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

## 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