## A Course of Pure MathematicsThere 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 |

### Common terms and phrases

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