Dynamical Systems and Differential Geometry via MAPLE
Dynamical Systems and Differential Geometry via MAPLE

Author: Constantin Udriste

Publisher: Cambridge Scholars Publishing

Published: 2021-10-01

Total Pages: 254

ISBN-13: 1527572951

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The area of dynamical systems and differential geometry via MAPLE is a field which has become exceedingly technical in recent years. In the field, everything is structured for the benefit of optimizing evolutionary geometric aspects that describe significant physical or engineering phenomena. This book is structured in terms of the importance, accessibility and impact of theoretical notions capable of shaping a future mathematician-computer scientist possessing knowledge of evolutionary dynamical systems. It provides a self-contained and accessible introduction for graduate and advanced undergraduate students in mathematics, engineering, physics, and economic sciences. This book is suitable for both self-study for students and professors with a background in differential geometry and for teaching a semester-long introductory graduate course in dynamical systems and differential geometry via MAPLE.

Dynamical Systems and Differential Geometry Via MAPLE
Dynamical Systems and Differential Geometry Via MAPLE

Author: Constantin Udriste

Publisher:

Published: 2021-10

Total Pages:

ISBN-13: 9781527572232

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The area of dynamical systems and differential geometry via MAPLE is a field which has become exceedingly technical in recent years. In the field, everything is structured for the benefit of optimizing evolutionary geometric aspects that describe significant physical or engineering phenomena. This book is structured in terms of the importance, accessibility and impact of theoretical notions capable of shaping a future mathematician-computer scientist possessing knowledge of evolutionary dynamical systems. It provides a self-contained and accessible introduction for graduate and advanced undergraduate students in mathematics, engineering, physics, and economic sciences. This book is suitable for both self-study for students and professors with a background in differential geometry and for teaching a semester-long introductory graduate course in dynamical systems and differential geometry via MAPLE.

Dynamical Systems with Applications using MAPLE
Dynamical Systems with Applications using MAPLE

Author: Stephen Lynch

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 400

ISBN-13: 1489928499

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Since the first edition of this book was published in 2001, MapleTM has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. This text is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering.

Dynamical Systems with Applications using MapleTM
Dynamical Systems with Applications using MapleTM

Author: Stephen Lynch

Publisher: Springer Science & Business Media

Published: 2009-12-23

Total Pages: 512

ISBN-13: 0817646051

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Excellent reviews of the first edition (Mathematical Reviews, SIAM, Reviews, UK Nonlinear News, The Maple Reporter) New edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions Two new chapters on neural networks and simulation have also been added Wide variety of topics covered with applications to many fields, including mechanical systems, chemical kinetics, economics, population dynamics, nonlinear optics, and materials science Accessible to a broad, interdisciplinary audience of readers with a general mathematical background, including senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering A hands-on approach is used with Maple as a pedagogical tool throughout; Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website with additional applications and further links of interest at Maplesoft’s Application Center

Differential Dynamical Systems, Revised Edition
Differential Dynamical Systems, Revised Edition

Author: James D. Meiss

Publisher: SIAM

Published: 2017-01-24

Total Pages: 410

ISBN-13: 161197464X

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Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.

Variational Calculus with Engineering Applications
Variational Calculus with Engineering Applications

Author: Constantin Udriste

Publisher: John Wiley & Sons

Published: 2023-02-13

Total Pages: 228

ISBN-13: 1119944368

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A comprehensive overview of foundational variational methods for problems in engineering Variational calculus is a field in which small alterations in functions and functionals are used to find their relevant maxima and minima. It is a potent tool for addressing a range of dynamic problems with otherwise counter-intuitive solutions, particularly ones incorporating multiple confounding variables. Its value in engineering fields, where materials and geometric configurations can produce highly specific problems with unconventional or unintuitive solutions, is considerable. Variational Calculus with Engineering Applications provides a comprehensive survey of this toolkit and its engineering applications. Balancing theory and practice, it offers a thorough and accessible introduction to the field pioneered by Euler, Lagrange and Hamilton, offering tools that can be every bit as powerful as the better-known Newtonian mechanics. It is an indispensable resource for those looking for engineering-oriented overview of a subject whose capacity to provide engineering solutions is only increasing. Variational Calculus with Engineering Applications readers will also find: Discussion of subjects including variational principles, levitation, geometric dynamics, and more Examples and instructional problems in every Chapter, along with MAPLE codes for performing the simulations described in each Engineering applications based on simple, curvilinear, and multiple integral functionals Variational Calculus with Engineering Applications is ideal for advanced students, researchers, and instructors in engineering and materials science.

Geometric Dynamics
Geometric Dynamics

Author: Constantin Udriște

Publisher: Springer Science & Business Media

Published: 2000

Total Pages: 416

ISBN-13: 9780792364016

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The theme of this text is the philosophy that any particle flow generates a particle dynamics, in a suitable geometrical framework. It covers topics that include: geometrical and physical vector fields; field lines; flows; stability of equilibrium points; potential systems and catastrophe geometry; field hypersurfaces; bifurcations; distribution orthogonal to a vector field; extrema with nonholonomic constraints; thermodynamic systems; energies; geometric dynamics induced by a vector field; magnetic fields around piecewise rectilinear electric circuits; geometric magnetic dynamics; and granular materials and their mechanical behaviour. The text should be useful for first-year graduate students in mathematics, mechanics, physics, engineering, biology, chemistry, and economics. It can also be addressed to professors and researchers whose work involves mathematics, mechanics, physics, engineering, biology, chemistry, and economics.

Mathematical Methods for Physics
Mathematical Methods for Physics

Author: J. R. Claycomb

Publisher: Stylus Publishing, LLC

Published: 2018-03-20

Total Pages: 1122

ISBN-13: 1683920996

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This book may be used by students and professionals in physics and engineering that have completed first-year calculus and physics. An introductory chapter reviews algebra, trigonometry, units and complex numbers that are frequently used in physics. Examples using MATLAB and Maple for symbolic and numerical calculations in physics with a variety of plotting features are included in all 16 chapters. The book applies many of mathematical concepts covered in Chapters 1-9 to fundamental physics topics in mechanics, electromagnetics; quantum mechanics and relativity in Chapters 10-16. Companion files are included with MATLAB and Maple worksheets and files, and all of the figures from the text. Features: • Each chapter includes the mathematical development of the concept with numerous examples • MATLAB & Maple examples are integrated in each chapter throughout the book • Applies the mathematical concepts to fundamental physics principles such as relativity, mechanics, electromagnetics, etc. • Introduces basic MATLAB and Maple commands and programming structures • Includes companion files with MATLAB and Maple files and worksheets, and all of the figures from the text

Exploring Discrete Mathematics with Maple
Exploring Discrete Mathematics with Maple

Author: Kenneth H. Rosen

Publisher: McGraw-Hill Science, Engineering & Mathematics

Published: 1997

Total Pages: 0

ISBN-13: 9780070541283

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This is the first supplement in discrete mathematics to concentrate on the computational aspects of the computer algebra system Maple. Detailed instructions for the use of Maple are included in an introductory chapter and in each subsequent chapter. Each chapter includes discussion of selected Computational and Exploration exercises in the corresponding chapter of Ken Rosen's text Discrete Math and It's Applications, Third Edition. New exercises and projects are included in each chapter to encourage further exploration of discrete mathematics using Maple. All of the Maple code in this supplement is available online via the Waterloo Maple Web site, in addition to new Maple routines that have been created which extend the current capabilities of Maple.

Dynamical Systems with Applications using Mathematica®
Dynamical Systems with Applications using Mathematica®

Author: Stephen Lynch

Publisher: Springer Science & Business Media

Published: 2007-09-20

Total Pages: 481

ISBN-13: 0817645861

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This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.