## Linear Algebra and Its Applications

Author: Peter D. Lax
Publisher: John Wiley & Sons
ISBN: 1118626923
Format: PDF, Mobi

## Principles of Linear Algebra with Mathematica

Author: Kenneth M. Shiskowski
Publisher: John Wiley & Sons
ISBN: 1118627261
Format: PDF, ePub, Docs

A hands-on introduction to the theoretical and computationalaspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationallyintensive, and computer algebra systems such as Mathematica®are essential not only for learning to apply the concepts tocomputationally challenging problems, but also for visualizing manyof the geometric aspects within this field of study. Principles ofLinear Algebra with Mathematica uniquely bridges the gap betweenbeginning linear algebra and computational linear algebra that isoften encountered in applied settings, and the commands required tosolve complex and computationally challenging problems usingMathematica are provided. The book begins with an introduction to the commands andprogramming guidelines for working with Mathematica. Next, theauthors explore linear systems of equations and matrices,applications of linear systems and matrices, determinants,inverses, and Cramer's rule. Basic linear algebra topics, such asvectors, dot product, cross product, and vector projection areexplored, as well as a unique variety of more advanced topicsincluding rotations in space, 'rolling' a circle along a curve, andthe TNB Frame. Subsequent chapters feature coverage of lineartransformations from Rn to Rm, the geometry of linear and affinetransformations, with an exploration of their effect on arclength,area, and volume, least squares fits, and pseudoinverses. Mathematica is used to enhance concepts and is seamlesslyintegrated throughout the book through symbolic manipulations,numerical computations, graphics in two and three dimensions,animations, and programming. Each section concludes with standardproblems in addition to problems that were specifically designed tobe solved with Mathematica, allowing readers to test theircomprehension of the presented material. All related Mathematicacode is available on a corresponding website, along with solutionsto problems and additional topical resources. Extensively class-tested to ensure an accessible presentation,Principles of Linear Algebra with Mathematica is an excellent bookfor courses on linear algebra at the undergraduate level. The bookis also an ideal reference for students and professionals who wouldlike to gain a further understanding of the use of Mathematica tosolve linear algebra problems.

## Time Dependent Problems and Difference Methods

Author: Bertil Gustafsson
Publisher: John Wiley & Sons
ISBN: 9780471507345
Format: PDF, ePub

Time dependent problems frequently pose challenges in areas of science and engineering dealing with numerical analysis, scientific computation, mathematical models, and most importantly—numerical experiments intended to analyze physical behavior and test design. Time Dependent Problems and Difference Methods addresses these various industrial considerations in a pragmatic and detailed manner, giving special attention to time dependent problems in its coverage of the derivation and analysis of numerical methods for computational approximations to Partial Differential Equations (PDEs). The book is written in two parts. Part I discusses problems with periodic solutions; Part II proceeds to discuss initial boundary value problems for partial differential equations and numerical methods for them. The problems with periodic solutions have been chosen because they allow the application of Fourier analysis without the complication that arises from the infinite domain for the corresponding Cauchy problem. Furthermore, the analysis of periodic problems provides necessary conditions when constructing methods for initial boundary value problems. Much of the material included in Part II appears for the first time in this book. The authors draw on their own interests and combined extensive experience in applied mathematics and computer science to bring about this practical and useful guide. They provide complete discussions of the pertinent theorems and back them up with examples and illustrations. For physical scientists, engineers, or anyone who uses numerical experiments to test designs or to predict and investigate physical phenomena, this invaluable guide is destined to become a constant companion. Time Dependent Problems and Difference Methods analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations.

## Functional Differential Equations

Author: Constantin Corduneanu
Publisher: John Wiley & Sons
ISBN: 1119189489
Format: PDF, Mobi

## Fibonacci and Lucas Numbers with Applications

Author: Thomas Koshy
Publisher: John Wiley & Sons
ISBN: 1118031318
Format: PDF, Docs

The first comprehensive survey of mathematics' most fascinatingnumber sequences Fibonacci and Lucas numbers have intrigued amateur and professionalmathematicians for centuries. This volume represents the firstattempt to compile a definitive history and authoritative analysisof these famous integer sequences, complete with a wealth ofexciting applications, enlightening examples, and fun exercisesthat offer numerous opportunities for exploration andexperimentation. The author has assembled a myriad of fascinating properties of bothFibonacci and Lucas numbers-as developed by a wide range ofsources-and catalogued their applications in a multitude of widelyvaried disciplines such as art, stock market investing,engineering, and neurophysiology. Most of the engaging anddelightful material here is easily accessible to college and evenhigh school students, though advanced material is included tochallenge more sophisticated Fibonacci enthusiasts. A historicalsurvey of the development of Fibonacci and Lucas numbers,biographical sketches of intriguing personalities involved indeveloping the subject, and illustrative examples round out thisthorough and amusing survey. Most chapters conclude with numericand theoretical exercises that do not rely on long and tediousproofs of theorems. Highlights include: * Balanced blend of theory and real-world applications * Excellent reference material for student reports andprojects * User-friendly, informal, and entertaining writing style * Historical interjections and short biographies that add a richerperspective to the topic * Reference sections providing important symbols, problemsolutions, and fundamental properties from the theory of numbersand matrices Fibonacci and Lucas Numbers with Applications providesmathematicians with a wealth of reference material in oneconvenient volume and presents an in-depth and entertainingresource for enthusiasts at every level and from any background.

## Solutions Manual to Accompany Beginning Partial Differential Equations

Author: Peter V. O'Neil
Publisher: John Wiley & Sons
ISBN: 1118630092
Format: PDF, Docs

Solutions Manual to Accompany Beginning Partial Differential Equations, 3rd Edition Featuring a challenging, yet accessible, introduction to partial differential equations, Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms. Thoroughly updated with novel applications, such as Poe's pendulum and Kepler's problem in astronomy, this third edition is updated to include the latest version of Maples, which is integrated throughout the text. New topical coverage includes novel applications, such as Poe's pendulum and Kepler's problem in astronomy.

## Orthogonal Sets and Polar Methods in Linear Algebra

Author: Enrique Castillo
Publisher: John Wiley & Sons
ISBN: 1118031148
Format: PDF, Mobi

A unique, applied approach to problem solving in linearalgebra Departing from the standard methods of analysis, this unique bookpresents methodologies and algorithms based on the concept oforthogonality and demonstrates their application to both standardand novel problems in linear algebra. Covering basic theory oflinear systems, linear inequalities, and linear programming, itfocuses on elegant, computationally simple solutions to real-worldphysical, economic, and engineering problems. The authors clearlyexplain the reasons behind the analysis of different structures andconcepts and use numerous illustrative examples to correlate themathematical models to the reality they represent. Readers aregiven precise guidelines for: * Checking the equivalence of two systems * Solving a system in certain selected variables * Modifying systems of equations * Solving linear systems of inequalities * Using the new exterior point method * Modifying a linear programming problem With few prerequisites, but with plenty of figures and tables,end-of-chapter exercises as well as Java and Mathematica programsavailable from the authors' Web site, this is an invaluabletext/reference for mathematicians, engineers, applied scientists,and graduate students in mathematics.

## Principles of Differential Equations

Author: Nelson G. Markley
Publisher: John Wiley & Sons
ISBN: 1118031539
Format: PDF, Kindle

An accessible, practical introduction to the principles ofdifferential equations The field of differential equations is a keystone of scientificknowledge today, with broad applications in mathematics,engineering, physics, and other scientific fields. Encompassingboth basic concepts and advanced results, Principles ofDifferential Equations is the definitive, hands-on introductionprofessionals and students need in order to gain a strong knowledgebase applicable to the many different subfields of differentialequations and dynamical systems. Nelson Markley includes essential background from analysis andlinear algebra, in a unified approach to ordinary differentialequations that underscores how key theoretical ingredientsinterconnect. Opening with basic existence and uniqueness results,Principles of Differential Equations systematically illuminates thetheory, progressing through linear systems to stable manifolds andbifurcation theory. Other vital topics covered include: Basic dynamical systems concepts Constant coefficients Stability The Poincaré return map Smooth vector fields As a comprehensive resource with complete proofs and more than200 exercises, Principles of Differential Equations is the idealself-study reference for professionals, and an effectiveintroduction and tutorial for students.

## Numerical Solution of Ordinary Differential Equations

Author: Kendall Atkinson
Publisher: John Wiley & Sons
ISBN: 1118164520
Format: PDF, Docs

A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

## Bulletin

Author:
Publisher:
ISBN:
Format: PDF, Mobi