Contents
The book carries the subtitle "A text-book for the use of students of mathematics and physics, founded upon the lectures of J. Willard Gibbs Ph.D. LL.D." The first chapter covers vectors in three spatial dimensions, the concept of a (real) scalar, and the product of a scalar with a vector. The second chapter introduces the dot and cross products for pairs of vectors. These are extended to a scalar triple product and a quadruple product. Pages 77–81 cover the essentials of spherical trigonometry, a topic of considerable interest at the time because of its use in celestial navigation. The third chapter introduces the vector calculus notation based on the del operator.
The final eight pages develop bivectors as these were integral to the course on the electromagnetic theory of light that Professor Gibbs taught at Yale. First Wilson associates a bivector with an ellipse. The product of the bivector with a complex number on the unit circle is then called an elliptical rotation. Wilson continues with a description of elliptic harmonic motion and the case of stationary waves.
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