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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.
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
In the four previous editions the author presented a text firmly grounded in the mathematics that engineers and scientists must understand and know how to use. Tapping into decades of teaching at the US Navy Academy and the US Military Academy and serving for twenty-five years at (NASA) Goddard Space Flight, he combines a teaching and practical experience that is rare among authors of advanced engineering mathematics books. This edition offers a smaller, easier to read, and useful version of this classic textbook. While competing textbooks continue to grow, the book presents a slimmer, more concise option. Instructors and students alike are rejecting the encyclopedic tome with its higher and higher price aimed at undergraduates. To assist in the choice of topics included in this new edition, the author reviewed the syllabi of various engineering mathematics courses that are taught at a wide variety of schools. Due to time constraints an instructor can select perhaps three to four topics from the book, the most likely being ordinary differential equations, Laplace transforms, Fourier series and separation of variables to solve the wave, heat, or Laplace's equation. Laplace transforms are occasionally replaced by linear algebra or vector calculus. Sturm-Liouville problem and special functions (Legendre and Bessel functions) are included for completeness. Topics such as z-transforms and complex variables are now offered in a companion book, Advanced Engineering Mathematics: A Second Course by the same author. MATLAB is still employed to reinforce the concepts that are taught. Of course, this Edition continues to offer a wealth of examples and applications from the scientific and engineering literature, a highlight of previous editions. Worked solutions are given in the back of the book.
This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigenproblems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
This work is based on the experience and notes of the authors while teaching mathematics courses to engineering students at the Indian Institute of Technology, New Delhi. It covers syllabi of two core courses in mathematics for engineering students.
Exploring Linear Algebra: Labs and Projects with MATLAB® is a hands-on lab manual that can be used by students and instructors in classrooms every day to guide the exploration of the theory and applications of linear algebra. For the most part, labs discussed in the book can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems using Mathematica demonstrations (an online tool that can be used with a browser with Java capabilities) and MATLAB® coding. This allows students to discover the theory and applications of linear algebra in a meaningful and memorable way. Features: The book’s inquiry-based approach promotes student interaction Each chapter contains a project set which consists of application-driven projects emphasizing the chapter’s materials Adds a project component to any Linear Algebra course Explores many applications to a variety of fields that can promote research projects Employs MATLAB® to calculate and explore concepts and theories of linear algebra
Since its introduction in 1984, MATLAB's ever-growing popularity and functionality have secured its position as an industry-standard software package. The user-friendly, interactive environment of MATLAB 6.x, which includes a high-level programming language, versatile graphics capabilities, and abundance of intrinsic functions, helps users focus on
The techniques of linear algebra are used extensively across the applied sciences, and in many different areas of algebra such as group theory, module theory, representation theory, ring theory, and Galois theory. Written by experienced researchers with a decades of teaching experience, Introduction to Linear Algebra is a clear and rigorous introductory text on this key topic for students of both applied sciences and pure mathematics.