Book:D.E. Rutherford/Vector Methods/Ninth Edition

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D.E. Rutherford: Vector Methods (9th Edition)

Published $1957$, Oliver & Boyd Ltd.


Subject Matter


Contents

PREFACE (St. Andrews, June 1939)
PREFACE TO THE SEVENTH EDITION (St. Andrews, May 1951)
VECTOR ALGEBRA
Addition of Vectors
Products of Vectors
Differentiation of Vectors
Examples
Points, Lines and Planes
Applications to Geometry
Examples
DIFFERENTIAL GEOMETRY
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
Forces and Moments
Systems of Particles
Rigid Bodies
Angular Velocities
Moving Axes
Moments and Products of Inertia
Virtual Work
Energy
Examples
THE VECTOR OPERATOR "$\nabla$"
Gradient, Curl and Divergence
Identities involving "$\nabla$"
Orthogonal Curvilinear Coordinates
Stokes's Theorem and Gauss's theorem
Green's Theorem
Examples
POTENTIAL THEORY
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
Stream and Vortex Lines
Differentiation following the Motion
Equation of Continuity
Equations of Motion
Vorticity
Examples
LAPLACE'S EQUATION
Conditions satisfied by the Potential
Determination of the Distribution
The Electrostatic Problem
Solutions of Laplace's Equation
Examples
FOUR-DIMENSTONAL VECTORS
Four-Dimensional Vector Calculus
The Space Time World
Electro-Magnetic Field Equations
Momentum World-Vector
Conservation of Energy
BIBLIOGRAPHY
INDEX