## Vector Methods Applied to Differential Geometry, Mechanics, and Potential TheoryDesigned 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. This includes applications to the theories of gravitation, hydrodynamics, and electricity. A brief chapter on four-dimensional vectors concludes the text. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

a x b acceleration algebra ANALYSIS angle applications atom axes axis CALCULUS called chemistry Classic closed curve closed surface components conductor constant coordinates curl cylinder define denote density differential equations dipole direction cosines electric intensity equipotential surfaces evaluate external forces field lines field vector fixed point fluid formula function Gauss's Gauss's law Gauss's theorem geometry given Hence integral INTRODUCTION irrotational J. P. Den Hartog kinetic energy Laplace's equation line integral line of action lines of curvature magnetic magnitude mass centre MATHEMATICS matrix momentum motion normal obtain origin osculating plane parametric lines perpendicular physics position vector potential due potential energy problems quantum mechanics radius represents rigid body rotation scalar product Show side solution space sphere spherical stream lines strength surface distribution tangent TENSOR theorem theory tion variable world vector y x a zero