ISBN: Ostalo
Godina izdanja: 1962
Jezik: Engleski
Oblast: Matematika
Autor: Strani

D. E. Rutherford - Vector Methods
Oliver and Boyd Ltd., 1962
135 str.
tvrdi povez
stanje: vrlo dobro

Vector Methods Applied to Differential Geometry, Mechanics, and Potential Theory [University Mathematics Texts]

Designed to familiarize undergraduates with the methods of vector algebra and vector calculus, this text offers both a clear view of the abstract theory as well as a concise survey of the theory`s applications to various branches of pure and applied mathematics. A brief chapter on 4-dimensional vectors concludes the text.

Designed to familiarize undergraduates with the methods of vector algebra and vector calculus, this text offers both a clear view of the abstract theory as well as a concise survey of the theory`s applications to various branches of pure and applied mathematics. A chapter on differential geometry introduces readers to the study of this subject by the methods of vector algebra. The next section explores the many aspects of the theory of mechanics adaptable to the use of vectors, and a full discussion of the vector operator "nabla" proceeds to a treatment of potential theory and Laplace`s equation

Contents:
Vector algebra
Differential geometry
Applications to mechanics
The vector operator `[nabla / del]`
Potential theory
Hydrodynamics
Laplaces`s equation
Four-dimensional vectors

VECTOR ALGEBRA
Addition of Vectors - -
Products of Vectors - -
Differentiation of Vectors -
Examples — - -
Points, Lines and Planes -
Applications to Geometry -
Examples - - -
DIFFERENTIAL GEOMETRY P. 16
Osculating Plane - -
Frenet`s Formulae - -
Curvature - — ~
Intrinsic Equations - -
Canonical Equations - -
The Helix -
Examples - - -
Fundamental Quadratic Forms
Lines of Curvature -
Euler`s Theorem - -
Asymptotic Lines - -
The Paraboloid of Revolution
Examples -
APPLICATIONS TO MECHANICS p
Forces and Moments - -
Svstems of Particles - -
Rigid Bodies -- - -
Angular Velocities - -
Moving Axes ---
Moments and Products of Inertia
Virtual Work --.-
Energy — - -
Examples
THE VECTOR OPERATOR `v` P- BO
Gradient, Curl and Divergence —
Identities involving ` v` - —
Orthogonal Curvilinear Coordinates
Stokes`s Theorem and Gauss`s Theorem
Green`s Theorem - -
Examples - - -
POTENTIAL THEORY p. 78
Scalar Potential - -
Field Tubes -
Sources, Sinks and Dipoles -
Equations of Poisson and Laplace
Surface Distributions -
Potentials of Given Distributions
Equipotential Surfaces -
Vector Potential -- -
Conductors and Dielectrics -
Examples - - -
HYDRODYNAMICS p. 102
Stream and Vortex Lines -
Differentiation following the Motion
Equation of Continuity - —
Equations of Motion ---
Vorticitv - — - -
Examples — _ _ -
LAPLACE`S EQUATION p. 111
Conditions satisfied bv the Potential
Determination of the Distribution -
The Electrostatic Problem - -
Solutions of Laplace`s Equation —
Examples _ _ _ —
FOUR-DIMENSIONAL VECTORS p. 123
Four-Dimensional Vector Calculus -
The Space Time World - -
Electro-Magnetic Field Equations -
Momentum World-Vector - -
Conservation of Energy


Nonfiction, Mathematics