Short calculus简明微积分
2001-11
Lang, Serge
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This is a reprint of A First Course in Calculus, which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students¿ background was not as substantial as it might be. We are now back to those times, so it¿s time to start over again. There are no epsilon-deltas, but this does not imply that the book is not rigorous. Lang learned this attitude from Emil Artin, around 1950.
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.
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