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Author: Victor A. Sadovnichiy Publisher: Springer ISBN: 331996755X Category : Technology & Engineering Languages : en Pages : 564
Book Description
In this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical systems. These abstract mathematical approaches are applied to problem-solving in solid mechanics, hydro- and aerodynamics, optimization, decision making theory and control theory. This volume is therefore relevant to mathematicians as well as engineers working at the interface of these fields.
Author: Victor A. Sadovnichiy Publisher: Springer ISBN: 331996755X Category : Technology & Engineering Languages : en Pages : 564
Book Description
In this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical systems. These abstract mathematical approaches are applied to problem-solving in solid mechanics, hydro- and aerodynamics, optimization, decision making theory and control theory. This volume is therefore relevant to mathematicians as well as engineers working at the interface of these fields.
Author: V.I. Arnol'd Publisher: Springer Science & Business Media ISBN: 1475720637 Category : Mathematics Languages : en Pages : 530
Book Description
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Author: David Yang Gao Publisher: Springer Science & Business Media ISBN: 1461302471 Category : Science Languages : en Pages : 329
Book Description
As any human activity needs goals, mathematical research needs problems -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the ben eficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a du ality gap between the two partners, and this gap is growing wider. Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications which fall into the two following complementary categories: 1. An annual book dedicated to the latest developments in mechanics and mathematics; 2. Monographs, advanced textbooks, handbooks, edited vol umes and selected conference proceedings. The AMMA annual book publishes invited and contributed compre hensive reviews, research and survey articles within the broad area of modern mechanics and applied mathematics. Mechanics is understood here in the most general sense of the word, and is taken to embrace relevant physical and biological phenomena involving electromagnetic, thermal and quantum effects and biomechanics, as well as general dy namical systems. Especially encouraged are articles on mathematical and computational models and methods based on mechanics and their interactions with other fields. All contributions will be reviewed so as to guarantee the highest possible scientific standards.
Author: David Y. Gao Publisher: CRC Press ISBN: 1420011731 Category : Mathematics Languages : en Pages : 270
Book Description
Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m
Author: Stephanie Frank Singer Publisher: Springer Science & Business Media ISBN: 1461201896 Category : Mathematics Languages : en Pages : 201
Book Description
"And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is required: we introduce and illustrate all necessary con structs.
Author: W.-H. Steeb Publisher: Springer Science & Business Media ISBN: 9401153329 Category : Science Languages : en Pages : 247
Book Description
This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. Audience: The book is suitable for graduate students in physics and mathematics.
Author: Martin Kružík Publisher: Springer ISBN: 3030020657 Category : Science Languages : en Pages : 624
Book Description
This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.
Author: Ellis D Cooper Publisher: World Scientific ISBN: 981446631X Category : Mathematics Languages : en Pages : 390
Book Description
This unprecedented book offers all the details of the mathematical mechanics underlying modern modeling of skeletal muscle contraction. The aim is to provide an integrated vision of mathematics, physics, chemistry and biology for this one understanding. The method is to take advantage of latest mathematical technologies — Eilenberg-Mac Lane category theory, Robinson infinitesimal calculus and Kolmogorov probability theory — to explicate Particle Mechanics, The Theory of Substances (categorical thermodynamics), and computer simulation using a diagram-based parallel programming language (stochastic timing machinery). Proofs rely almost entirely on algebraic calculations without set theory. Metaphors and analogies, and distinctions between representational pictures, mental model drawings, and mathematical diagrams are offered.AP level high school calculus students, high school science teachers, undergraduates and graduate college students, and researchers in mathematics, physics, chemistry, and biology may use this integrated publication to broaden their perspective on science, and to experience the precision that mathematical mechanics brings to understanding the molecular mechanism vital for nearly all animal behavior.
Author: Shijun Liao Publisher: CRC Press ISBN: 1135438293 Category : Mathematics Languages : en Pages : 335
Book Description
Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.
Author: Victor A. Sadovnichiy
Author: Victor A. Sadovnichiy
Author: V.I. Arnol'd
Author: David Yang Gao
Author: David Y. Gao
Author: Michael Spivak
Author: Stephanie Frank Singer
Author: W.-H. Steeb
Author: Martin Kružík
Author: Ellis D Cooper
Author: Shijun Liao