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高等數(shù)學(xué)基礎(chǔ):Ⅰ:[英文本] 版權(quán)信息
- ISBN：7040154846
- 條形碼：9787040154849 ; 978-7-04-015484-9
- 裝幀：一般膠版紙
- 冊數(shù)：暫無
- 重量：暫無
- 所屬分類：>
高等數(shù)學(xué)基礎(chǔ):Ⅰ:[英文本] 內(nèi)容簡介
本書以英文版的形式，介紹了高等數(shù)學(xué)基礎(chǔ)知識。
高等數(shù)學(xué)基礎(chǔ):Ⅰ:[英文本] 目錄
~IntroductionChapter l Theoretical Basis of Calculus1．1 Sets and Functions1．1．1 Sets and their operations1．1．2 Concepts of mappings and functions1．1．3 Composition of mappings and composition of functions1．1．4 Inverse mappings and inverse functions1．1．5 Elementary functions and hyperbolic functions1．1．6 Some examples for modelling of functions in practical problemsExercises 1．11．2 Limit of Sequence1．2．1 Concept of limit of a sequence1．2．2 Conditions for c onvergenc e of a sequenc e1．2．3 Rules of operations on convergent sequenc esExercises 1．2l-3 Limit of Function1-3．1 The concept of limit of a function1．3．2 The properties and operation rules of functional limits1-3-3 Two important limitsExercises 1．31．4 Infinitesimal and Infinite Quantities1．4．1 Infinitesimal quantities and their order1．4．2 Equivalence transformations of infinitesimals1．4．3 Infinite quantitiesExereIses 1．41．5 ContinUOUS Functions1．5．1 The concept of continuous function and classification ofdisc ontinuous points1．5．2 Operations on continuous functions and the continuAy of elementary funct~~ns1．5．3 Properties of continuous funct~~ns on a closed intervalExercises 1．5Chapter 2 The Differcmtial Caleukls and Its Applications2．1 Concept of Derivatives2．1．1 Definition of derivatives2．1．2 Relationship between derivability and continuity2．1．3 Some examples of derivative prob~~ms in sconce and technology
Exercises 2．12．2 Fundamental Derivation Rules2．2．1 Derivation rules for sum，difference，product and quotient of functions2．2．2 Derivation rule for composite functions2．2．3 The derivative of an inverse function2．2．4 Higher-order derivativesExercises 2．22．3 Derivation of Implicit Functions and Functions Defined by Parametric Equations2．3．1 Method of derivation of implicit functions2．3．2 Method of derivation of a function defmed by parametric equations2．3．3 Related rates of changeExercises 2．32．4 The Differential2．4．1 Concept of the differential2．4．2 Geometric meaning of the differential2．4．3 Rules of operations on differentials2．4．4 Application of the differential in approximate computationExercises 2．42．5 The Mean Value Theorem in Differential Calculus and L'Hospital'S Rules2．5．1 Mean value theorems in differential calculus2．5．2 L'Hospital'S rulesExercises 2．52．6 Taylor'S Theorem and Its Applications2．6．1 Taylor'S theorem2．6．2 Maclaurin formulae for some elementary functions2．6．3 Some applications of Taylor'S theoremExerc ises 2．62．7 Study of Properties of Functions2．7．1 Monotonicity of functmns2．7．2 Extreme values of functions2．7．3 Global maxima and minima2．7．4 Convexity of functmnsExercises 2．7
Synthetic exerc isesChapter 3 The Integral Calculus and Its Applications3．1 Concept and Properties of Definite Integrals3．1．1 Examples of definite integral problems3．1．2 The definition of definite integral3．1．3 Properties of defmite integralsExercises 3．13．2 The Newton-Leibniz Formula and the Fundamental Theorems of Calculus3．2．1 Newton-Leibniz formula3．2．2 Fundamental theorems of CalcUlusExercises 3．23．3 Indefinite Integrals and Integration3．3．1 IndeKmite integrals3．3．2 Integration by substitutions3．3．3 Integration by parts3．3．4 Quadrature problems for elementary fundamental functionsExercises 3．33．4 Applications of Definite Integrals3．4．1 Method of elements for setting up integral representations3．4．2 Some examples on the applications of the defmite integral in geometry3．4．3 Some examples of applications ofthe definite integralin physicsExercises 3．43．5 Some Types of Simple Differential Equations3．5．1 Some fundamental concepts3．5．2 First order differential equations with variables separable3．5．3 Linear equations offirst order3．5．4 Equations of first order solvable by transformations of variables3．5．5 Differential equations of second order solvable by reduced ordermethods3．5．6 Some examples of application of differential equationsExertises 3．53．6 Improper Integrals3．6．1 Integration on an infinite interval3．6．2 Integrals of unbounded functionsExercises 3．6
Chapter 4 Infinte Series4．1 Series of Constant Terms4．I．I Concepts and properties of series with constant terms4．1．2 Convergence tests for series of positive terms4．1．3 Series with variation of signs and tests for convergenceExercises 4．14 2 Power Series4．2．I Concepts of series of functions4．2．2 Convergence of power series and operations on power series4．2．3 Expansion of functions in power series4．2．4 Some examples of applications of power series4．2．5 Uniform convergence of series of functionsExercises 4．24．3 Fourier Series4．3．1 Periodic functions and trigonometric series4．3．2 Orthogonality of the system of trigonometric functions and Fourier series4．3．3 Fourier expansions of periodic functions4．3．4 Fourier expansion of functions defined on the interval[O，l]
4．3．5 Complex form of Fourier seriesExercises 4．3Synthetic exerc isesAppendix Answers and Hints for Exercises~
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