## Calculus for Scientists and Engineers: An Analytical ApproachFocusing on the "why's" of mathematics rather than the "how's," the unique approach of this text will appeal to a wide range of readers, from those taking a first course in calculus to those seeking deeper insights or needing a transition from calculus to analysis. The author takes care to supply strong motivations for abstract concepts, thereby helping beginners overcome the intimidation often felt when first confronting abstraction. While emphasizing the "why's," the book does not entirely neglect the "how's" and provides sufficient exposure to the techniques through numerous exercises, with answers supplied in the back of the book. |

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### Contents

NATURE OF MATHEMATICS | 1 |

NATURE OF CALCULUS IN GENERAL | 41 |

SEQUENCES AND SERIES | 91 |

CONTINUITY AND DERIVATIVES | 181 |

INTEGRATION | 323 |

equate | 377 |

APPLICATIONS OF INTEGRALS | 445 |

CONSTRUCTION OF REAL NUMBERS | 610 |

CONSTRUCTION OF IFINITESIMALS | 623 |

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### Common terms and phrases

absolutely convergent angle apply approximation arc length assume average calculus called Cauchy circle concave concept constant continuous function convergent curvature curve defined denote derivative differentiable double integrals equals equation equivalent evaluate example exists fact finite number follows formula geometric given gives graph hence Hint hyperreal hyperreal number implies improper integrals inequality infimum infinite infinitesimally integer interval intuitively L'Hopital's rule last exercise lim f(x limit logarithms mathematics maximum method monotonically increasing n=l n=l neighbourhood non-negative notation Note parametrisation partition plane polynomial positive integer power series problem proof of Theorem properties Prove radius rational number real number respectively result Riemann integrable Riemann sums Section sequence Similarly sinx statement subintervals subset Suppose supremum tangent tends triangle triangle inequality uniform convergence uniformly uniformly continuous upper bound variable vector