This concise introduction to the methods and techniques of vector analysis is suitable for college undergraduates in mathematics as well as students of physics and engineering. Rich in exercises and examples, the straightforward presentation focuses on physical ideas rather than mathematical rigor. The treatment begins with a chapter on vectors and vector addition, followed by a chapter on products of vector. Two succeeding chapters on vector calculus cover a variety of topics, including functions of a vector; line, surface, and volume integrals; the Laplacian operator, and more. The text concludes with a survey of standard applications, including Poinsot's central axis, Gauss's theorem, gravitational potential, Green's theorems, and other subjects.
In engineering and applied science, the practical problems that arise are often described using mathematical models. In order to interpret these figures and make a judicious decision relating to such problems, engineers and scientists need ample knowledge of vector analysis. Illustrating the application of vector analysis to physical problems, this new edition of Applied Vector Analysis expands its coverage of the field to encompass new concepts, such as the divergence theorem, position vectors, and Berouilli's equation. It provides the grounding in vector analysis engineers and scientists require with an emphasis on practical applications This user-friendly volume is divided into seven chapters, each providing a clear manifestation of theory and its application to real-life problems. Beginning with a brief historical background of vector calculus, the authors introduce the algebra of vectors using a single variable. Within this framework, the book goes on to discuss the Del operator, which plays a significant role in displaying physical problems in mathematical notation. Chapter 6 contains important integral theorems, such as Green's theorem, Stokes theorem, and divergence theorem. Specific applications of these theorems are described using selected examples in fluid flow, electromagnetic theory, and the Poynting vector in Chapter 7. The appendices supply important vector formulas at a glance and mathematical explanations to selected examples from within the text. One of the most valuable branches of mathematics, vector analysis is pertinent to the investigation of physical problems encountered in many disciplines. Using real-world applications, concise explanations of fundamental concepts, and extensive examples, Applied Vector Analysis, Second Edition provides a clear cut exposition of the fields' practical uses.
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
Basic Mathematics for the Biological and Social Sciences deals with the applications of basic mathematics in the biological and social sciences. Mathematical concepts that are discussed in this book include graphical methods, differentiation, trigonometrical or circular functions, limits and convergence, integration, vectors, and differential equations. The exponential function and related functions are also considered. This monograph is comprised of 11 chapters and begins with an overview of basic algebra, followed by an introduction to infinitesimal calculus, scalar and vector quantities, complex numbers, and the simplest types of differential equation. The use of graphs in the presentation of data is also described, along with limits and convergence, rules for differentiation, the exponential function, and maxima and minima. Techniques of integration, vectors and their derivatives, and simultaneous differential equations are explored as well. Examples from biology, economics and related subjects, probability theory, and physics are provided. This text will be a useful resource for mathematicians as well as biologists and social scientists interested in applying mathematics to their work.
Vector analysis is a very useful and a powerful tool for physicists and engineers alike. It has applications in multiple fields. Although it is not a particularly difficult subject to learn, students often lack a proper understanding of the concepts on a deeper level. This restricts its usage to a mere mathematical tool.That's where this book hope to be different. We don't want this subject to be treated just as a mathematical tool. We hope to go beyond it. Therefore, the emphasis is to provide physical interpretation to the various concepts in the subject with the help of illustrative figures and intuitive reasoning. Having said that, we have given adequate importance to the mathematical aspect of the subject as well. 100+ solved examples given in the book will give the reader a definite edge when it comes to problem solving.For beginners this book will provide a concise introduction to the world of vectors in a unique way. The various concepts of the subject are arranged logically and explained in a simple reader-friendly language, so that they can learn with minimum effort in quick time. For experts, this book will a great refresher.The first 2 chapters focus on the basics of vectors. In chapters 3 to 5 we dig into vector calculus. Chapter 6 is all about vectors in different coordinate systems and finally chapter 7 focuses on the applications of vectors in various fields like engineering mechanics, electromagnetism, fluid mechanics etc.