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CRC Standard Curves and Surfaces with Mathematica Second Edition

CRC Standard Curves and Surfaces with Mathematica  Second Edition Author David H. von Seggern
ISBN-10 1584885998
Release 2006-10-20
Pages 556
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Since the publication of the first edition, Mathematica® has matured considerably and the computing power of desktop computers has increased greatly. This enables the presentation of more complex curves and surfaces as well as the efficient computation of formerly prohibitive graphical plots. Incorporating both of these aspects, CRC Standard Curves and Surfaces with Mathematica®, Second Edition is a virtual encyclopedia of curves and functions that depicts nearly all of the standard mathematical functions rendered using Mathematica. While the easy-to-use format remains unchanged from the previous edition, many chapters have been reorganized and better graphical representations of numerous curves and surfaces have been produced. An introductory chapter describes the basic properties of curves and surfaces, includes two handy tables of 2-D and 3-D curve and surface transformations, and provides a quick understanding of the basic nature of mathematical functions. To facilitate more efficient and more thorough use of the material, the whole gamut of curves and surfaces is divided into sixteen individual chapters. The accompanying CD-ROM includes Mathematica notebooks of code to construct plots of all the functions presented in the book. New to the Second Edition Chapters on minimal surfaces and Green's functions that involve Poisson, wave, diffusion, and Helmholtz equations Knots and links in the 3-D curves chapter Archimedean solids, duals of Platonic solids, and stellated forms in the regular polyhedra chapter Additional curves and surfaces in almost every chapter Expanded index for quick access to curves or surfaces of interest and to find definitions of common mathematical terms Upgraded Mathematica notebooks with more uniform formatting, more complete documentation on particular curves and surfaces, an explanation of the plotting algorithms, and more explicit designations of variable parameters to easily adjust curve or surface plots



CRC Standard Curves and Surfaces with Mathematica Third Edition

CRC Standard Curves and Surfaces with Mathematica  Third Edition Author David H. von Seggern
ISBN-10 9781315355290
Release 2017-07-12
Pages 474
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Since the publication of this book’s bestselling predecessor, Mathematica® has matured considerably and the computing power of desktop computers has increased greatly. The Mathematica® typesetting functionality has also become sufficiently robust that the final copy for this edition could be transformed directly from Mathematica R notebooks to LaTex input. Incorporating these aspects, CRC Standard Curves and Surfaces with Mathematica®, Third Edition is a virtual encyclopedia of curves and functions that depicts nearly all of the standard mathematical functions and geometrical figures in use today. The overall format of the book is largely unchanged from the previous edition, with function definitions and their illustrations presented closely together. New to the Third Edition: A new chapter on Laplace transforms New curves and surfaces in almost every chapter Several chapters that have been reorganized Better graphical representations for curves and surfaces throughout A CD-ROM, including the entire book in a set of interactive CDF (Computable Document Format) files The book presents a comprehensive collection of nearly 1,000 illustrations of curves and surfaces often used or encountered in mathematics, graphics design, science, and engineering fields. One significant change with this edition is that, instead of presenting a range of realizations for most functions, this edition presents only one curve associated with each function. The graphic output of the Manipulate function is shown exactly as rendered in Mathematica, with the exact parameters of the curve’s equation shown as part of the graphic display. This enables readers to gauge what a reasonable range of parameters might be while seeing the result of one particular choice of parameters.



CRC Standard Curves and Surfaces

CRC Standard Curves and Surfaces Author David H. von Seggern
ISBN-10 0849301963
Release 1992-12-15
Pages 416
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CRC Standard Curves and Surfaces is a comprehensive illustrated catalog of curves and surfaces of geometric figures and algebraic, transcendental, and integral equations used in elementary and advanced mathematics. More than 800 graphics images are featured. Based on the successful CRC Handbook of Mathematical Curves and Surfaces, this new volume retains the easy to use "catalog" format of the original book. Illustrations are presented in a common format organized by type of equation. Associated equations are printed in their simplest form along with any notes required to understand the illustrations. Equations and graphics appear in a side-by-side format, with figures printed on righthand pages and text on lefthand pages. Most curves and surfaces are plotted with several parameter selections so that the variation of the mathematical functions are easily understandable. Coverage on algebraic surfaces and transcendental surfaces has been expanded by 30% over the original edition; material on functions in mathematical physics has expanded by 50%. New material on functions of random processes and functions of complex variable surfaces has been added. A complementary software program (see the next title listed in this catalog) enables you to plot all of the functions found in this book.



Modern Differential Geometry of Curves and Surfaces with Mathematica Third Edition

Modern Differential Geometry of Curves and Surfaces with Mathematica  Third Edition Author Elsa Abbena
ISBN-10 9781351992206
Release 2017-09-06
Pages 1016
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Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.



CRC Standard Curves and Surfaces

CRC Standard Curves and Surfaces Author David H. von Seggern
ISBN-10 0849301963
Release 1992-12-15
Pages 416
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CRC Standard Curves and Surfaces is a comprehensive illustrated catalog of curves and surfaces of geometric figures and algebraic, transcendental, and integral equations used in elementary and advanced mathematics. More than 800 graphics images are featured. Based on the successful CRC Handbook of Mathematical Curves and Surfaces, this new volume retains the easy to use "catalog" format of the original book. Illustrations are presented in a common format organized by type of equation. Associated equations are printed in their simplest form along with any notes required to understand the illustrations. Equations and graphics appear in a side-by-side format, with figures printed on righthand pages and text on lefthand pages. Most curves and surfaces are plotted with several parameter selections so that the variation of the mathematical functions are easily understandable. Coverage on algebraic surfaces and transcendental surfaces has been expanded by 30% over the original edition; material on functions in mathematical physics has expanded by 50%. New material on functions of random processes and functions of complex variable surfaces has been added. A complementary software program (see the next title listed in this catalog) enables you to plot all of the functions found in this book.



Modern differential geometry of curves and surfaces

Modern differential geometry of curves and surfaces Author Alfred Gray
ISBN-10 UOM:39015036086471
Release 1993-08
Pages 664
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This is the first advanced text/reference to explain the mathematics of curves and surfaces and describe how to draw the pictures illustrating them using Mathematica. Learn not only the classical concepts, ideas, and methods of differential geometry, but also how to define, construct, and compute standard functions. Also learn how to create new curves and surfaces from old ones. Material includes 150+ exercises, 175 Mathematica programs, and 225 geometric figures to develop the topics presented. A tutorial explaining how to use Mathematica in differential geometry is included as well. This text/reference is excellent for mathematicians, scientists, and engineers who use differential geometric methods and investigate geometrical structures.



CRC Concise Encyclopedia of Mathematics Second Edition

CRC Concise Encyclopedia of Mathematics  Second Edition Author Eric W. Weisstein
ISBN-10 9781420035223
Release 2002-12-12
Pages 3252
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Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the dedication of author Eric Weisstein to collecting, cataloging, and referencing mathematical facts, formulas, and definitions. He has now updated most of the original entries and expanded the Encyclopedia to include 1000 additional pages of illustrated entries. The accessibility of the Encyclopedia along with its broad coverage and economical price make it attractive to the widest possible range of readers and certainly a must for libraries, from the secondary to the professional and research levels. For mathematical definitions, formulas, figures, tabulations, and references, this is simply the most impressive compendium available.



Submanifolds and Holonomy Second Edition

Submanifolds and Holonomy  Second Edition Author Jurgen Berndt
ISBN-10 9781482245165
Release 2016-02-22
Pages 456
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Submanifolds and Holonomy, Second Edition explores recent progress in the submanifold geometry of space forms, including new methods based on the holonomy of the normal connection. This second edition reflects many developments that have occurred since the publication of its popular predecessor. New to the Second Edition New chapter on normal holonomy of complex submanifolds New chapter on the Berger–Simons holonomy theorem New chapter on the skew-torsion holonomy system New chapter on polar actions on symmetric spaces of compact type New chapter on polar actions on symmetric spaces of noncompact type New section on the existence of slices and principal orbits for isometric actions New subsection on maximal totally geodesic submanifolds New subsection on the index of symmetric spaces The book uses the reduction of codimension, Moore’s lemma for local splitting, and the normal holonomy theorem to address the geometry of submanifolds. It presents a unified treatment of new proofs and main results of homogeneous submanifolds, isoparametric submanifolds, and their generalizations to Riemannian manifolds, particularly Riemannian symmetric spaces.



Submanifolds and Holonomy

Submanifolds and Holonomy Author Jurgen Berndt
ISBN-10 9780203499153
Release 2003-04-28
Pages 352
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With special emphasis on new techniques based on the holonomy of the normal connection, this book provides a modern, self-contained introduction to submanifold geometry. It offers a thorough survey of these techniques and their applications and presents a framework for various recent results to date found only in scattered research papers. The treatment introduces all the basics of the subject, and along with some classical results and hard-to-find proofs, presents new proofs of several recent results. Appendices furnish the necessary background material, exercises give readers practice in using the techniques, and discussion of open problems stimulates readers' interest in the field.



An Introduction to Partial Differential Equations with MATLAB Second Edition

An Introduction to Partial Differential Equations with MATLAB  Second Edition Author Matthew P. Coleman
ISBN-10 9781439898475
Release 2016-04-19
Pages 683
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An Introduction to Partial Differential Equations with MATLAB®, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat, the propagation of sound waves, the spread of algae along the ocean’s surface, the fluctuation in the price of a stock option, and the quantum mechanical behavior of a hydrogen atom. Suitable for a two-semester introduction to PDEs and Fourier series for mathematics, physics, and engineering students, the text teaches the equations based on method of solution. It provides both physical and mathematical motivation as much as possible. The author treats problems in one spatial dimension before dealing with those in higher dimensions. He covers PDEs on bounded domains and then on unbounded domains, introducing students to Fourier series early on in the text. Each chapter’s prelude explains what and why material is to be covered and considers the material in a historical setting. The text also contains many exercises, including standard ones and graphical problems using MATLAB. While the book can be used without MATLAB, instructors and students are encouraged to take advantage of MATLAB’s excellent graphics capabilities. The MATLAB code used to generate the tables and figures is available in an appendix and on the author’s website.



Practical Linear Algebra

Practical Linear Algebra Author Gerald Farin
ISBN-10 9781498759779
Release 2015-09-15
Pages 514
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Through many examples and real-world applications, Practical Linear Algebra: A Geometry Toolbox, Third Edition teaches undergraduate-level linear algebra in a comprehensive, geometric, and algorithmic way. Designed for a one-semester linear algebra course at the undergraduate level, the book gives instructors the option of tailoring the course for the primary interests: math, engineering, science, computer graphics, and geometric modeling. New to the Third Edition More exercises and applications Coverage of singular value decomposition and its application to the pseudoinverse, principal components analysis, and image compression More attention to eigen-analysis, including eigenfunctions and the Google matrix Greater emphasis on orthogonal projections and matrix decompositions, which are tied to repeated themes such as the concept of least squares To help students better visualize and understand the material, the authors introduce the fundamental concepts of linear algebra first in a two-dimensional setting and then revisit these concepts and others in a three-dimensional setting. They also discuss higher dimensions in various real-life applications. Triangles, polygons, conics, and curves are introduced as central applications of linear algebra. Instead of using the standard theorem-proof approach, the text presents many examples and instructional illustrations to help students develop a robust, intuitive understanding of the underlying concepts. The authors’ website also offers the illustrations for download and includes Mathematica® code and other ancillary materials.



Simulation For The Social Scientist

Simulation For The Social Scientist Author Gilbert, Nigel
ISBN-10 0335216005
Release 2005-02-01
Pages 295
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Social sciences -- Simulation methods. Social interaction -- Computer simulation. Social sciences -- Mathematical models. (publisher)



Connecting with Computer Science

Connecting with Computer Science Author Greg Anderson
ISBN-10 9781439080351
Release 2010-01-14
Pages 640
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Written for the beginning computing student, this text engages readers by relating core computer science topics to their industry application. The book is written in a comfortable, informal manner, and light humor is used throughout the text to maintain interest and enhance learning. All chapters contain a multitude of exercises, quizzes, and other opportunities for skill application. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.



Differential Geometry and Topology

Differential Geometry and Topology Author Keith Burns
ISBN-10 1584882530
Release 2005-05-27
Pages 400
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Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.



Practical Guide To Chemometrics Second Edition

Practical Guide To Chemometrics  Second Edition Author Paul Gemperline
ISBN-10 9781420018301
Release 2006-04-16
Pages 552
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The limited coverage of data analysis and statistics offered in most undergraduate and graduate analytical chemistry courses is usually focused on practical aspects of univariate methods. Drawing in real-world examples, Practical Guide to Chemometrics, Second Edition offers an accessible introduction to application-oriented multivariate methods of data analysis and procedures that are highly beneficial to solving a variety of problems using analytical chemistry and statistics. Rather than overshadowing the concepts with theoretical background, this book uses application-oriented examples to illustrate how chemometrics techniques can be applied to complex scenarios with multiple and dynamic variables. The book presents a diverse selection of topics that include sampling, modeling, experimental design, calibration, pattern recognition, data analysis techniques, algorithms, and error. This second edition has been completely revised to feature new chapters on principal component analysis, self-modeling curve resolution, and multi-way analysis methods. It includes expanded material on normal distributions, sampling theory, signal processing, and digital filtering. Embracing the growing role of chemometrics in some of the latest research trends, such as quantitative biology, bioinformatics, and proteomics, this book also identifies several areas for future development and applications. Practical Guide to Chemometrics, Second Edition continues to offer a reliable source of useful information in a style that is accessible to all levels of students, professionals, and researchers involved in analyzing scientific data.



The Mathematics of Soap Films

The Mathematics of Soap Films Author John Oprea
ISBN-10 9780821821183
Release 2000
Pages 266
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Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the MapleR applications, the reader is given tools for creating the shapes that are being studied. Thus, you can ``see'' a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the ``true'' shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. It would make an excellent text for a senior seminar or for independent study by upper-division mathematics or science majors.



Optimal Estimation of Dynamic Systems Second Edition

Optimal Estimation of Dynamic Systems  Second Edition Author John L. Crassidis
ISBN-10 9781439839850
Release 2011-10-26
Pages 749
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Optimal Estimation of Dynamic Systems, Second Edition highlights the importance of both physical and numerical modeling in solving dynamics-based estimation problems found in engineering systems. Accessible to engineering students, applied mathematicians, and practicing engineers, the text presents the central concepts and methods of optimal estimation theory and applies the methods to problems with varying degrees of analytical and numerical difficulty. Different approaches are often compared to show their absolute and relative utility. The authors also offer prototype algorithms to stimulate the development and proper use of efficient computer programs. MATLAB® codes for the examples are available on the book’s website. New to the Second Edition With more than 100 pages of new material, this reorganized edition expands upon the best-selling original to include comprehensive developments and updates. It incorporates new theoretical results, an entirely new chapter on advanced sequential state estimation, and additional examples and exercises. An ideal self-study guide for practicing engineers as well as senior undergraduate and beginning graduate students, the book introduces the fundamentals of estimation and helps newcomers to understand the relationships between the estimation and modeling of dynamical systems. It also illustrates the application of the theory to real-world situations, such as spacecraft attitude determination, GPS navigation, orbit determination, and aircraft tracking.