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A Synopsis of Elementary Results in Pure and Applied Mathematics 1st Edition by George Shoobridge Carr ISBN 1139248545 9781139248549

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Author(s): George Shoobridge Carr
ISBN(s): 9781139248549, 1139248545
Edition: 1
File Details: PDF, 11.60 MB
Year: 2013
Language: english
SKU: EB-11762294 Category: Tag:

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ISBN 10: 1139248545 
ISBN 13: 9781139248549
Author: George Shoobridge Carr

When George Shoobridge Carr (1837–1914) wrote his Synopsis of Elementary Results he intended it as an aid to students preparing for degree-level examinations such as the Cambridge Mathematical Tripos, for which he provided private tuition. He would have been startled to see the two volumes, first published in 1880 and 1886 respectively, reissued more than a century later. Notably, in 1903 the work fell into the hands of the Indian prodigy Srinivasa Ramanujan (1887–1920) and greatly influenced his mathematical education. It is the interaction between a methodical teaching aid and the soaring spirit of a self-taught genius which gives this reissue its interest. Volume 1, presented here in its 1886 printing, contains sections on mathematical tables, algebra, the theory of equations, plane trigonometry, spherical trigonometry, elementary geometry and geometrical conics.

A Synopsis of Elementary Results in Pure and Applied Mathematics 1st Table of contents:

  • Algebra
    • Powers and Logarithms
    • Square and Cube Roots
    • Involution
    • Theory of Quadratic Expressions
    • Binomial Theorem
    • Continued Fractions and Convergents
    • Imaginary Expressions
    • Miscellaneous Series
    • Interest
    • Inequalities
    • Common and Hyperbolic Logarithms
    • Recurring Series
    • Summation of Series by the Method of Differences
    • Direct Factorial Series
    • Polygonal Numbers
    • Probabilities
    • Theory of Numbers
  • Theory of Equations
    • Commensurable Roots
    • Equal Roots of an Equation
    • Introductory Theorems
    • Symmetrical Functions of the Roots of an Equation
    • Highest Common Factor
  • Plane Trigonometry
    • Angular Measurement
    • Sum of sines or cosines of Angles in A.P.
    • Properties of the Triangle
    • Examples of the Solution of Triangles
  • Spherical Trigonometry
    • Spherical Areas
  • Elementary Geometry
    • The Problems of the Tangencies
    • Important Principles and Theorems (e.g., properties of triangles, parallelograms, lines perpendicular to planes)
  • Geometrical Conics
    • The Parabola
    • Methods of Drawing a Conic
    • Analytical Conics (often introduced in terms of trilinear coordinates)

Volume 2 (or Part II of a combined edition):

  • Differential Calculus
    • Expansions of Implicit Functions
    • Jacobians
    • Quantics
    • Functions of Two Independent Variables
    • Change of the Independent Variable
  • Integral Calculus
    • Standard Integrals
  • Calculus of Variations
  • Differential Equations
    • Singular Solutions
    • First Order Nonlinear Equations
    • Higher Order Nonlinear Equations
    • Approximate solution of Differential Equations
    • Partial Differential Equations
    • Second Order Partial Differential Equations
    • Law of Reciprocity
    • Solution of Linear Differential Equations by Series
  • Calculus of Finite Differences
  • Plane Coordinate Geometry
    • Transformation of Coordinates
    • Intercept equation of a conic
    • Theory of Plane Curves
    • Singularities of Curves
    • Transcendental and Other Curves (e.g., Spiral of Archimedes, Witch of Agnesi)
    • The Mechanical Integrator
  • Solid Coordinate Geometry
    • Cylindrical and Conical Surfaces
    • Perimeters, Areas, Volumes, Centers of Mass, and Moments

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Tags: George Shoobridge Carr, Mathematics, Elementary