Essential Linear Algebra with Applications

A Problem-Solving Approach

Author: Titu Andreescu

Publisher: Springer

ISBN: 0817646361

Category: Mathematics

Page: 491

View: 9402

Rooted in a pedagogically successful problem-solving approach to linear algebra, the present work fills a gap in the literature that is sharply divided between elementary texts and books that are too advanced to appeal to a wide audience. It clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications and connections to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science. Ideal as an introduction to linear algebra, the extensive exercises and well-chosen applications also make this text suitable for advanced courses at the junior or senior undergraduate level. Furthermore, it can serve as a colorful supplementary problem book, reference, or self-study manual for professional scientists and mathematicians. Complete with bibliography and index, "Essential Linear Algebra with Applications" is a natural bridge between pure and applied mathematics and the natural and social sciences, appropriate for any student or researcher who needs a strong footing in the theory, problem-solving, and model-building that are the subject’s hallmark.

3,000 Solved Problems in Linear Algebra

Author: Seymour Lipschutz

Publisher: McGraw Hill Professional

ISBN: 9780070380233

Category: Mathematics

Page: 480

View: 1543

Covers vectors, matrix algebra, linear-algebra, linear-equations, determinants, mappings, canonical forms, linear functions, and quadratic forms

Linear Algebra Problem Book

Author: Paul R. Halmos

Publisher: MAA

ISBN: 9780883853221

Category: Mathematics

Page: 336

View: 6438

Takes the student step by step from basic axioms to advanced concepts. 164 problems, each with hints and full solutions.

Linear Algebra

Author: Reg Allenby

Publisher: Butterworth-Heinemann

ISBN: 0080571794

Category: Mathematics

Page: 240

View: 1606

As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the mathematics undergraduate. The whole text has been written in a connected way with ideas introduced as they occur naturally. As with the other books in the series, there are many worked examples.

Schaum's Outline of Linear Algebra, 5th Edition

612 Solved Problems + 25 Videos

Author: Seymour Lipschutz,Marc Lipson

Publisher: McGraw Hill Professional

ISBN: 0071794573

Category: Study Aids

Page: 432

View: 1185

Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately, there's Schaum's. This all-in-one-package includes 612 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you 612 fully solved problems Concise explanations of all course concepts Support for all major textbooks for linear algebra courses Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!

Linear Algebra For Dummies

Author: Mary Jane Sterling

Publisher: John Wiley & Sons

ISBN: 0470538163

Category: Mathematics

Page: 384

View: 2283

Learn to: Solve linear algebra equations in several ways Put data in order with matrices Determine values with determinants Work with eigenvalues and eigenvectors Your hands-on guide to real-world applications of linear algebra Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction. Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices Relate vectors and linear transformations — link vectors and matrices with linear combinations and seek solutions of homogeneous systems Evaluate determinants — see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule Hone your skills with vector spaces — determine the properties of vector spaces and their subspaces and see linear transformation in action Tackle eigenvalues and eigenvectors — define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices Open the book and find: Theoretical and practical ways of solving linear algebra problems Definitions of terms throughout and in the glossary New ways of looking at operations How linear algebra ties together vectors, matrices, determinants, and linear transformations Ten common mathematical representations of Greek letters Real-world applications of matrices and determinants

Solutions Manual for Lang’s Linear Algebra

Author: Rami Shakarchi

Publisher: Springer Science & Business Media

ISBN: 146120755X

Category: Mathematics

Page: 200

View: 1700

This solutions manual for Lang’s Undergraduate Analysis provides worked-out solutions for all problems in the text. They include enough detail so that a student can fill in the intervening details between any pair of steps.

Intelligent Routines II

Solving Linear Algebra and Differential Geometry with Sage

Author: George A. Anastassiou,Iuliana F. Iatan

Publisher: Springer Science & Business Media

ISBN: 3319019678

Category: Computers

Page: 306

View: 5426

“Intelligent Routines II: Solving Linear Algebra and Differential Geometry with Sage” contains numerous of examples and problems as well as many unsolved problems. This book extensively applies the successful software Sage, which can be found free online Sage is a recent and popular software for mathematical computation, available freely and simple to use. This book is useful to all applied scientists in mathematics, statistics and engineering, as well for late undergraduate and graduate students of above subjects. It is the first such book in solving symbolically with Sage problems in Linear Algebra and Differential Geometry. Plenty of SAGE applications are given at each step of the exposition.

Computational Methods of Linear Algebra

Third Edition

Author: Granville Sewell

Publisher: World Scientific Publishing Company

ISBN: 9814603880

Category: Mathematics

Page: 328

View: 6907

This book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming problems. The book also includes a chapter on the fast Fourier transform and a very practical introduction to the solution of linear algebra problems on modern supercomputers. The book contains the relevant theory for most of the methods employed. It also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs for solving linear algebraic problems. Highly readable FORTRAN and MATLAB codes are presented which solve all of the main problems studied.

A Reference Guide to Vector Algebra

Author: Trevor P. Humphreys

Publisher: Jain Publishing Company

ISBN: 9780875730950

Category: Mathematics

Page: 200

View: 9585

A Reference Guide to Vector Algebra is an introductory vector algebra handbook that also serves as a companion guide to solving vector algebra problems using the accompanying Vector Algebra Tools software. It is written to complement AP high-school and first year college curriculum topics in vector algebra and can be conveniently used as a quick reference guide to vector algebra concepts, methods, laws and problem solving applications in geometry, physics and engineering. Clear and illustrative figures are used throughout the text to emphasis the vector algebra concepts and problem solving applications. In addition, numerous worked examples of varying difficulty are included to augment the student's understanding of vector algebra topics and to develop the student's problem solving skills through the use of the Vector Algebra Tools. The Vector Algebra Tools themselves comprise of a comprehensive set of specialized vector calculators that facilitates the algebraic determination and manipulation of vectors quantities. Therefore, whether you are studying vectors for the first time or you want to improve your proficiency in vector algebra, this reference guide and the accompanying Vector Algebra Tools will help you acquire a better understanding of vectors and their applications.

Linear Algebra

An Introductory Approach

Author: Charles W. Curtis

Publisher: Springer Science & Business Media

ISBN: 1461211360

Category: Mathematics

Page: 350

View: 2234

This revised and updated fourth edition designed for upper division courses in linear algebra includes the basic results on vector spaces over fields, determinants, the theory of a single linear transformation, and inner product spaces. While it does not presuppose an earlier course, many connections between linear algebra and calculus are worked into the discussion. A special feature is the inclusion of sections devoted to applications of linear algebra, which can either be part of a course, or used for independent study, and new to this edition is a section on analytic methods in matrix theory, with applications to Markov chains in probability theory. Proofs of all the main theorems are included, and are presented on an equal footing with methods for solving numerical problems. Worked examples are integrated into almost every section, to bring out the meaning of the theorems, and illustrate techniques for solving problems. Many numerical exercises make use of all the ideas, and develop computational skills, while exercises of a theoretical nature provide opportunities for students to discover for themselves.

Fundamentals and Linear Algebra for the Chemical Engineer

Solving Numerical Problems

Author: Guido Buzzi-Ferraris,Flavio Manenti

Publisher: John Wiley & Sons

ISBN: 3527325522

Category: Technology & Engineering

Page: 375

View: 1162

A practical engineer's companion to using numerical methods for the solution of complex mathematical problems. It thus enables readers to use and implement standard numerical tools in their work, explaining the theory behind the various functions and problem solvers, while showcasing applications in diverse scientific and engineering fields. The material is based on several tried-and-tested courses for scientists and engineers taught by the authors, and all the exercises and problems are classroom-tested. The required software is freeware developed and maintained by the authors, included on the accompanying CD-ROM, together with an installation tutorial, all the examples and sample codes described in the book, as well as a host of additional examples.

Linear Algebra

Author: N.A

Publisher: Pearson South Africa

ISBN: 9781868910588

Category: Algebras, Linear

Page: 87

View: 9041

Solving Applied Mathematical Problems with MATLAB

Author: N.A

Publisher: CRC Press

ISBN: 9781420082517

Category: Mathematics

Page: 446

View: 5481

This textbook presents a variety of applied mathematics topics in science and engineering with an emphasis on problem solving techniques using MATLAB®. The authors provide a general overview of the MATLAB language and its graphics abilities before delving into problem solving, making the book useful for readers without prior MATLAB experience. They explain how to generate code suitable for various applications so that readers can apply the techniques to problems not covered in the book. Examples, figures, and MATLAB scripts enable readers with basic mathematics knowledge to solve various applied math problems in their fields while avoiding unnecessary technical details.

Vector Algebra and Calculus

Author: Hari Kishan

Publisher: Atlantic Publishers & Dist

ISBN: 9788126908066

Category: Calculus

Page: 430

View: 5768

The Present Book Aims At Providing A Detailed Account Of The Basic Concepts Of Vectors That Are Needed To Build A Strong Foundation For A Student Pursuing Career In Mathematics. These Concepts Include Addition And Multiplication Of Vectors By Scalars, Centroid, Vector Equations Of A Line And A Plane And Their Application In Geometry And Mechanics, Scalar And Vector Product Of Two Vectors, Differential And Integration Of Vectors, Differential Operators, Line Integrals, And Gauss S And Stoke S Theorems.It Is Primarily Designed For B.Sc And B.A. Courses, Elucidating All The Fundamental Concepts In A Manner That Leaves No Scope For Illusion Or Confusion. The Numerous High-Graded Solved Examples Provided In The Book Have Been Mainly Taken From The Authoritative Textbooks And Question Papers Of Various University And Competitive Examinations Which Will Facilitate Easy Understanding Of The Various Skills Necessary In Solving The Problems. In Addition, These Examples Will Acquaint The Readers With The Type Of Questions Usually Set At The Examinations. Furthermore, Practice Exercises Of Multiple Varieties Have Also Been Given, Believing That They Will Help In Quick Revision And In Gaining Confidence In The Understanding Of The Subject. Answers To These Questions Have Been Verified Thoroughly. It Is Hoped That A Thorough Study Of This Book Would Enable The Students Of Mathematics To Secure High Marks In The Examinations. Besides Students, The Teachers Of The Subject Would Also Find It Useful In Elucidating Concepts To The Students By Following A Number Of Possible Tracks Suggested In The Book.

Numerical Linear Algebra with Applications


Author: William Ford

Publisher: Academic Press

ISBN: 0123947847

Category: Mathematics

Page: 628

View: 7398

Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra Detailed explanations and examples A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra Examples from engineering and science applications

Algebra Through Practice: Volume 4, Linear Algebra

A Collection of Problems in Algebra with Solutions

Author: T. S. Blyth,E. F. Robertson

Publisher: CUP Archive

ISBN: 9780521272896

Category: Mathematics

Page: 116

View: 5093

Problem-solving is an art central to understanding and ability in mathematics. With this series of books, the authors have provided a selection of worked examples, problems with complete solutions and test papers designed to be used with or instead of standard textbooks on algebra. For the convenience of the reader, a key explaining how the present books may be used in conjunction with some of the major textbooks is included. Each volume is divided into sections that begin with some notes on notation and prerequisites. The majority of the material is aimed at the students of average ability but some sections contain more challenging problems. By working through the books, the student will gain a deeper understanding of the fundamental concepts involved, and practice in the formulation, and so solution, of other problems. Books later in the series cover material at a more advanced level than the earlier titles, although each is, within its own limits, self-contained.

Introduction to Linear Algebra in Geology

Author: J. Ferguson

Publisher: Springer Science & Business Media

ISBN: 9780412493508

Category: Mathematics

Page: 203

View: 4595

Introduction to Linear Algebra in Geology introduces linear algebra to students of geology and explores the possibilities of using the techniques as an aid to solving geological problems which can be solved numerically. A basic knowledge of geology is assumed.

Guaranteed Accuracy in Numerical Linear Algebra

Author: S.K. Godunov,A.G. Antonov,O.P. Kiriljuk,V.I. Kostin

Publisher: Springer Science & Business Media

ISBN: 9780792323525

Category: Computers

Page: 537

View: 7006

There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interest ing problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solv ing linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of com lead putations is guaranteed. As far as the final program product is con cerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where abso lutely all errors of input data and machine round-offs are taken into account. 2.

Introduction to Matrices and Vectors

Author: Jacob T. Schwartz

Publisher: Courier Corporation

ISBN: 0486143708

Category: Mathematics

Page: 192

View: 9187

DIVIn this concise undergraduate text, the first three chapters present the basics of matrices — in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition. /div