Lineare Algebra

Author: Gilbert Strang

Publisher: Springer-Verlag

ISBN: 3642556310

Category: Mathematics

Page: 656

View: 7295

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.

Introduction to Calculus and Classical Analysis

Author: Omar Hijab

Publisher: Springer Science & Business Media

ISBN: 0387693165

Category: Mathematics

Page: 342

View: 9137

Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.

Linear Algebra and Its Applications

Author: Gilbert Strang

Publisher: Editorial Paraninfo

ISBN: 9780030105678

Category: Mathematics

Page: 487

View: 3234

Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on the proofs. Strang's emphasis is on providing understanding.

Solutions Manual to Accompany Linear Algebra

Ideas and Applications

Author: Richard C. Penney

Publisher: John Wiley & Sons

ISBN: 1118911830

Category: Mathematics

Page: 120

View: 5874

This Student Solutions Manual to Accompany Linear Algebra: Ideas and Applications, Fourth Edition contains solutions to the odd numbered problems to further aid in reader comprehension, and an Instructor's Solutions Manual (inclusive of suggested syllabi) is available via written request to the Publisher. Both the Student and Instructor Manuals have been enhanced with further discussions of the applications sections, which is ideal for readers who wish to obtain a deeper knowledge than that provided by pure algorithmic approaches. Linear Algebra: Ideas and Applications, Fourth Edition provides a unified introduction to linear algebra while reinforcing and emphasizing a conceptual and hands-on understanding of the essential ideas. Promoting the development of intuition rather than the simple application of methods, this book successfully helps readers to understand not only how to implement a technique, but why its use is important.

Computing the Continuous Discretely

Integer-point Enumeration in Polyhedra

Author: Matthias Beck,Sinai Robins

Publisher: Springer Science & Business Media

ISBN: 0387461124

Category: Mathematics

Page: 227

View: 8864

This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.

Linear Algebra: Volume 2

An Introduction with Concurrent Examples

Author: A. G. Hamilton

Publisher: Cambridge University Press

ISBN: 9780521310420

Category: Mathematics

Page: 328

View: 5315

Emphasis is placed on applications in preference to more theoretical aspects throughout this readable introduction to linear algebra for specialists as well as non-specialists. An expanded version of A First Course in Linear Algebra.

Calculus of Several Variables

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461210682

Category: Mathematics

Page: 619

View: 6835

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

Linear Algebra with Applications

Author: Gareth Williams

Publisher: Jones & Bartlett Learning

ISBN: 0763782483

Category: Mathematics

Page: 554

View: 9631

Revised and edited, Linear Algebra with Applications, Seventh Edition is designed for the introductory course in linear algebra and is organized into 3 natural parts. 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 this material, introducing the concept 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 many of the important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition. Offering 28 core sections, the Seventh Edition successfully blends theory, important numerical techniques, and interesting applications making it ideal for engineers, scientists, and a variety of other majors.

Linear Algebra

Author: A. Ramachandra Rao,P Bhimasankaram

Publisher: Springer

ISBN: 9386279010

Category: Mathematics

Page: 428

View: 1703

The vector space approach to the treatment of linear algebra is useful for geometric intuition leading to transparent proofs; it's also useful for generalization to infinite-dimensional spaces. The Indian School, led by Professors C.R. Rao and S.K. Mitra, successfully employed this approach. This book follows their approach and systematically develops the elementary parts of matrix theory, exploiting the properties of row and column spaces of matrices. Developments in linear algebra have brought into focus several techniques not included in basic texts, such as rank-factorization, generalized inverses, and singular value decomposition. These techniques are actually simple enough to be taught at the advanced undergraduate level. When properly used, they provide a better understanding of the topic and give simpler proofs, making the subject more accessible to students. This book explains these techniques.

Introduction to Abstract Algebra

Author: W. Keith Nicholson

Publisher: John Wiley & Sons

ISBN: 1118135350

Category: Mathematics

Page: 535

View: 2100

Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.

Linear Algebra

Ideas and Applications

Author: Richard C. Penney

Publisher: John Wiley & Sons

ISBN: 1118909585

Category: Mathematics

Page: 512

View: 2789

Praise for the Third Edition "This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications." — Electric Review A comprehensive introduction, Linear Algebra: Ideas and Applications, Fourth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique. The book introduces each new concept in the context of an explicit numerical example, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fourth Edition also features: Two new and independent sections on the rapidly developing subject of wavelets A thoroughly updated section on electrical circuit theory Illuminating applications of linear algebra with self-study questions for additional study End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB® code A companion website with translations of the book’s computer exercises into MapleTM code Linear Algebra: Ideas and Applications, Fourth Edition is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference. Richard C. Penney, PhD, is Professor in the Department of Mathematics and Director of the Mathematics/Statistics Actuarial Science Program at Purdue University. He has authored numerous journal articles, received several major teaching awards, and is an active researcher.

Introduction to Linear Algebra with Applications

Author: Jim DeFranza,Daniel Gagliardi

Publisher: Waveland Press

ISBN: 1478628820

Category: Mathematics

Page: 488

View: 6275

Over the last few decades, linear algebra has become more relevant than ever. Applications have increased not only in quantity but also in diversity, with linear systems being used to solve problems in chemistry, engineering, economics, nutrition, urban planning, and more. DeFranza and Gagliardi introduce students to the topic in a clear, engaging, and easy-to-follow manner. Topics are developed fully before moving on to the next through a series of natural connections. The result is a solid introduction to linear algebra for undergraduates’ first course.

A First Course in Linear Algebra

With Concurrent Examples

Author: A. G. Hamilton

Publisher: CUP Archive

ISBN: 9780521310413

Category: Mathematics

Page: 148

View: 4418

This is a short, readable introduction to basic linear algebra, as usually encountered in a first course. The development of the subject is integrated with a large number of worked examples that illustrate the ideas and methods. The format of the book, with text and relevant examples on facing pages means that the reader can follow the text uninterrupted. The student should be able to work through the book and learn from it sequentially. Stress is placed on applications of the methods rather than on developing a logical system of theorems. Numerous exercises are provided.

An Introduction to Optimization

Author: Edwin K. P. Chong,Stanislaw H. Zak

Publisher: John Wiley & Sons

ISBN: 1118515153

Category: Mathematics

Page: 640

View: 6365

Praise for the Third Edition ". . . guides and leads thereader through the learning path . . . [e]xamples are stated veryclearly and the results are presented with attention todetail." —MAA Reviews Fully updated to reflect new developments in the field, theFourth Edition of Introduction to Optimization fillsthe need for accessible treatment of optimization theory andmethods with an emphasis on engineering design. Basic definitionsand notations are provided in addition to the related fundamentalbackground for linear algebra, geometry, and calculus. This new edition explores the essential topics of unconstrainedoptimization problems, linear programming problems, and nonlinearconstrained optimization. The authors also present an optimizationperspective on global search methods and include discussions ongenetic algorithms, particle swarm optimization, and the simulatedannealing algorithm. Featuring an elementary introduction toartificial neural networks, convex optimization, andmulti-objective optimization, the Fourth Edition alsooffers: A new chapter on integer programming Expanded coverage of one-dimensional methods Updated and expanded sections on linear matrix inequalities Numerous new exercises at the end of each chapter MATLAB exercises and drill problems to reinforce the discussedtheory and algorithms Numerous diagrams and figures that complement the writtenpresentation of key concepts MATLAB M-files for implementation of the discussed theory andalgorithms (available via the book's website) Introduction to Optimization, Fourth Edition is an idealtextbook for courses on optimization theory and methods. Inaddition, the book is a useful reference for professionals inmathematics, operations research, electrical engineering,economics, statistics, and business.

Lineare Algebra

Einführung, Grundlagen, Übungen

Author: Howard Anton

Publisher: Springer Verlag

ISBN: 9783827403247

Category: Mathematics

Page: 680

View: 662

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.

An Introduction to Analysis

Author: James R. Kirkwood

Publisher: Brooks/Cole


Category: Mathematical analysis

Page: 276

View: 6066

This text makes a real effort to ease the transition from computational to theoretical mathematics. It is written clearly and simply, as if it is the first time a student has really had to understand a proof.

Linear Algebra: A Modern Introduction

Author: David Poole

Publisher: Cengage Learning

ISBN: 1285982835

Category: Mathematics

Page: 720

View: 5369

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.