Short calculus简明微积分
出版日期:2001-11
ISBN:9780387953274
作者:Lang, Serge
页数:272页
书籍目录
CHAPTER 1 Numbers and FunctionsCHAPTER 2 Graphs and CurvesCHAPTER 3 The DerivativeCHAPTER 4 Sine and CosineCHAPTER 5 The Mean Value TheoremCHAPTER 6 Sketching CurvesCHAPTER 7 Inverse FunctionsCHAPTER 8 Exponents and LogarithmsCHAPTER 9 IntegrationCHAPTER 10 Properties of the IntegralCHAPTER 11 Techniques of IntegrationCHAPTER 12 Some Substantial ExercisesCHAPTER 13 Applications of IntegrationCHAPTER 14 Taylor's FormulaCHAPTER 15 SeriesAppendix 1. Epsilon and DeltaAppendix 2. Physics and MathematicsAnswersIndex.
作者简介
From the reviews "This is a reprint of the original edition of Lang's 'A First Course in Calculus', which was first published in 1964...The treatment is 'as rigorous as any mathematician would wish it'...[The exercises] are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging...There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able." --Mathematical Gazette
发布书评
精彩短评 (总计1条)
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一点感想：虽然是一本简明扼要的单变量微积分导论，但作者对逻辑严密性的遵循，还是值得称道的，譬如，对以e为底的对数函数的定义并不是从初等数学中已经介绍过的各种性质出发，而是将其定义为经过(1, 0)点的（初始条件）、1/x的面积函数，证明它是具有该性质的唯一原函数，以此推导出上述各种性质，再将以e为底的指数函数定义为其反函数，之后再定义一般指数函数。以这种方式刻画对数函数，更容易过渡到对定积分的定义。作者先从不定积分讲起，从几何直观的角度证明面积函数也是不定积分，再抛弃几何直观，给出面积函数的形式化定义及其唯一性，从而给出定积分的定义，最后介绍黎曼求和，证明上和（下和）的下确界（上确界）函数满足面积函数的形式化定义，最终说明了不定积分与定积分之间的关系。总体而论，不失为一本很好的入门教材。