Vladimir Dobrushkin's Books

Handbook of Differential Equations

By: Daniel Zwillinger,Vladimir Dobrushkin

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Handbook of Differential Equations

By: Daniel Zwillinger,Vladimir Dobrushkin

Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers. The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.

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Page Count

737

Publisher

CRC Press

Published Date

ISBN 10

100046816X

ISBN 13

9781000468168

Methods in Algorithmic Analysis

By: Vladimir A. Dobrushkin

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Methods in Algorithmic Analysis

By: Vladimir A. Dobrushkin

Explores the Impact of the Analysis of Algorithms on Many Areas within and beyond Computer Science A flexible, interactive teaching format enhanced by a large selection of examples and exercises Developed from the author’s own graduate-level course, Methods in Algorithmic Analysis presents numerous theories, techniques, and methods used for analyzing algorithms. It exposes students to mathematical techniques and methods that are practical and relevant to theoretical aspects of computer science. After introducing basic mathematical and combinatorial methods, the text focuses on various aspects of probability, including finite sets, random variables, distributions, Bayes’ theorem, and Chebyshev inequality. It explores the role of recurrences in computer science, numerical analysis, engineering, and discrete mathematics applications. The author then describes the powerful tool of generating functions, which is demonstrated in enumeration problems, such as probabilistic algorithms, compositions and partitions of integers, and shuffling. He also discusses the symbolic method, the principle of inclusion and exclusion, and its applications. The book goes on to show how strings can be manipulated and counted, how the finite state machine and Markov chains can help solve probabilistic and combinatorial problems, how to derive asymptotic results, and how convergence and singularities play leading roles in deducing asymptotic information from generating functions. The final chapter presents the definitions and properties of the mathematical infrastructure needed to accommodate generating functions. Accompanied by more than 1,000 examples and exercises, this comprehensive, classroom-tested text develops students’ understanding of the mathematical methodology behind the analysis of algorithms. It emphasizes the important relation between continuous (classical) mathematics and discrete mathematics, which is the basis of computer science.

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Page Count

824

Publisher

CRC Press

Published Date

ISBN 10

142006830X

ISBN 13

9781420068306

Applied Differential Equations

The Primary Course

By: Vladimir A. Dobrushkin

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Applied Differential Equations

The Primary Course

By: Vladimir A. Dobrushkin

A Contemporary Approach to Teaching Differential Equations Applied Differential Equations: An Introduction presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. Designed for a two-semester undergraduate course, the text offers a true alternative to books published for past generations of students. It enables students majoring in a range of fields to obtain a solid foundation in differential equations. The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations. This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results.

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Page Count

723

Publisher

CRC Press

Published Date

ISBN 10

1498728359

ISBN 13

9781498728355

Fundamentals of Structural Optimization

Stability and Contact Mechanics

By: Vladimir Kobelev

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Fundamentals of Structural Optimization

Stability and Contact Mechanics

By: Vladimir Kobelev

This book serves as a complementary resource to the courses "Advanced structural optimization" and "Structural optimization in automotive engineering" taught by the author at the University of Siegen, North-Rhine-Westphalia, Germany since 2001. Focusing on optimization problems in the field of structural engineering, this book offers a rigorous and analytical approach to problem-solving. Each chapter of the book begins with a brief overview of classical results and the derivation of governing equations. The solutions to optimization problems are then presented in a closed form, with the author guiding readers through several analytical methods for solving stability and contact tasks. Throughout the book, the author takes care to ensure that even readers without extensive experience in numerical computations can understand the conclusion of each relation. The book features several basic optimization problems, selected from a large pool of previously solved problems, with a particular emphasis on the unique features of optimization problems. By presenting analytical solutions, readers can better understand other known optimization problems and gain the skills needed to independently set and solve new problems. With its comprehensive and rigorous approach to problem-solving, this book is sure to enhance the reader's understanding of the field and equip them with the skills needed to tackle new challenges.

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Page Count

368

Publisher

Springer Nature

Published Date

ISBN 10

3031346327

ISBN 13

9783031346323

Methods of the Classical Theory of Elastodynamics

By: Vladimir B. Poruchikov

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Methods of the Classical Theory of Elastodynamics

By: Vladimir B. Poruchikov

Methods of the Classical Theory of Elastodynamics" deals not only with classical methods as developed in the past decades, but presents also very recent approaches. Applications and solutions to specific problems serve to illustrate the theoretical presentation. Keywords: Smirnov-Sobolev method with further developments; integral transforms; Wiener-Hopf technique; mixed boundary-value problems; time-dependent boundaries; solutions for unisotropic media (Willis method); 3-d dynamical problems for mixed boundary conditions.

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Page Count

329

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642770991

ISBN 13

9783642770999

Classical Vector Algebra

By: Vladimir Lepetic

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Classical Vector Algebra

By: Vladimir Lepetic

Every physicist, engineer, and certainly a mathematician, would undoubtedly agree that vector algebra is a part of basic mathematical instruments packed in their toolbox. Classical Vector Algebra should be viewed as a prerequisite, an introduction, for other mathematical courses dealing with vectors, following typical form and appropriate rigor of more advanced mathematics texts. Vector algebra discussed in this book briefly addresses vectors in general 3-dimensional Euclidian space, and then, in more detail, looks at vectors in Cartesian 3 space. These vectors are easier to visualize and their operational techniques are relatively simple, but they are necessary for the study of Vector Analysis. In addition, this book could also serve as a good way to build up intuitive knowledge for more abstract structures of -dimensional vector spaces. Definitions, theorems, proofs, corollaries, examples, and so on are not useless formalism, even in an introductory treatise -- they are the way mathematical thinking has to be structured. In other words, "introduction" and "rigor" are not mutually exclusive. The material in this book is neither difficult nor easy. The text is a serious exposition of a part of mathematics students need to master in order to be proficient in their field. In addition to the detailed outline of the theory, the book contains literally hundreds of corresponding examples/exercises.

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Page Count

155

Publisher

CRC Press

Published Date

ISBN 10

1000803686

ISBN 13

9781000803686

Applied Differential Equations

The Primary Course

By: Vladimir A. Dobrushkin

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Applied Differential Equations

The Primary Course

By: Vladimir A. Dobrushkin

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Page Count

723

Publisher

CRC Press

Published Date

ISBN 10

1498728359

ISBN 13

9781498728355

Applied Differential Equations with Boundary Value Problems

By: Vladimir Dobrushkin

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Applied Differential Equations with Boundary Value Problems

By: Vladimir Dobrushkin

Applied Differential Equations with Boundary Value Problems presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. This new edition of the author’s popular textbook adds coverage of boundary value problems. The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations. This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results.

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Page Count

699

Publisher

CRC Press

Published Date

ISBN 10

1498733689

ISBN 13

9781498733687

Book's by Vladimir Dobrushkin

Handbook of Differential Equations

Handbook of Differential Equations

Methods in Algorithmic Analysis

Methods in Algorithmic Analysis

Applied Differential Equations

Applied Differential Equations

Fundamentals of Structural Optimization

Fundamentals of Structural Optimization

Methods of the Classical Theory of Elastodynamics

Methods of the Classical Theory of Elastodynamics

Classical Vector Algebra

Classical Vector Algebra

Applied Differential Equations

Applied Differential Equations

Applied Differential Equations with Boundary Value Problems

Applied Differential Equations with Boundary Value Problems

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