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

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

Published $\text {1957}$, Oliver & Boyd Ltd

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

Next

Cited by

• 1964: D.E. Rutherford: Classical Mechanics (3rd ed.)

Further Editions

• 1939: D.E. Rutherford: Vector Methods

Source work progress

From Next:

• 1957: D.E. Rutherford: Vector Methods (9th ed.) ... (previous) ... (next): Chapter $\text I$: Vector Algebra: $\S 9$: $(17)$

From start:

• 1957: D.E. Rutherford: Vector Methods (9th ed.) ... (previous) ... (next): Chapter $\text I$: Vector Algebra: $\S 7$