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Course of Pure Mathematics Centenary Edition

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ISBN-10: 0521720559

ISBN-13: 9780521720557

Edition: 10th 2008

Authors: G. H. Hardy, T. W. K�rner

List price: $61.95
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Description:

There are few textbooks of mathematics as well-known as Hardys Pure Mathematics. Since its publication in 1908, this classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of the missionary with the rigour of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit. Celebrating 100 years in print with Cambridge, this edition includes a Foreword by T. W. Krner, describing the huge influence the book has had on the teaching and development of mathematics…    
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Book details

List price: $61.95
Edition: 10th
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 3/13/2008
Binding: Paperback
Pages: 530
Size: 5.91" wide x 8.90" long x 1.10" tall
Weight: 1.848
Language: English

Real variables
Rational numbers
Irrational numbers
Real numbers
Relations of magnitude between real numbers
Algebraical operations with real numbers
The number [radical]2
Quadratic surds
The continuum
The continuous real variable
Sections of the real numbers. Dedekind's theorem
Points of accumulation
Weierstrass's theorem
Miscellaneous examples
Decimals
Gauss's theorem
Graphical solution of quadratic equations
Important inequalities
Arithmetical and geometrical means
Cauchy's inequality
Cubic and other surds
Algebraical numbers
Functions of real variables
The idea of a function
The graphical representation of functions. Coordinates
Polar coordinates
Polynomials
Rational functions
Algebraical functions
Transcendental functions
Graphical solution of equations
Functions of two variables and their graphical representation
Curves in a plane
Loci in space
Miscellaneous examples
Trigonometrical functions
Arithmetical functions
Cylinders
Contour maps
Cones
Surfaces of revolution
Ruled surfaces
Geometrical constructions for irrational numbers
Quadrature of the circle
Complex numbers
Displacements
Complex numbers
The quadratic equation with real coefficients
Argand's diagram
De Moivre's theorem
Rational functions of a complex variable
Roots of complex numbers
Miscellaneous examples
Properties of a triangle
Equations with complex coefficients
Coaxal circles
Bilinear and other transformations
Cross ratios
Condition that four points should be concyclic
Complex functions of a real variable
Construction of regular polygons by Euclidean methods
Imaginary points and lines
Limits of functions of a positive integral variable
Functions of a positive integral variable
Interpolation
Finite and infinite classes
Properties possessed by a function of n for large values of n
Definition of a limit and other definitions
Oscillating functions
General theorems concerning limits
Steadily increasing or decreasing functions
Alternative proof of Weierstrass's theorem
The limit of x[superscript n]
The limit of [characters not reproducible]
Some algebraical lemmas
The limit of [characters not reproducible]
Infinite series
The infinite geometrical series
The representation of functions of a continuous real variable by means of limits
The bounds of a bounded aggregate
The bounds of a bounded function
The limits of indetermination of a bounded function
The general principle of convergence
Limits of complex functions and series of complex terms
Applications to z[superscript n] and the geometrical series
The symbols O, o, [tilde]
Miscellaneous examples
Oscillation of sin n[theta pi]
Limits of [characters not reproducible]
Decimals
Arithmetic series
Harmonic series
Equation x[subscript n+1]=f(x[subscript n])
Limit of a mean value
Expansions of rational functions
Limits of functions of a continuous variable. Continuous and discontinuous functions
Limits as x to [infinity] or x to - [infinity]
Limits as x to a
The symbols O, o, [tilde]: orders of smallness and greatness
Continuous functions of a real variable
Properties of continuous functions. Bounded functions. The oscillation of a function in an interval
Sets of intervals on a line. The Heine-Borel theorem
Continuous functions of several variables
Implicit and inverse functions
Miscellaneous examples
Limits and continuity of polynomials and rational functions
Limit of [characters not reproducible]
Limit of [characters not reproducible]
Infinity of a function
Continuity of cos x and sin x
Classification of discontinuities
Semicontinuity
Derivatives and integrals
Derivatives
General rules for differentiation
Derivatives of complex functions
The notation of the differential calculus
Differentiation of polynomials
Differentiation of rational functions
Differentiation of algebraical functions
Differentiation of transcendental functions
Repeated differentiation
General theorems concerning derivatives. Rolle's theorem
Maxima and minima
The mean value theorem
Cauchy's mean value theorem
A theorem of Darboux
Integration. The logarithmic function
Integration of polynomials
Integration of rational functions
Integration of algebraical functions. Integration by rationalisation. Integration by parts
Integration of transcendental functions
Areas of plane curves
Lengths of plane curves
Miscellaneous examples
Derivative of x[superscript m]
Derivatives of cos x and sin x
Tangent and normal to a curve
Multiple roots of equations
Rolle's theorem for polynomials
Leibniz's theorem
Maxima and minima of the quotient of two quadratics
Axes of a conic
Lengths and areas in polar coordinates
Differentiation of a determinant
Formulae of reduction
Additional theorems in the differential and integral calculus
Taylor's theorem
Taylor's series
Applications of Taylor's theorem to maxima and minima
The calculation of certain limits
The contact of plane curves
Differentiation of functions of several variables
The mean value theorem for functions of two variables
Differentials
Definite integrals
The circular functions
Calculation of the definite integral as the limit of a sum
General properties of the definite integral
Integration by parts and by substitution
Alternative proof of Taylor's theorem
Application to the binomial series
Approximate formulae for definite integrals. Simpson's rule
Integrals of complex functions
Miscellaneous examples
Newton's method of approximation to the roots of equations
Series for cos x and sin x
Binomial series
Tangent to a curve
Points of inflexion
Curvature
Osculating conics
Differentiation of implicit functions
Maxima and minima of functions of two variables
Fourier's integrals
The second mean value theorem
Homogeneous functions
Euler's theorem
Jacobians
Schwarz's inequality
The convergence of infinite series and infinite integrals
Series of positive terms. Cauchy's and d'Alembert's tests of convergence
Ratio tests
Dirichlet's theorem
Multiplication of series of positive terms
Further tests for convergence. Abel's theorem. Maclaurin's integral test
The series [Sigma]n[superscript -3]
Cauchy's condensation test
Further ratio tests
Infinite integrals
Series of positive and negative terms
Absolutely convergent series
Conditionally convergent series
Alternating series
Abel's and Dirichlet's tests of convergence
Series of complex terms
Power series
Multiplication of series
Absolutely and conditionally convergent infinite integrals
Miscellaneous examples
The series [Sigma]n[superscript k]r[superscript n] and allied series
Hypergeometric series
Binomial series
Transformation of infinite integrals by substitution and integration by parts
The series [Sigma]a[subscript n] cos n[theta], [Sigma]a[subscript n] sin n[theta]
Alteration of the sum of a series by rearrangement
Logarithmic series
Multiplication of conditionally convergent series
Recurring series
Difference equations
Definite integrals
The logarithmic, exponential, and circular functions of a real variable
The logarithmic function
The functional equation satisfied by log x
The behaviour of log x as x tends to infinity or to zero
The logarithmic scale of infinity
The number e
The exponential function
The general power a[superscript x]
The exponential limit
The logarithmic limit
Common logarithms
Logarithmic tests of convergence
The exponential series
The logarithmic series
The series for arc tan x
The binomial series
Alternative development of the theory
The analytical theory of the circular functions
Miscellaneous examples
Integrals containing the exponential function
The hyperbolic functions
Integrals of certain algebraical functions
Euler's constant
Irrationality of e
Approximation to surds by the binomial theorem
Irrationality of log[subscript 10] n
Definite integrals
The general theory of the logarithmic, exponential, and circular functions
Functions of a complex variable
Curvilinear integrals
Definition of the logarithmic function
The values of the logarithmic function
The exponential function
The general power a[superscript zeta]
The trigonometrical and hyperbolic functions
The connection between the logarithmic and inverse trigonometrical functions
The exponential series
The series for cos z and sin z
The logarithmic series
The exponential limit
The binomial series
Miscellaneous examples
The functional equation satisfied by Log z
The function e[superscript zeta]
Logarithms to any base
The inverse cosine, sine, and tangent of a complex number
Trigonometrical series
Roots of transcendental equations
Transformations
Stereographic projection
Mercator's projection
Level curves
Definite integrals
The proof that every equation has a root
A note on double limit problems
The infinite in analysis and geometry
The infinite in analysis and geometry
Index