicine, economics, ecology, sociology, psychology, political science, etc. are all considered through this uniform lens. The author describes different classes of models, including lumped and distributed parameter systems, deterministic and stochastic models, continuous and discrete models, static and dynamical systems, and more. From a mathematical point of view, the considered models can be understood as equations and systems of equations of different nature and variational principles. In addition to this, mathematical features of mathematical models, applied control and optimization problems based on mathematical models, and identification of mathematical models are also presented.Features Each chapter includes four levels: a lecture (main chapter material), an appendix (additional information), notes (explanations, technical calculations, literature review) and tasks for independent work; this is suitable for undergraduates and graduate students and does not require the reader to take any prerequisite course, but may be useful for researchers as well Described mathematical models are grouped both by areas of application and by the types of obtained mathematical problems, which contributes to both the breadth of coverage of the material and the depth of its understanding Can be used as the main textbook on a mathematical modelling course, and is also recommended for special courses on mathematical models for physics, chemistry, biology, economics, etc.

Optimization: 100 Examples is a book devoted to the analysis of scenarios for which the use of well-known optimization methods encounter certain difficulties. Analysing such examples allows a deeper understanding of the features of these optimization methods, including the limits of their applicability. In this way, the book seeks to stimulate further development and understanding of the theory of optimal control. The study of the presented examples makes it possible to more effectively diagnose problems that arise in the practical solution of optimal control problems, and to find ways to overcome the difficulties that have arisen. FeaturesVast collection of examplesSimple. accessible presentationSuitable as a research reference for anyone with an interest in optimization and optimal control theory, including mathematicians and engineersExamples differ in properties, i.e. each effect for each class of problems is illustrated by a unique example.Simon Serovajsky is a professor of mathematics at Al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of optimization and optimal control theory, mathematical physics, mathematical modelling, philosophy and history of mathematics as well as a long list of high-quality publications in learned journals.

The equations of mathematical physics are the mathematical models of the large class of phenomenon of physics, chemistry, biology, economics, etc. In Sequential Models of Mathematical Physics, the author considers the justification of the process of constructing mathematical models. The book seeks to determine the classic, generalized and sequential solutions, the relationship between these solutions, its direct physical sense, the methods of its practical finding, and its existence.Features Describes a sequential method based on the construction of space completion, as well as its applications in number theory, the theory of distributions, the theory of extremum, and mathematical physics Presentation of the material is carried out on the simplest example of a one-dimensional stationary heat transfer process; all necessary concepts and constructions are introduced and illustrated with elementary examples, which makes the material accessible to a wide area of readers The solution of a specific mathematical problem is obtained as a result of the joint application of methods and concepts from completely different mathematical directions

Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject.Features All notions and properties are introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture.