## Articles by "Linear Algebra"

Showing posts with label Linear Algebra. Show all posts

### Introduction to Linear Algebra with Applications

Jim DeFranza, Daniel Gagliardi ... 416 pages - Publisher: McGraw-Hill; (September, 2008) ... Language: English - ISBN-10: 0073532355 - ISBN-13: 978-0073532356 ...

Linear Algebra with Applications is an introductory text targeted to second or advanced first year undergraduates in engineering or mathematics. The organization of this text is motivated by the authors' experience which tells them what essential concepts should be mastered by students in a one semester undergraduate Linear Algebra course. The authors' main objectives are to fully develop each topic before moving on and to connect topics naturally. The authors take great care to meet both these objectives, because this organization will allow instructors teaching from this text to stay on task so that each topic can be covered with the depth required before progressing to the next logical one. As a result the reader is prepared for each new unit and there is no need to repeat a concept in a subsequent chapter when it is utilized. This text is geared towards an introductory linear algebra course taken by first or second year undergraduate students. However, it offers the opportunity to introduce the importance of abstraction, not only in mathematics, but in many other areas where Linear Algebra is used. The textbook’s approach is to take advantage of this opportunity by presenting abstract vector spaces as early as possible. Throughout the text, the authors are mindful of the difficulties that students at this level have with abstraction and introduce new concepts first through examples which gently illustrate the idea. To motivate the definition of an abstract vector space, and the subtle concept of linear independence, the authors use addition and scalar multiplication of vectors in Euclidean Space. The authors have strived to create a balance between computation, problem solving, and abstraction. This approach equips students with the necessary skills and problem solving strategies in an abstract setting that allows for a greater understanding and appreciation for the numerous applications of the subject.

### Introduction to Probability with Statistical Applications

GÃ©za Schay ... 318 pages - Publisher: BirkhÃ¤user; (August, 2007) ... Language: English - ISBN-10: 0817644970 - ISBN-13: 978-0817644970 ...

Introduction to Probability with Statistical Applications targets non-mathematics students, undergraduates and graduates, who do not need an exhaustive treatment of the subject. The presentation is rigorous and contains theorems and proofs, and linear algebra is largely avoided so only a minimal amount of multivariable calculus is needed. The book contains clear definitions, simplified notation and techniques of statistical analysis, which combined with well-chosen examples and exercises, motivate the exposition. Theory and applications are carefully balanced. Throughout the book there are references to more advanced concepts if required.

### Introduction to Linear Programming with MATLAB

Shashi Kant Mishra, Bhagwat Ram ... 327 pages - Publisher: Chapman and Hall/CRC; 1st edition (August, 2017) - Language: English - ISBN-10: 1138092266 - ISBN-13: 978-1138092266 ...

This book is based on the lecture notes of the author delivered to the students at the Institute of Science, Banaras Hindu University, India. It covers simplex, revised simplex, two-phase method, duality, dual simplex, complementary slackness, transportation and assignment problems with good number of examples, clear proofs, MATLAB codes and homework problems. The book will be useful for both students and practitioners.

### Concrete Mathematics: A Foundation for Computer Science

Ronald L. Graham,‎ Donald E. Knuth,‎ Oren Patashnik ... 672 pages - Publisher: Addison-Wesley Professional; 2nd edition (March, 1994) ... Language: English - ISBN-10: 0201558025 - ISBN-13: 978-0201558029 ...

This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums * Recurrences * Integer functions * Elementary number theory * Binomial coefficients * Generating functions * Discrete probability * Asymptotic methods. This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.

### Getting Started with Maple 3rd Edition

Douglas B. Meade, S. J. M. May, C-K. Cheung, G. E. Keough ... 220 pages - Publisher: Wiley; 3rd edition (March, 2009) ... Language: English - ISBN-10: 0470455543 - ISBN-13: 978-0470455548 ...

The purpose of this guide is to give a quick introduction on how to use Maple. It primarily covers Maple 12, although most of the guide will work with earlier versions of Maple. Also, throughout this guide, we will be suggesting tips and diagnosing common problems that users are likely to encounter. This should make the learning process smoother. This guide is designed as a self-study tutorial to learn Maple. Our emphasis is on getting you quickly up to speed. This guide can also be used as a supplement (or reference) for students taking a mathematics (or science) course that requires use of Maple, such as Calculus, Multivariable Calculus, Advanced Calculus, Linear Algebra, Discrete Mathematics, Modeling, or Statistics.

### Scientific Computing with MATLAB 2nd Edition

Dingyu Xue, YangQuan Chen ... 604 pages - Publisher: Chapman&Hall/CRC; 2nd edition (March, 2016) ... Language: English - ISBN-10: 1498757774 - ISBN-13: 978-1498757775 ...

Enhance Your Students’ Mathematical Problem-Solving Ability: Scientific Computing with MATLAB, Second Edition improves students’ ability to tackle mathematical problems. It helps students understand the mathematical background and find reliable and accurate solutions to mathematical problems with the use of MATLAB, avoiding the tedious and complex technical details of mathematics. This edition retains the structure of its predecessor Solving Applied Mathematical Problems with MATLAB® while expanding and updating the content of each chapter. Based on the authors’ extensive teaching, research, and industrial experiences, the text adheres to the following course sequence: An overview of the computer languages suitable for mathematics - Fundamentals of MATLAB programming - Calculus problems - Linear algebra problems - Integral transforms and complex variable functions - Nonlinear equations and optimization problems - Differential equations problems - Data interpolation and functional approximation problems - Probability and statistics problems -Nontraditional methods, such as fuzzy logic, rough sets, neural networks, evolution algorithms, wavelets, and fractional calculus. The book bridges the gap between problems and solutions through well-grouped topics and clear MATLAB example scripts and reproducible MATLAB-generated plots. Students can effortlessly experiment with the scripts for a deep, hands-on exploration. Each chapter also includes a set of problems to strengthen understanding of the material.

### Linear Algebra: A First Course with Applications

Larry E. Knop ... 752 pages- Publisher: Chapman and Hall/CRC; 1st edition (August, 2008) ...
Language: English - ASIN: B005H6YSBE by Amazon Digital Services ...

Linear Algebra: A First Course with Applications explores the fundamental ideas of linear algebra, including vector spaces, subspaces, basis, span, linear independence, linear transformation, eigenvalues, and eigenvectors, as well as a variety of applications, from inventories to graphics to Google’s PageRank.

Unlike other texts on the subject, this classroom-tested book gives students enough time to absorb the material by focusing on vector spaces early on and using computational sections as numerical interludes. It offers introductions to Maple™, MATLAB®, and TI-83 Plus for calculating matrix inverses, determinants, eigenvalues, and eigenvectors.

Moving from the specific to the general, the author raises questions, provides motivation, and discusses strategy before presenting answers. Discussions of motivation and strategy include content and context to help students learn.

### Linear Algebra with Applications 5th Edition

Otto Bretscher ... 508 pages - Publisher: Pearson; 5th edition (December, 2012) ... Language: English - ISBN-10: 0321796977 - ISBN-13: 978-0321796974 ...

Offering the most geometric presentation available, Linear Algebra with Applications, Fifth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Exercise sets are broad and varied and reflect the author’s creativity and passion for this course. This revision reflects careful review and appropriate edits throughout, while preserving the order of topics of the previous edition.

### Linear Algebra with Applications

Roger Baker, Kenneth Kuttler ... 332 pages - Publisher: World Scientific Publishing Company; (May, 2014) ... Language: English - ISBN-10: 9814590533 - ISBN-13: 978-9814590532 ...

This book gives a self- contained treatment of linear algebra with many of its most important applications. It is very unusual if not unique in being an elementary book which does not neglect arbitrary fields of scalars and the proofs of the theorems. It will be useful for beginning students and also as a reference for graduate students and others who need an easy to read explanation of the important theorems of this subject. It presents a self- contained treatment of the algebraic treatment of linear differential equation which includes all proofs. It also contains many different proofs of the Cayley Hamilton theorem. Other applications include difference equations and Markov processes, the latter topic receiving a more thorough treatment than usual, including the theory of absorbing states. In addition it contains a complete introduction to the singular value decomposition and related topics like least squares and the pseudo-inverse. Most major topics receive more than one discussion, one in the text and others being outlined in the exercises. The book also gives directions for using maple in performing many of the difficult algorithms.

### Linear Algebra with Applications 8th Edition

Gareth Williams ... 560 pages - Publisher: Jones & Bartlett Learning; 8th edition (September, 2012) ... Language: English - ISBN-10: 1449679544 - ISBN-13: 978-1449679545 ...

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

### MatLab R2016a: The Language of Technical Computing

MatLab R2016a v9.0.0.341360 [Size: 7.7 GB x64] ... Millions of engineers and scientists worldwide use MATLAB® to analyze and design the systems and products transforming our world. MATLAB is in automobile active safety systems, interplanetary spacecraft, health monitoring devices, smart power grids, and LTE cellular networks. It is used for machine learning, signal processing, image processing, computer vision, communications, computational finance, control design, robotics, and much more. Math. Graphics. Programming: The MATLAB platform is optimized for solving engineering and scientific problems. The matrix-based MATLAB language is the world’s most natural way to express computational mathematics. Built-in graphics make it easy to visualize and gain insights from data. A vast library of prebuilt toolboxes lets you get started right away with algorithms essential to your domain. The desktop environment invites experimentation, exploration, and discovery. These MATLAB tools and capabilities are all rigorously tested and designed to work together. Scale. Integrate. Deploy: MATLAB helps you take your ideas beyond the desktop. You can run your analyses on larger data sets and scale up to clusters and clouds. MATLAB code can be integrated with other languages, enabling you to deploy algorithms and applications within web, enterprise, and production systems.

Why MATLAB?: MATLAB® is the easiest and most productive software for engineers and scientists. Whether you’re analyzing data, developing algorithms, or creating models, MATLAB provides an environment that invites exploration and discovery. It combines a high-level language with a desktop environment tuned for iterative engineering and scientific workflows. The matrix-based MATLAB language is the world’s most natural way to express computational mathematics. Linear algebra in MATLAB looks like linear algebra in a textbook. This makes it straightforward to capture the mathematics behind your ideas, which means your code is easier to write, easier to read and understand, and easier to maintain. You can trust the results of your computations. MATLAB, which has strong roots in the numerical analysis research community, is known for its impeccable numerics. A MathWorks team of 350 engineers continuously verifies quality by running millions of tests on the MATLAB code base every day. MATLAB does the hard work to ensure your code runs quickly. Math operations are distributed across multiple cores on your computer, library calls are heavily optimized, and all code is just-in-time compiled. You can run your algorithms in parallel by changing for-loops into parallel for-loops or by changing standard arrays into GPU or distributed arrays. Run parallel algorithms in infinitely scalable public or private clouds with no code changes. The MATLAB language also provides features of traditional programming languages, including flow control, error handling, object-oriented programming, unit testing, and source control integration.

### Learning to Program with MATLAB: Building GUI Tools

Craig S. Lent ... 320 pages -Publisher: Wiley; 1st edition (January 9, 2013) ... Language: English - ISBN-10: 0470936444 - ISBN-13: 978-0470936443 ...

The text is for instructors who want to use MATLAB to teach introductory programming concepts. Since many students struggle with applying the concepts that underlie good programming practice,  Learning to Program with MATLAB: Building GUI Tools was designed upon the observation that student learning is enhanced if the students themselves build the GUI (graphical user interface) tool, construct the computational model, implement the visualization of results, and design the GUI. This text teaches the core concepts of computer programming—arrays, loops, functions, and basic data structures—using MATLAB. The chapter sequence covers text-based programs, then programs that produce graphics, building up to an emphasis on GUI tools. This progression unleashes the real power of MATLAB—creating visual expressions of the underlying mathematics of a problem or design.

### Linear Algebra with Applications

Steve Leon ... 552 pages - Publisher: Pearson; 8th edition (September 5, 2009) ...
Language: English - ISBN-10: 0136009298 - ISBN-13: 978-0136009290 ...

This book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite: This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra. Lay-flat type.

### Numerical Linear Algebra with Applications Using MATLAB

William Ford ... 628 pages - Publisher: Academic Press; 1st edition (September 16, 2014) ...
Language: English - ISBN-10: 012394435X - ISBN-13: 978-0123944351 ...

Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications 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. It provides necessary mathematical background information for those who want to learn to solve linear algebra problems, and offers a thorough explanation of the issues and methods for practical computing, using MATLAB as the vehicle for computation. The 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.

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.

### MatLab R2015b

MatLab R2015b v8.6.0.267246 [Size: 7.3 GB] ... The Language of Technical Computing: Explore new ideas-MATLAB® is the high-level language and interactive environment used by millions of engineers and scientists worldwide. It lets you explore and visualize ideas and collaborate across disciplines including signal and image processing, communications, control systems, and computational finance. Put your ideas into action-You can use MATLAB in projects such as modeling energy consumption to build smart power grids, developing control algorithms for hypersonic vehicles, analyzing weather data to visualize the track and intensity of hurricanes, and running millions of simulations to pinpoint optimal dosing for antibiotics. MATLAB® is a high-level language and interactive environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java®. You can use MATLAB for a range of applications, including signal processing and communications, image and video processing, control systems, test and measurement, computational finance, and computational biology. More than a million engineers and scientists in industry and academia use MATLAB, the language of technical computing. Language Fundamentals: Syntax, operators, data types, array indexing and manipulation * Mathematics: Linear algebra, basic statistics, differentiation and integrals, Fourier transforms, and other mathematics * Graphics: Two- and three-dimensional plots, images, animation, visualization * Programming Scripts and Functions: Program files, control flow, editing, debugging * Data Import and Export: Text files, spreadsheets, and other file formats; big data; web access * GUI Building: Application development using GUIDE and callbacks * Advanced Software Development: Object-oriented programming; code performance; unit testing; external interfaces to Java , C/C++, .NET and other languages * Desktop Environment: Preferences and settings, platform differences * Supported Hardware: Support for third-party hardware, such as webcam, Raspberry Pi™, and Arduino® hardware.

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