## A course of mathematical analysis, Volume 1 |

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### Contents

Some Historical Notes | 9 |

CHAPTER I | 22 |

Elementary Investigation of Functions | 36 |

Copyright | |

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### Common terms and phrases

abscissa absolute value absolutely convergent algebraic arctan argument asymptote called circle co-ordinate coefficients constant continuous function convergent convergent series convex corresponding curvature curve curvilinear trapezoid decreasing defined definite integral derivative differential discontinuity divergent domain of definition elementary functions equal equation example exists exponential function expression fact ff(x)dx finite number fraction function f(x geometrical given graph Hence improper integral increasing increment indefinitely independent variable inequality infinitesimal infinity integrand inverse inverse trigonometric functions length Let us find limit logarithmic mathematical analysis maximum error method negative neighbourhood obtained ordinate parabola point x0 polynomial positive number power series problem Proof radius rate of change rational function right-hand side segment straight line sub-interval tangent Taylor series Taylor's formula tends to zero theorem trigonometric functions uniformly convergent vanishes velocity whilst