Vector Analysis - Contents

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.

Read more about this topic:  Vector Analysis

Famous quotes containing the word contents:

    Yet to speak of the whole world as metaphor
    Is still to stick to the contents of the mind
    And the desire to believe in a metaphor.
    It is to stick to the nicer knowledge of
    Belief, that what it believes in is not true.
    Wallace Stevens (1879–1955)

    The permanence of all books is fixed by no effort friendly or hostile, but by their own specific gravity, or the intrinsic importance of their contents to the constant mind of man.
    Ralph Waldo Emerson (1803–1882)

    Conversation ... is like the table of contents of a dull book.... All the greatest subjects of human thought are proudly displayed in it. Listen to it for three minutes, and you ask yourself which is more striking, the emphasis of the speaker or his shocking ignorance.
    Stendhal [Marie Henri Beyle] (1783–1842)