A Course of Pure Mathematics

Front Cover
Cambridge University Press, 1952 - Mathematics - 509 pages
3 Reviews
There can be few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned 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.
  

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Contents

CHAPTER
1
Real numbers
14
The number V 2
20
The continuous real variable
27
Gausss theorem 7 Graphical solution of quadratic equa
34
CHAPTER II
40
Polynomia s
46
Graphical solution of equations
60
Derivative of xm 214 Derivatives of cos x and sin x 214 Tangent
274
Formulae of redu cion
282
Taylors series
291
The mean value theorem for functions of two variables
305
The circular functions
316
Integration by parts and by substitution
324
Integrals of complex functions
331
functions of two variables 311 Fouriers integrals 318 323 The second
340

Trigonometrical functions 55 Arithmetical functions 58 Cylinders
70
COMPLEX NUMBERS
72
The quadratic equation with real coefficients
84
Rational functions of a complex variable
90
Properties of a triangle 92 104 Equations with complex coefficients
106
Interpolation
112
Oscillating functions
126
Alternative proof of Weierstrasss theorem
138
The limit of nrl
144
The representation of functions of a continuous real
153
SECT PAGE
162
Equation zn+ixB 166 Limit of a mean value 167 Expansions
170
SECT PAGE
171
orders of smallness and greatness
183
Continuous functions of several variables
201
CHAPTER VI
210
General rules for differentiation
216
Differentiation of rational functions
223
General theorems concerning derivatives Rolles
231
Cauchys mean value theorem
244
SECT PAGE
245
Areas of plane curves
268
tests of convergence
341
Dirichlets theorem
347
Cauchys condensation test
354
Series of positive and negative terms
371
Abels and Dirichlets tests of convergence
379
Multiplication of series
386
CHAPTER IX
398
The number e
405
SECT PAGE
412
The exponential series
422
The binomial series
429
Integrals containing the exponential function 413 The hyperbolic func
445
The values of the logarithmic function
451
The general power a 409
457
The connection between the logarithmic and inverse
466
The exponential limit 410
474
The functional equation satisfied by Log z 454 The function e1 460
480
Stereographic projection 482 Mercators projection 482 Level curves
486
APPENDIX IT A note on double limit problems
493
The infinite in analysis and geometry
502
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