Download or read book Solving Equations with Physical Understanding written by John Reginald Acton and published by CRC Press. This book was released on 1985-08 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: In creating mathematical models of real processes, scientists, engineers and students frequently encounter differential equations whose exact solutions are necessarily complicated and are normally solvable only by computer or through complex formal mathematics. This practical book demonstrates how approximate methods may be used to minimize these mathematical difficulties, giving the reader physical understanding both of the solution process and the final result. Intended for undergraduates and graduate students, teachers of physics, engineering and other applied sciences, professional and applied scientists and engineers.
Download or read book Thinking About Equations written by Matt A. Bernstein and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences. Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including: Approximation and estimation Isolating important variables Generalization and special cases Dimensional analysis and scaling Pictorial methods and graphical solutions Symmetry to simplify equations Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension. Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Download or read book Solving Equations With Physical Understanding written by J.R. Acton and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematics for Physical Chemistry written by Robert G. Mortimer and published by Elsevier. This book was released on 2005-06-10 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data. Numerous examples and problems interspersed throughout the presentations Each extensive chapter contains a preview, objectives, and summary Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory Provides chemistry specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Download or read book Algebraic Approaches to Partial Differential Equations written by Xiaoping Xu and published by Springer Science & Business Media. This book was released on 2013-04-23 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrodinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer problems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations, linearization techniques and special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.
Download or read book Scaling of Differential Equations written by Hans Petter Langtangen and published by Springer. This book was released on 2016-06-15 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
Download or read book Distributions in the Physical and Engineering Sciences Volume 2 written by Alexander I. Saichev and published by Springer Science & Business Media. This book was released on 2013-09-05 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis. Volume 2: Linear and Nonlinear Dynamics of Continuous Media continues the multivolume project which endeavors to show how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researchers in applied mathematics, physical sciences, and engineering. It contains an analysis of the three basic types of linear partial differential equations--elliptic, parabolic, and hyperbolic--as well as chapters on first-order nonlinear partial differential equations and conservation laws, and generalized solutions of first-order nonlinear PDEs. Nonlinear wave, growing interface, and Burger’s equations, KdV equations, and the equations of gas dynamics and porous media are also covered. The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. Features · Application oriented exposition of distributional (Dirac delta) methods in the theory of partial differential equations. Abstract formalism is keep to a minimum. · Careful and rich selection of examples and problems arising in real-life situations. Complete solutions to all exercises appear at the end of the book. · Clear explanations, motivations, and illustration of all necessary mathematical concepts.
Download or read book Understanding Scientific Understanding written by Henk W. de Regt and published by Oxford University Press. This book was released on 2017-07-24 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is widely acknowledged that a central aim of science is to achieve understanding of the world around us, and that possessing such understanding is highly important in our present-day society. But what does it mean to achieve this understanding? What precisely is scientific understanding? These are philosophical questions that have not yet received satisfactory answers. While there has been an ongoing debate about the nature of scientific explanation since Carl Hempel advanced his covering-law model in 1948, the related notion of understanding has been largely neglected, because most philosophers regarded understanding as merely a subjective by-product of objective explanations. By contrast, this book puts scientific understanding center stage. It is primarily a philosophical study, but also contains detailed historical case studies of scientific practice. In contrast to most existing studies in this area, it takes into account scientists' views and analyzes their role in scientific debate and development. The aim of Understanding Scientific Understanding is to develop and defend a philosophical theory of scientific understanding that can describe and explain the historical variation of criteria for understanding actually employed by scientists. The theory does justice to the insights of such famous physicists as Werner Heisenberg and Richard Feynman, while bringing much-needed conceptual rigor to their intuitions. The scope of the proposed account of understanding is the natural sciences: while the detailed case studies derive from physics, examples from other sciences are presented to illustrate its wider validity.
Download or read book Introduction to Partial Differential Equations with Applications written by E. C. Zachmanoglou and published by Courier Corporation. This book was released on 2012-04-20 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.
Download or read book Partial Differential Equations and Boundary Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Download or read book The Numerical Solution of Elliptic Equations written by Garrett Birkhoff and published by SIAM. This book was released on 1971-01-01 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing?the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering.
Download or read book Solving Hyperbolic Equations with Finite Volume Methods written by M. Elena Vázquez-Cendón and published by Springer. This book was released on 2015-04-16 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields. The selection of content is based on the author’s experience giving PhD and master courses in different universities. In the book the introduction of new concepts and numerical methods go together with simple exercises, examples and applications that contribute to reinforce them. In addition, some of them involve the execution of MATLAB codes. The author promotes an understanding of common terminology with a balance between mathematical rigor and physical intuition that characterizes the origin of the methods. This book aims to be a first contact with finite volume methods. Once readers have studied it, they will be able to follow more specific bibliographical references and use commercial programs or open source software within the framework of Computational Fluid Dynamics (CFD).
Download or read book Symbolic Computation Solving Equations in Algebra Geometry and Engineering written by Edward L. Green and published by American Mathematical Soc.. This book was released on 2001 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings from the research conference, Symbolic Computation: Solving Equations in Algebra, Analysis, and Engineering, held at Mount Holyoke College, USA. It provides an overview of contemporary research in symbolic computation as it applies to the solution of polynomial systems. The conference brought together pure and applied mathematicians, computer scientists, and engineers, who use symbolic computation to solve systems of equations or who develop the theoretical background and tools needed for this purpose. Within this general framework, the conference focused on several themes: systems of polynomials, systems of differential equations, noncommutative systems, and applications.
Download or read book Physics for Mathematicians written by Michael Spivak and published by . This book was released on 2010 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exploring ODEs written by Lloyd N. Trefethen and published by SIAM. This book was released on 2017-12-21 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring ODEs is a textbook of ordinary differential equations for advanced undergraduates, graduate students, scientists, and engineers. It is unlike other books in this field in that each concept is illustrated numerically via a few lines of Chebfun code. There are about 400 computer-generated figures in all, and Appendix B presents 100 more examples as templates for further exploration.?
