Sir Isaac Newton, one of the greatest scientists and mathematicians of all time, introduced the notion of a vector to define the existence of gravitational forces, the motion of the planets around the sun, and the motion of the moon around the earth. Vector calculus is a fundamental scientific tool that allows us to investigate the origins and evolution of space and time, as well as the origins of gravity, electromagnetism, and nuclear forces. Vector calculus is an essential language of mathematical physics, and plays a vital role in differential geometry and studies related to partial differential equations widely used in physics, engineering, fluid flow, electromagnetic fields, and other disciplines. Vector calculus represents physical quantities in two or three-dimensional space, as well as the variations in these quantities. The machinery of differential geometry, of which vector calculus is a subset, is used to understand most of the analytic results in a more general form. Many topics in the physical sciences can be mathematically studied using vector calculus techniques. This book is designed under the assumption that the readers have no prior knowledge of vector calculus. It begins with an introduction to vectors and scalars, and also covers scalar and vector products, vector differentiation and integrals, Gauss's theorem, Stokes's theorem, and Green's theorem. The MATLAB programming is given in the last chapter. This book includes many illustrations, solved examples, practice examples, and multiple-choice questions.

This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. MATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers.

Excerpt from Elementary Vector Analysis With Application to Geometry and Physics My object in writing this book was to provide a simple exposition of elementary Vector Analysis, and to show how it may be employed with advantage in Geometry and Mechanics. It was thought unnecessary, in the present volume, to enter upon the more advanced parts of the subject, built upon the ideas of gradient, curl and divergence. Vector algebra and the differentiation of vectors with respect to one scalar variable furnish a powerful instrument even for the higher parts of dynamics. The work does not claim to be a complete text-book in either Geometry or Mechanics, though a good deal of ground is covered in both subjects. The use of vector analysis in the former is abundantly illustrated by the treatment of the straight line, the plane, the sphere and the twisted curve, which are dealt with as fully as in most elementary books, and a good deal more concisely. In Mechanics I have explained and proved all the important elementary principles. The equations of equilibrium for a rigid body are deduced from the equations of motion. This is contrary to the ordinary practice and, of course, is not recommended for young beginners. But for a student who is able to read this volume, it is certainly desirable to show that the principles of statics are only particular cases of the dynamical ones, and that the long line of argument followed by text-books in Statics, to prove the theorems about moments, parallel forces, couples and the equilibrium of bodies, is really unnecessary. All these theorems are immediately deducible from the equations of motion of a rigid body, as shown in Chapter VIII. Another departure from the ordinary practice has been made in connection with the theory of centroids. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

This book focuses on solving practical problems in calculus with MATLAB. Descriptions and sketching of functions and sequences are introduced first, followed by the analytical solutions of limit, differentiation, integral and function approximation problems of univariate and multivariate functions. Advanced topics such as numerical differentiations and integrals, integral transforms as well as fractional calculus are also covered in the book.

From the PREFACE. This volume embodies the lectures given on the subject to graduate students over a period of four repetitions. The point of view is the result of many years of consideration of the whole field. The author has examined the various methods that go under the name of Vector, and finds that for all purposes of the physicist and for most of those of the geometer, the use of quaternions is by far the simplest in theory and in practice. The various points of view are mentioned in the introduction, and it is hoped that the essential differences are brought out. The tables of comparative notation scattered through the text will assist in following the other methods. The place of vector work according to the author is in the general field of associative algebra, and every method so far proposed can be easily shown to be an imperfect form of associative algebra. From this standpoint the various discussions as to the fundamental principles may be understood. As far as the mere notations go, there is not much difference save in the actual characters employed. These have assumed a somewhat national character. It is unfortunate that so many exist. The attempt in this book has been to give a text to the mathematical student on the one hand, in which every physical term beyond mere elementary terms is carefully defined. On the other hand for the physical student there will be found a large collection of examples and exercises which will show him the utility of the mathematical methods. So very little exists in the numerous treatments of the day that does this, and so much that is labeled vector analysis is merely a kind of short-hand, that it has seemed very desirable to show clearly the actual use of vectors as vectors. It will be rarely the case in the text that any use of the components of vectors will be found. The triplexes in other texts are very seldom much different from the ordinary Cartesian forms, and not worth learning as methods. The difficulty the author has found with other texts is that after a few very elementary notions, the mathematical student (and we may add the physical student) is suddenly plunged into the profundities of mathematical physics, as if he were familiar with them. This is rarely the case, and the object of this text is to make him familiar with them by easy gradations. It is not to be expected that the book will be free from errors, and the author will esteem it a favor to have all errors and oversights brought to his attention. He desires to thank specially Dr. C. F. Green, of the University of Illinois, for his careful assistance in reading the proof, and for other useful suggestions. Finally he has gathered his material widely, and is in debt to many authors for it, to all of whom he presents his thanks.

Engineers around the world depend on MATLAB for its power, usability, and outstanding graphics capabilities. Yet too often, engineering students are either left on their own to acquire the background they need to use MATLAB, or they must learn the program concurrently within an advanced course. Both of these options delay students from solving realistic design problems, especially when they do not have a text focused on applications relevant to their field and written at the appropriate level of mathematics. Ideal for use as a short-course textbook and for self-study Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB fills that gap. Accessible after just one semester of calculus, it introduces the many practical analytical and numerical tools that are essential to success both in future studies and in professional life. Sharply focused on the needs of the electrical and computer engineering communities, the text provides a wealth of relevant exercises and design problems. Changes in MATLAB's version 6.0 are included in a special addendum. The lack of skills in fundamental quantitative tools can seriously impede progress in one's engineering studies or career. By working through this text, either in a lecture/lab environment or by themselves, readers will not only begin mastering MATLAB, but they will also hone their analytical and computational skills to a level that will help them to enjoy and succeed in subsequent electrical and computer engineering pursuits.