This second edition has been almost completely rewritten to create a textbook designed to provide flexibility for nearly any desired degree of rigor and depth of coverage. This is achieved with a linear development ensuring that material at any point is not dependent on subsequent developments and by means of graduated levels of sophistication. The text moves from traditional first principles in early chapters to deeper topics involving both theory and applications in later chapters. This allows for a traditional single-term course based on roughly half of the text without having to refer to more advanced topics while the later portion of the book facilitates a seamless two-term course covering the range of theory and applications generally reserved for discussions beyond fundamentals. Rigor is present throughout, but the level is adaptable because all major theorems have ample accompanying discussions and illustrative examples designed to convince readers and students of the validity of a result without a deep dive into the proof. Moreover, there is an expanded emphasis on both the depth and breadth of applications that are designed to illuminate the utility of the subject across broad areas of science and engineering. At major junctures there are photos and historical remarks concerning the personalities who created and contributed to the subject’s development. Throughout there are carefully constructed exercises ranging from easy to moderately challenging to difficult, many of which condition students for topics that follow.

"A handy book like this," noted The Mathematical Gazette, "will fill a great want." Devoted to fully worked out examples, this unique text constitutes a self-contained introductory course in vector analysis for undergraduate and graduate students of applied mathematics. Opening chapters define vector addition and subtraction, show how to resolve and determine the direction of two or more vectors, and explain systems of coordinates, vector equations of a plane and straight line, relative velocity and acceleration, and infinitely small vectors. The following chapters deal with scalar and vector multiplication, axial and polar vectors, areas, differentiation of vector functions, gradient, curl, divergence, and analytical properties of the position vector. Applications of vector analysis to dynamics and physics are the focus of the final chapter, including such topics as moving rigid bodies, energy of a moving rigid system, central forces, equipotential surfaces, Gauss's theorem, and vector flow. Dover (2014) republication of Introduction to Vector Analysis, originally published by Macmillan and Company, Ltd., London, 1931. See every Dover book in print at www.doverpublications.com

Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

The ultimate aim of the field of numerical analysis is to provide convenient methods for obtaining useful solutions to mathematical problems and for extracting useful information from available solutions which are not expressed in tractable forms. This well-known, highly respected volume provides an introduction to the fundamental processes of numerical analysis, including substantial grounding in the basic operations of computation, approximation, interpolation, numerical differentiation and integration, and the numerical solution of equations, as well as in applications to such processes as the smoothing of data, the numerical summation of series, and the numerical solution of ordinary differential equations. Chapter headings include: l. Introduction 2. Interpolation with Divided Differences 3. Lagrangian Methods 4. Finite-Difference Interpolation 5. Operations with Finite Differences 6. Numerical Solution of Differential Equations 7. Least-Squares Polynomial Approximation In this revised and updated second edition, Professor Hildebrand (Emeritus, Mathematics, MIT) made a special effort to include more recent significant developments in the field, increasing the focus on concepts and procedures associated with computers. This new material includes discussions of machine errors and recursive calculation, increased emphasis on the midpoint rule and the consideration of Romberg integration and the classical Filon integration; a modified treatment of prediction-correction methods and the addition of Hamming's method, and numerous other important topics. In addition, reference lists have been expanded and updated, and more than 150 new problems have been added. Widely considered the classic book in the field, Hildebrand's Introduction to Numerical Analysis is aimed at advanced undergraduate and graduate students, or the general reader in search of a strong, clear introduction to the theory and analysis of numbers.

This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.

Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, app

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics. A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field. - Topics are covered from a historical perspective with biographical information on key contributors to the field - The text contains more than 500 exercises - Includes practical applications of the equations to problems in both engineering and physics

To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A website contains supplementary material including programs and answers to exercises.

The aim of this book is to cover various aspects of the Production and Operations Analysis. Apart from the introduction to basic understanding of each topic, the book will also provide insights to various conventional techniques as well as, various other mathematical and nature-based techniques extracted from the existing literature. Concepts like smart factories, intelligent manufacturing, and various techniques of manufacturing will also be included. Various types of numerical examples will also be presented in each chapter and the descriptions will be done in lucid style with figures, point-wise descriptions, tables, pictures to facilitate easy understanding of the subject.

This second edition introduces an additional set of new mathematical problems with their detailed solutions in real analysis. It also provides numerous improved solutions to the existing problems from the previous edition, and includes very useful tips and skills for the readers to master successfully. There are three more chapters that expand further on the topics of Bernoulli numbers, differential equations and metric spaces.Each chapter has a summary of basic points, in which some fundamental definitions and results are prepared. This also contains many brief historical comments for some significant mathematical results in real analysis together with many references.Problems and Solutions in Real Analysis can be treated as a collection of advanced exercises by undergraduate students during or after their courses of calculus and linear algebra. It is also instructive for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the Prime Number Theorem through several exercises. This volume is also suitable for non-experts who wish to understand mathematical analysis.