A History Of Vector Analysis

Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.

This text was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into the subjects' manifold applications. 1957 edition. 86 figures.

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.

This text combines the logical approach of a mathematical subject with the intuitive approach of engineering and physical topics. Applications include kinematics, mechanics, and electromagnetic theory. Includes exercises and answers. 1955 edition.

Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.

The first eight chapters of this book were originally published in 1966 as the successful Introduction to Elementary Vector Analysis. In 1970, the text was considerably expanded to include six new chapters covering additional techniques (the vector product and the triple products) and applications in pure and applied mathematics. It is that version which is reproduced here. The book provides a valuable introduction to vectors for teachers and students of mathematics, science and engineering in sixth forms, technical colleges, colleges of education and universities.

The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables. Key topics include vectors and vector fields, line integrals, regular k-surfaces, flux of a vector field, orientation of a surface, differential forms, Stokes' theorem, and divergence theorem. This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables. The book can also be useful to engineering and physics students who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.