Bøger i Textbooks in Mathematics serien

This second edition is a valuable, up-to-date tool for instructors teaching courses about differential equations. It serves as an excellent introductory textbook for undergraduate students. Tthe textbook will aide them greatly in their professional careers because of its instructions on how to use computers to solve equations.

Previous edition: Mathematical groups / Tony Barnard and Hugh Neill (London: Teach Yourself Books, 1996).

The study of nonlinear optimization is both fundamental and a key course for applied mathematics, operations research, management science, industrial engineering, and economics at most colleges and universities.

This book provides the traditional role of exercises in a course to provide more-or-less routine applications of the main results, for the student's edification and also as possible material for examinations. It discusses Noetherian rings and prime ideals for algebraic geometry.

Complex Variables: A Physical Approach with Applications, Second Edition offers a notable revision. The emphasis remains on theory and practice. The first part of the text focuses on the fundamental concepts. The author then moves on to a detailed look at how complex variables are used in the real world.

Designed for an introductory course on differential equations, this book uses explicit explanation to ensure students fully comprehend the subject matter. Emphasizing modeling and applications, the third edition of this classic text presents a substantial new section on Gauss¿s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity, the text includes unique examples and exercises, as well as the author¿s distinctive historical notes, throughout.

This book covers core computational science concepts and techniques. It shows how to apply a model, select a numerical method, implement computer simulations, and assess the ensuing results. Providing a wealth of MATLAB, Fortran, and C++ code online for download, the second edition includes a new chapter with sections on the finite element method, shallow water waves, and the driven cavity problem. It introduces multiprocessor/multicore computers, parallel MATLAB, and MPI in the chapter on high-performance computing, as well as updates and adds code and documentation.

This text provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem. The text starts with basic questions about images and pre-images of mappings, injectivity, surjectivity, and distortion. In the process of answering these questions in the linear setting, the book covers all the standard topics for a first course on linear algebra.

This is an introduction to proofs book for the course offering a transition to more advanced mathematics. It contains logic, sets, functions, relations, the construction of rational, real and complex numbers and their properties. It also has a chapter on cardinality and a chapter on counting techniques. The book explains various proof techniques and has many examples which help with the transition to more advanced classes like Real Analysis, Groups, rings and fields or topology.

This text is meant to be a hands-on lab manual that can be used in class every day to guide the exploration of the theory and applications of differential and integral calculus. For the most part, labs 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, technology, Mathematica R visualization, and Mathematica CDFs that allow students to discover the theory and applications of differential and integral calculus in a meaningful and memorable way.

This book provides students with a clear understanding of the utility of MATLAB in complex arithmetic. The book allows professors to quickly find and assign MATLAB programming problems that will strengthen students¿ knowledge of the language and concepts of complex variable theory.

Written in clear and concise language, this book covers the standard topics in a second linear algebra course. The book first introduces general fields and emphasizes matrix algebra over finite fields and complex numbers. It then proceeds to cover vector spaces in depth, addressing vector spaces over general fields. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, and spectral theory. Additional material covers dual spaces, quotient spaces, and tensor products. It includes well-designed exercises and full solutions to almost all exercises.

This book demonstrates the power of numerical methods in the context of solving complex engineering and scientific problems. With a wealth of exercises, it emphasizes the practical aspects of numerical methods and addresses their advantages and disadvantages. Each chapter contains many computational examples, as well as a section on applications that contains additional engineering examples.

This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. It emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. The book covers theorems and differentiation in Rn , Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. This second edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the ¿-¿ theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated.

This classroom-tested, student-friendly text covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbert¿s tenth problem. Ideal for a one- or two-semester undergraduate-level course, the second edition features a more flexible structure, adds several new sections, expands exercise sets to encompass a wider variety of problems, and provides calculations, tutorials, and code via an author-maintained website.

This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to reveal common errors in many examples. It is intended for students who are interested in developing a deeper understanding of the topics of calculus. The gathered counterexamples may also be used by calculus instructors in their classes.

Designed for an undergraduate course on mathematical modeling or differential equations, this text provides students with an understanding of the practical and theoretical aspects of mathematical models involving ODEs and PDEs. It develops students¿ intuition by building the theory from the ground up and illustrates the analysis of more than 20 distinct models through concrete applications in physics, engineering, finance, and many other areas. The book also uses MATLAB® GUIs that enable students to discover patterns and make conjectures.

This text presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon¿delta methods. Readers can fully prove fundamental results, such as the Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness. The book includes numerous exercises throughout and at the end of each chapter.

Covers how to define and compute standard geometric functions using Mathematica for constructing various curves and surfaces from existing ones. This book addresses important topics, such as quaternions. It presents techniques that help reader to understand concepts geometrically, plotting curves and surfaces on a monitor and printing them.

This text presents a unified treatment of the three classical geometries: Euclidean, hyperbolic, and spherical (elliptic). This unique approach of combining all three geometries simultaneously using twelve concise axioms has never appeared in book form before at this level. The text introduces each axiom, including its reasons for use and implications, and then explains it in detail. In addition to numerous figures, examples, and exercises, the book includes Geometera (TM)s Sketchpad to help students build and investigate math models, objects, figures, and graphs. The author provides programs for students to use on a supporting website. A solutions manual is available for qualifying instructors.

Explores the fundamental ideas of linear algebra as well as a variety of applications. This book discusses proofs to show how to correctly create and write them. It offers the option of using Maple, MATLAB[registered], and TI-83 Plus to help solve problems and reinforce the learning of standard procedures. It includes examples of applications.

This is an introductory game theory book that quickly moves readers through the fundamental ideas of game theory to enable them to engage in creative modeling projects based on game theoretic concepts.

This book delivers a stimulating exposition of modeling and computing, preparing students for higher-level mathematical and analytical thinking. Designed for an undergraduate-level course on ordinary differential equations, the text presents classical ideas and cutting-edge techniques in dynamical systems and other areas, highlighting applications from engineering, physics, and applied science. This version adds coverage of Sturm-Liouville theory and problems, streamlines content for the interests of engineers, enhances examples, and augments the substantial and valuable exercise sets. A solutions manual is available with qualifying course adoption.

Provides an introduction to the basics of modern topology. This work presents the traditional concepts of topological space, open and closed sets, separation axioms, and more, along with applications of the ideas in Morse, manifold, homotopy, and homology theories.

This version of the author's DE text will include a new chapter on Linear Boundary Value Problems for instructors who want to add this coverage to their DE course.