CounterExamples —— From Elementary Calculus to the Beginnings of Analysis

----- 反例:从初等微积分开始分析

ISBN: 9781482246674 出版年：2014 页码：358 Bourchtein, Andrei Bourchtein, Ludmila CRC Press

Introduction Comments On the structure of this book On mathematical language and notation Background (elements of theory) Sets Functions FUNCTIONS OF ONE REAL VARIABLE Elementary properties of functions Elements of theory Function definition Boundedness Periodicity Even/odd functions Monotonicity Extrema Exercises Limits Elements of theory Concepts Elementary properties (arithmetic and comparative) Exercises Continuity Elements of theory Local properties Global properties: general results Global properties: the famous theorems Mapping sets Weierstrass theorems Intermediate Value theorem Uniform continuity Exercises Differentiation Elements of theory Concepts Local properties Global properties Applications Tangent line Monotonicity and local extrema Convexity and inflection Asymptotes L'Hospital's rule Exercises Integrals Elements of theory Indefinite integral Definite (Riemann) integral Improper integrals Applications Exercises Sequences and series Elements of theory Numerical sequences Numerical series: convergence and elementary properties Numerical series: convergence tests Power series Exercises FUNCTIONS OF TWO REAL VARIABLES Limits and continuity Elements of theory One-dimensional links Concepts and local properties Global properties Multidimensional essentials Exercises Differentiability Elements of Theory One-dimensional links Concepts and local properties Global properties and applications Multidimensional essentials Exercises Integrability Elements of theory One-dimensional links Multidimensional essentials Exercises Bibliography Symbol Description Index