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  • Vector Methods Applied to Differential Geometry, Mechanics, and Potential Theory by D. E. Rutherford book cover
  • Vector Methods Applied to Differential Geometry, Mechanics, and Potential Theory by D. E. Rutherford book cover
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Vector Methods Applied to Differential Geometry, Mechanics, and Potential Theory

by D. E. Rutherford

Vector methods across mathematical fields

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AlbakiReads Editorial

Vector methods across mathematical fields

D. E. Rutherford’s text connects the abstract foundations of vector algebra and vector calculus with their use in several areas of mathematics. Its progression moves from an introduction to differential geometry through vector-based treatments of mechanics, then develops the operator nabla and its role in potential theory and Laplace’s equation. Applications include gravitation, hydrodynamics, and electricity, while a closing chapter introduces four-dimensional vectors. The book therefore offers both a grounding in vector methods and a tour of the subjects where those methods are applied.

Good fit for readers who enjoy

  • Undergraduates seeking an introduction to vector algebra and vector calculus.
  • Readers interested in applications of vector methods to geometry, mechanics, and potential theory.
  • Students exploring mathematical treatments of gravitation, hydrodynamics, or electricity.

Themes

Vector algebra and calculusDifferential geometryMechanicsPotential theory and Laplace’s equationApplications to physics

Based on publisher information and book metadata.

Book overview

Designed 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.
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