Book:D.E. Rutherford/Vector Methods

Subject Matter

 * Vector Algebra

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