Linear Algebra: Concepts and Methods


Author: Martin Anthony,Michele Harvey
Publisher: Cambridge University Press
ISBN: 0521279488
Category: Mathematics
Page: 516
View: 9598
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Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book.

Exam Prep for: Linear Algebra; Concepts and Methods


Author: David Mason
Publisher: Rico Publications
ISBN: N.A
Category: Education
Page: 800
View: 9287
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5,600 Exam Prep questions and answers. Ebooks, Textbooks, Courses, Books Simplified as questions and answers by Rico Publications. Very effective study tools especially when you only have a limited amount of time. They work with your textbook or without a textbook and can help you to review and learn essential terms, people, places, events, and key concepts.

Linear Algebra and Its Applications


Author: Gilbert Strang
Publisher: Academic Press
ISBN: 1483265110
Category: Mathematics
Page: 428
View: 6871
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Linear Algebra and Its Applications, Second Edition fulfills the need for a book that will permit the teaching of the applications of linear algebra, in combination with the underlying mathematics. Comprised of eight chapters, the book aims to provide a comprehensive presentation of the concepts and methods in linear algebra. The text starts with the discussion of the Gaussian elimination, the simplest and most useful method of solution. This chapter is followed by chapters that focus on the study of vector spaces, projections and inner products, determinants, and eigenvalues. Discussions on positive definite matrices, computations with matrices, and introduction to linear programming and game theory are provided as well. This text is intended for use by college students.

Mathematisches Denken

Vom Vergnügen am Umgang mit Zahlen
Author: T.W. Körner
Publisher: Springer-Verlag
ISBN: 3034850018
Category: Science
Page: 719
View: 5890
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Dieses Buch wendet sich zuallererst an intelligente Schüler ab 14 Jahren sowie an Studienanfänger, die sich für Mathematik interessieren und etwas mehr als die Anfangsgründe dieser Wissenschaft kennenlernen möchten. Es gibt inzwischen mehrere Bücher, die eine ähnliche Zielstellung verfolgen. Besonders gern erinnere ich mich an das Werk Vom Einmaleins zum Integral von Colerus, das ich in meiner Kindheit las. Es beginnt mit der folgenden entschiedenen Feststellung: Die Mathematik ist eine Mausefalle. Wer einmal in dieser Falle gefangen sitzt, findet selten den Ausgang, der zurück in seinen vormathematischen Seelenzustand leitet. ([49], S. 7) Einige dieser Bücher sind im Anhang zusammengestellt und kommen tiert. Tatsächlich ist das Unternehmen aber so lohnenswert und die Anzahl der schon vorhandenen Bücher doch so begrenzt, daß ich mich nicht scheue, ihnen ein weiteres hinzuzufügen. An zahlreichen amerikanischen Universitäten gibt es Vorlesungen, die gemeinhin oder auch offiziell als ,,Mathematik für Schöngeister'' firmieren. Dieser Kategorie ist das vorliegende Buch nicht zuzuordnen. Statt dessen soll es sich um eine ,,Mathematik für Mathematiker'' handeln, für Mathema tiker freilich, die noch sehr wenig von der Mathematik verstehen. Weshalb aber sollte nicht der eine oder andere von ihnen eines Tages den Autor dieses 1 Buches durch seine Vorlesungen in Staunen versetzen? Ich hoffe, daß auch meine Mathematikerkollegen Freude an dem Werk haben werden, und ich würde mir wünschen, daß auch andere Leser, bei denen die Wertschätzung für die Mathematik stärker als die Furcht vor ihr ist, Gefallen an ihm finden mögen.

Moduln und Ringe


Author: N.A
Publisher: Springer-Verlag
ISBN: 3663057038
Category: Technology & Engineering
Page: 328
View: 9223
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Lineare Algebra


Author: Gilbert Strang
Publisher: Springer-Verlag
ISBN: 3642556310
Category: Mathematics
Page: 656
View: 905
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Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

Mathematics for Physicists

Introductory Concepts and Methods
Author: Alexander Altland,Jan von Delft
Publisher: Cambridge University Press
ISBN: 1108471226
Category: Mathematics
Page: 600
View: 4430
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Introduces fundamental concepts and computational methods of mathematics from the perspective of physicists.

Calculus: Concepts and Methods


Author: Ken Binmore,Joan Davies
Publisher: Cambridge University Press
ISBN: 1139643622
Category: Mathematics
Page: N.A
View: 6638
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The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in detail before generalisation to higher dimensions. Although there are no theorems or formal proofs, this is a serious book in which conceptual issues are explained carefully using numerous geometric devices and a wealth of worked examples, diagrams and exercises. Mathematica has been used to generate many beautiful and accurate, full-colour illustrations to help students visualise complex mathematical objects. This adds to the accessibility of the text, which will appeal to a wide audience among students of mathematics, economics and science.

Differential Equations and Linear Algebra


Author: Charles Henry Edwards,David E. Penney
Publisher: Prentice Hall
ISBN: 9780136054252
Category: Mathematics
Page: 762
View: 8343
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Acclaimed authors Edwards and Penney combine core topics in elementary differential equations with those concepts and methods of elementary linear algebra needed for a contemporary combined introduction to differential equations and linear algebra. Known for its real-world applications and its blend of algebraic and geometric approaches, this book discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. First-Order Differential Equations; Mathematical Models and Numerical Methods; Linear Systems and Matrices; Vector Spaces; Higher-Order Linear Differential Equations; Eigenvalues and Eigenvectors; Linear Systems of Differential Equations; Matrix Exponential Methods; Nonlinear Systems and Phenomena; Laplace Transform Methods; Power Series Methods. For future math majors, engineers, or scientists that have taken two or three semesters of Calculus.

Linear Algebra with Applications


Author: Gareth Williams
Publisher: Jones & Bartlett Publishers
ISBN: 1449679544
Category: Mathematics
Page: 589
View: 5500
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Updated and revised to increase clarity and further improve student learning, the Eighth Edition of Gareth Williams' classic text is designed for the introductory course in linear algebra. It provides a flexible blend of theory and engaging applications for students within engineering, science, mathematics, business management, and physics. It is organized into three parts that contain core and optional sections. There is then ample time for the instructor to select the material that gives the course the desired flavor. Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of Rn, matrices, linear transformations, determinants, and eigenvectors. Part 2 builds on the material presented in Part1 and goes on to introduce the concepts of general vector spaces, discussing properties of bases, developing the rank/nullity theorem, and introducing spaces of matrices and functions. Part 3 completes the course with important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition. Throughout the text the author takes care to fully and clearly develop the mathematical concepts and provide modern applications to reinforce those concepts. The applications range from theoretical applications within differential equations and least square analysis, to practical applications in fields such as archeology, demography, electrical engineering and more. New exercises can be found throughout that tie back to the modern examples in the text. Key Features of the Eighth Edition: • Updated and revised throughout with new section material and exercises. • Each section begins with a motivating introduction, which ties material to the previously learned topics. • Carefully explained examples illustrate key concepts throughout the text. • Includes such new topics such as QR Factorization and Singular Value Decomposition. • Includes new applications such as a Leslie Matrix model that is used to predict birth and death patterns of animals. • Includes discussions of the role of linear algebra in many areas, such as the operation of the search engine Google and the global structure of the worldwide air transportation network. • A MATLAB manual that ties into the regular course material is included as an appendix. These ideas can be implemented on any matrix algebra software package. This manual consists of 28 sections that tie into the regular course material. • Graphing Calculator Manual included as an appendix. • A Student Solutions Manual that contains solutions to selected exercises is available as a supplement. An Instructors Complete Solutions Manual, test bank, and PowerPoint Lecture Outlines are also available. • Available with WebAssign Online Homework & Assessment

Advanced Linear Algebra for Engineers with MATLAB


Author: Sohail A. Dianat,Eli Saber
Publisher: CRC Press
ISBN: 1420095242
Category: Mathematics
Page: 346
View: 6843
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Arming readers with both theoretical and practical knowledge, Advanced Linear Algebra for Engineers with MATLAB® provides real-life problems that readers can use to model and solve engineering and scientific problems in fields ranging from signal processing and communications to electromagnetics and social and health sciences. Facilitating a unique understanding of rapidly evolving linear algebra and matrix methods, this book: Outlines the basic concepts and definitions behind matrices, matrix algebra, elementary matrix operations, and matrix partitions, describing their potential use in signal and image processing applications Introduces concepts of determinants, inverses, and their use in solving linear equations that result from electrical and mechanical-type systems Presents special matrices, linear vector spaces, and fundamental principles of orthogonality, using an appropriate blend of abstract and concrete examples and then discussing associated applications to enhance readers’ visualization of presented concepts Discusses linear operators, eigenvalues, and eigenvectors, and explores their use in matrix diagonalization and singular value decomposition Extends presented concepts to define matrix polynomials and compute functions using several well-known methods, such as Sylvester’s expansion and Cayley-Hamilton Introduces state space analysis and modeling techniques for discrete and continuous linear systems, and explores applications in control and electromechanical systems, to provide a complete solution for the state space equation Shows readers how to solve engineering problems using least square, weighted least square, and total least square techniques Offers a rich selection of exercises and MATLAB® assignments that build a platform to enhance readers’ understanding of the material Striking the appropriate balance between theory and real-life applications, this book provides both advanced students and professionals in the field with a valuable reference that they will continually consult.

Linear Algebra


Author: M. Thamban Nair,Arindama Singh
Publisher: Springer
ISBN: 9811309264
Category: Mathematics
Page: 341
View: 2703
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This book introduces the fundamental concepts, techniques and results of linear algebra that form the basis of analysis, applied mathematics and algebra. Intended as a text for undergraduate students of mathematics, science and engineering with a knowledge of set theory, it discusses the concepts that are constantly used by scientists and engineers. It also lays the foundation for the language and framework for modern analysis and its applications. Divided into seven chapters, it discusses vector spaces, linear transformations, best approximation in inner product spaces, eigenvalues and eigenvectors, block diagonalisation, triangularisation, Jordan form, singular value decomposition, polar decomposition, and many more topics that are relevant to applications. The topics chosen have become well-established over the years and are still very much in use. The approach is both geometric and algebraic. It avoids distraction from the main theme by deferring the exercises to the end of each section. These exercises aim at reinforcing the learned concepts rather than as exposing readers to the tricks involved in the computation. Problems included at the end of each chapter are relatively advanced and require a deep understanding and assimilation of the topics.

Handbook of Linear Algebra


Author: Leslie Hogben
Publisher: CRC Press
ISBN: 1420010573
Category: Mathematics
Page: 1400
View: 9302
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The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessibl

Linear Algebra and Projective Geometry


Author: Reinhold Baer
Publisher: Courier Corporation
ISBN: 0486154661
Category: Mathematics
Page: 336
View: 597
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Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.

Linear Algebra: A Modern Introduction


Author: David Poole
Publisher: Cengage Learning
ISBN: 1285982835
Category: Mathematics
Page: 720
View: 811
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David Poole's innovative LINEAR ALGEBRA: A MODERN INTRODUCTION, 4e emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning. Theoretical, computational, and applied topics are presented in a flexible yet integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Lineare Algebra

Einführung, Grundlagen, Übungen
Author: Howard Anton
Publisher: Springer Verlag
ISBN: 9783827403247
Category: Mathematics
Page: 680
View: 1013
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In Ihrer Hand liegt ein Lehrbuch - in sieben englischsprachigen Ausgaben praktisch erprobt - das Sie mit groem didaktischen Geschick, zudem angereichert mit zahlreichen Ubungsaufgaben, in die Grundlagen der linearen Algebra einfuhrt. Kenntnisse der Analysis werden fur das Verstandnis nicht generell vorausgesetzt, sind jedoch fur einige besonders gekennzeichnete Beispiele notig. Padagogisch erfahren, behandelt der Autor grundlegende Beweise im laufenden Text; fur den interessierten Leser jedoch unverzichtbare Beweise finden sich am Ende der entsprechenden Kapitel. Ein weiterer Vorzug des Buches: Die Darstellung der Zusammenhange zwischen den einzelnen Stoffgebieten - linearen Gleichungssystemen, Matrizen, Determinanten, Vektoren, linearen Transformationen und Eigenwerten.

Elementary Linear Algebra


Author: Howard Anton
Publisher: John Wiley & Sons
ISBN: 0470458216
Category: Mathematics
Page: 592
View: 8266
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When it comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized to bring up some of the more abstract topics and make the material more accessible. More theoretical exercises at all levels of difficulty are integrated throughout the pages, including true/false questions that address conceptual ideas. New marginal notes provide a fuller explanation when new methods and complex logical steps are included in proofs. Small-scale applications also show how concepts are applied to help engineers develop their mathematical reasoning.

Linear Algebra


Author: Jörg Liesen,Volker Mehrmann
Publisher: Springer
ISBN: 3319243462
Category: Mathematics
Page: 324
View: 6063
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This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.

Matrix Algebra

Theory, Computations, and Applications in Statistics
Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 0387708723
Category: Computers
Page: 528
View: 3380
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This much-needed work presents, among other things, the relevant aspects of the theory of matrix algebra for applications in statistics. Written in an informal style, it addresses computational issues and places more emphasis on applications than existing texts.

Konkrete Mathematik (nicht nur) für Informatiker

Mit vielen Grafiken und Algorithmen in Python
Author: Edmund Weitz
Publisher: Springer-Verlag
ISBN: 3658215658
Category: Mathematics
Page: 942
View: 3338
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Das etwas andere Mathe-Lehrbuch: Mathematik, die Informatiker (und nicht nur die!) wirklich brauchen, und die direkt am Computer umgesetzt wird in Form von kleinen Algorithmen, numerischen "Experimenten" und interaktiven Visualisierungen. Man lernt, wie man dem Computer das Rechnen überlässt, während man selbst den mathematischen Überblick behält, typische Fehler vermeidet und die Ergebnisse richtig interpretiert. (Und nebenbei lernt man noch die beliebte Programmiersprache Python sowie den Umgang mit einem Computeralgebrasystem.) Gleichzeitig wird die Mathematik aber nicht zur "Hilfswissenschaft" degradiert. Der Autor motiviert und begründet im "Plauderton" und mit konkreten Beispielen und Knobelaufgaben (und manchmal auch mit kleinen philosophischen und historischen Exkursen), um so den Leser zum Mitmachen und Mitdenken aufzufordern. Im Idealfall hat man am Ende nicht nur etwas gelernt, sondern verspürt Lust auf mehr - und sieht die Mathematik danach vielleicht mit anderen Augen. Mit informatik-spezifischen Anwendungen unter anderem aus der Kryptographie, der Kodierungs- und Komplexitätstheorie sowie der Computergrafik. Unterstützt durch viele farbige Grafiken, etwa 1000 Aufgaben mit Lösungen und nicht zuletzt Hunderte von Videos, in denen man sich das Gelesene vom Autor noch mal "persönlich" erklären lassen kann.