數(shù)學(xué)分析

內(nèi)容概要

本書是為貫徹教育部教學(xué)改革精神，實施全英語授課需要而編寫，此書書稿在實際教學(xué)中已獲得廣泛好評。其內(nèi)容包括：實數(shù)系統(tǒng)和函數(shù)；序列極限；函數(shù)極限及連續(xù)性；導(dǎo)數(shù)和微分；中值定理和導(dǎo)數(shù)的應(yīng)用；不定積分；定積分；定積分的應(yīng)用；微分方程初步。    本書可作為大學(xué)數(shù)學(xué)系及要求較高的專業(yè)的本科生教材，也可作為大學(xué)教師教學(xué)用書或教學(xué)參考書。

書籍目錄

Chapter 1  Real number system and functions　1.1  Real number system　1.2  Inequalities　1.3  FunctionsChapter 2  Sequence Limit　2.1  Concept of sequence limit　2.2  Properties of convergent sequences　2.3  Fundamental theorems of sequenqe limit　2.4  Upper limit and lower limit of a sequenceChapter 3  Function limits and continuity　3.1  Concept of function limits　3.2  Properties of function limits　3.3  Two important limits　3.4  Infinitesimal and infinity　3.5  Concept of continuity　3.6  Properties of continuous functions　3.7  Continuity of primary functions　3.8  Uniform continuityChapter 4  Derivatives and differentials　4.1  Concept of derivatives  　4.2  Computation of derivatives　4.3  Differentials 　4.4  Derivatives and differentials of higher orderChapter 5  Mean value theorems and applications of derivative　5.1 Mean value theorems　5.2  Monotony and extremum of functions　5.3  Graph of a function　5.4  L'Hospital rules　5.5  Newton-Raphson methodChapter 6  Indefinite integrals　6.1  Concept of indefinite integrals and fundamental formulas　6.2  Techniques of integration　6.3  Integration of some special kinds of functionsChapter 7  Definite integrals　7.1  Concept of definite integrals　7.2  Properties of definite integrals　7.3  The fundamental theorems of calculus　7.4  Integration techniques of definite integrals　7.5  Improper integrals　7.6  Numerical integrationChapter 8  Applications of definite integrals  　8.1  Applications in geometry　8.2  Applications in physicsChapter 9  Preliminary of differential equations　9.1  Basic concepts of differential equations  9.2  Differential equations of first-order 　　……

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