内容简介

微积分和数学分析引论 第1卷》共分为2卷三册,内容以及形式上有如下三个特点:一是引导者直达本学科的核心内容;二是注重应用,指导读者灵活运用所掌握的知识;三是突出了直觉思维在数学学习中的作用。作者不掩饰难点以使得该学科貌似简单,而是通过揭示概念之间的内在联系和直观背景努力帮助那些对这门学科真正感兴趣的读者。《微积分和数学分析引论 第1卷》第一章主要围绕着一元函数展开讨论,二、三、四章分别介绍了微积分的基本概念、运算及其在物理和几何中的应用,随后讲述了泰勒展开式、数值方法、数项级数、函数项级数、三角级数,最后介绍了一些与振动有关的类型简单的微分方程。《微积分和数学分析引论 第1卷》各章均提供了大量的例题和习题,其中一部分有相当的难度,但绝大部分是对正文内容的补充。

作者简介

微积分和数学分析引论 第1卷》第1作者库朗是纽约大学数学科学学院首任院长,著有Methodsofmathematicalphysics,Whatismathematics他发现的minmax原理在计算特征值时常被引用。

目录

Chapter1Introduction
1.1TheContinuumofNumbers
a.TheSystemofNaturalNumbersandItsExtension.CountingandMeasuring
b.RealNumbersandNestedIntervals
c.DecimalFractions.BasesOtherThanTen
d.DefinitionofNeighborhood
e.Inequalities
1.2TheConceptofFunction
a.Mapping-Graph
b.DefinitionoftheConceptofFunctionsofaContinuousVariable.DomainandRangeofaFunction
c.GraphicalRepresentation.MonotonicFunctions
d.Continuity
e.TheIntermediateValueTheorem.InverseFunctions
1.3TheElementaryFunctions
a.RationalFunctions
b.AlgebraicFunctions
c.TrigonometricFunctions
d.TheExponentialFunctionandtheLogarithm
e.CompoundFunctions,SymbolicProducts,InverseFunctions
1.4Sequences
1.5MathematicalInduction
1.6TheLimitofaSequence
1.7FurtherDiscussionoftheConceptofLimit
a.DefinitionofConvergenceandDivergence
b.RationalOperationswithLimits
c.IntrinsicConvergenceTests.MonotoneSequences
d.InfiniteSeriesandtheSummationSymbol
e.TheNumbere
f.TheNumberrasaLimit
1.8TheConceptofLimitforFunctionsofaContinuousVariable
a.SomeRemarksabouttheElementaryFunctions
Supplements
S.1LimitsandtheNumberConcept
a.TheRationalNumbers
b.RealNumbersDeterminedbyNestedSequencesofRationalIntervals
c.Order,Limits,andArithmeticOperationsforRealNumbers
d.CompletenessoftheNumberContinuum.CompactnessofClosedIntervals.ConvergenceCriteria
e.LeastUpperBoundandGreatestLowerBound
f.DenumerabilityoftheRationalNumbers
S.2TheoremsonContinuousFunctions
S.3PolarCoordinates
S.4RemarksonComplexNumbers
PROBLEMS

Chapter2TheFundamentalIdeasoftheIntegralandDifferentialCalculus
Chapter3TheTechniquesofCalculus
Chapter4ApplicationsinPhysicsandGeometry
Chapter5Taylor'sExpansion
Chapter6NumericalMethods
Chapter7InfiniteSumsandProducts
Chapter8TrigonometricSeries
Chapter9DifferentialEquationsfortheSimplestTypesofVibration
ListofBiographicalDates
Index

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