## 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 a missionary with the rigor of a 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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