A Synopsis of Elementary Results in Pure and Applied Mathematics: Volume 1: Containing Propositions, Formulae, and Methods of Analysis, with Abridged ... (Cambridge Library Collection - Mathematics)

Description

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. Front Cover PART Circle of similitude -MATHEMATICAL TABLES ELIMINATION- FACTORS 100 MULTIPLICATION AND DIVISION ANHARMONIC RATIO AND PENCIL LOWEST COMMON MULTIPLE ARITHMETICAL PROGRESSION SIMULTANEOUS EQUATIONS AND EXAMPLES CONTINUED FRACTIONS AND CONVERGENTS TO REDUCE A QUADRATIC SURD TO A CONTINUED FRACTION IMAGINARY EXPRESSIONS EXPANSION OF A FRACTION POLYGONAL NUMBERS INEQUALITIES Common and Hyperbolic Logarithms FACTORS OF AN EQUATION LIMITS OF THE ROOTS -THEORY OF EQUATIONS COMMENSURABle Roots SYMMETRICAL FUNCTIONS OF THE ROOTS OF AN EQUATION- Definitions JOINT PROPERTIES OF THE ELLIPSE AND HYPERBOLA— Symmetrical Determinants CS: CA CX Orthogonal Transformation -PLANE TRIGONOMETRY Squares of distances of P from equidistant points on RATIOS OF 45°, 60°, 15°, 18°, multiples ADDITIONAL FORMULE Explanation of the Table RIGHT-ANGLED TRIANGLES- POLYHEDRONS RADICAL AXIS- Of two Circles POLE AND POLAR Page 1151 1174 ASYMPTOTIC PROPERTIES OF THE HYPERBOLA— DIAMETERS CIRCLE OF CURVATURE THE GENERAL EQUATION —DIFFERENTIAL CALCULUS PARTIAL DIFFERENTIATION IMPLICIT FUNCTIONS- Abel's series JACOBIANS Expansion of cos no, &c in powers of sin and cos 0 One independent variable FUNCTIONS OF TWO INDEPENDENT VARIABLES CHANGE OF THE INDEPENDENT VARIABLE MAXIMA AND MINIMA- —INTEGRAL CALCULUS STANDARD INTEGRALS Taylor's and Maclaurin's theorems SUCCESSIVE INTEGRATION DEFINITE INTEGRALS- APPROXIMATE INTEGRATION BY BERNOULLI'S SERIES INTEGRATION OF LOGARITHMIC AND EXPONENTIAL FORMS INTEGRATION OF CIRCULAR FORMS INTEGRATION OF CIRCULAR LOGARITHMIC AND EXPONENTIAL FORMS MISCELLANEOUS THEOREMS- Fourier's formula Summation of series by the function MULTIPLE INTEGRALS- Method by Maclaurin's theorem EXPANSION OF FUNCTIONS IN TRIGONOMETRICAL SERIES FUNCTIONS OF ONE INDEPENDENT VARIABLE FUNCTIONS OF TWO DEPENDENT VARIABLES —CALCULUS OF VARIATIONS APPENDIX- SINGULAR SOLUTIONS Riccati's Equation HIGHER ORDER LINEAR EQUATIONS EXACT DIFFERENTIAL EQUATIONS EQUATIONS WITH MORE THAN TWO VARIABLES PARTIAL DIFFERENTIAL EQUATIONS SECOND ORDER P D EQUATIONS LAW OF RECIPROCITY SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS BY SERIES FORMULE FOR FIRST AND nth DIFFERENCES MECHANICAL QUADRATURE THE CIRCLE LENGTHS AND AREAS Co-axal circles THE ELLIPSE AND HYPERBOLA THE HYPERBOLA REFERRED TO ITS ASYMPTOTES ANALYTICAL CONICS IN TRILINEAR COORDINATES NINE-POINT CIRCLE ANHARMONIC RATIO PARTICULAR CONICS CONIC AND SELF-CONJUGATE TRIANGLE CARNOT'S, PASCAL'S, AND BRIANCHON'S THEOREMS THE METHOD OF RECIPROCAL POLARS ON THE INTERSECTION OF TWO CONICS- INVARIANTS AND COVARIANTS TANGENT AND NORMAL SINGULARITIES OF CURVES--- INVERSE CURves Instantaneous centre LINKAGES AND LINKWORK A linkage for drawing an Ellipse -SOLID COORDINATE GEOMETRY TRANSFORMATION OF COORDINATES CENTRAL QUADRIC SURFACE- THE GENERAL EQUATION OF A QUADRIC RECIPROCAL POLARS GENERAL THEORY OF SURFACES- GEODESICS Momental ellipsoids PERIMETERS, AREAS, VOLUMES, CENTRES OF MASS, AND MOMENTS ELLIPSOID, HYPERBOLOID, AND PARABOLOID Arbogast's method of expanding ø COLLINEAR AND CONCURRENT SYSTEMS 5626 3150 3380 5590 4001-28