图书信息

内容简介

目录

图书信息

出版社: 高等教育出版社; 第1版 (2005年1月1日)

平装: 390页

正文语种: 英语

开本: 16

ISBN: 7040154846

条形码: 9787040154849

尺寸: 22.4 x 17 x 1.2 cm

重量: 522 g

内容简介

The aim of this book is to meet the requirements of teaching Calculus in English or in bilin． gual education according to the customs of teaching and the present domestic conditions．It is divided into two volumes．The first volume contains Calculus of single variable，simple differential equations，infinite series，and the second volume contains the rest．

The selection of the contents is in accordance with the fundamental requirements of teaching issued by the Ministry of Education of China，and is based on the accOmDlishments of reform in teaching during the past ten years．The arrangement and explanation of the main contents in this book are approximately the same as the published Chinese version with the same title and edited in chief by the first two authors．It may help readers to understand the mathematics and to improve the level of their English by reading one of them and using the other one as a reference． This book may be used as a textbook for undergraduate students in the science and engi． neering schools whose majors are not mathematics，and may also be suitable to the readers at the same level．

目录

~Introduction

Chapter l Theoretical Basis of Calculus

1．1 Sets and Functions

1．1．1 Sets and their operations

1．1．2 Concepts of mappings and functions

1．1．3 Composition of mappings and composition of functions

1．1．4 Inverse mappings and inverse functions

1．1．5 Elementary functions and hyperbolic functions

1．1．6 Some examples for modelling of functions in practical problems

Exercises 1．1

1．2 Limit of Sequence

1．2．1 Concept of limit of a sequence

1．2．2 Conditions for c onvergenc e of a sequenc e

1．2．3 Rules of operations on convergent sequenc es

Exercises 1．2

l-3 Limit of Function

1-3．1 The concept of limit of a function

1．3．2 The properties and operation rules of functional limits

1-3-3 Two important limits

Exercises 1．3

1．4 Infinitesimal and Infinite Quantities

1．4．1 Infinitesimal quantities and their order

1．4．2 Equivalence transformations of infinitesimals

1．4．3 Infinite quantities

ExereIses 1．4

1．5 ContinUOUS Functions

1．5．1 The concept of continuous function and classification ofdisc ontinuous points

1．5．2 Operations on continuous functions and the continuAy of elementary funct~~ns

1．5．3 Properties of continuous funct~~ns on a closed interval

Exercises 1．5

Chapter 2 The Differcmtial Caleukls and Its Applications

2．1 Concept of Derivatives

2．1．1 Definition of derivatives

2．1．2 Relationship between derivability and continuity

2．1．3 Some examples of derivative prob~~ms in sconce and technology

Exercises 2．1

2．2 Fundamental Derivation Rules

2．2．1 Derivation rules for sum，difference，product and quotient of functions

2．2．2 Derivation rule for composite functions

2．2．3 The derivative of an inverse function

2．2．4 Higher-order derivatives

Exercises 2．2

2．3 Derivation of Implicit Functions and Functions Defined by Parametric Equations

2．3．1 Method of derivation of implicit functions

2．3．2 Method of derivation of a function defmed by parametric equations

2．3．3 Related rates of change

Exercises 2．3

2．4 The Differential

2．4．1 Concept of the differential

2．4．2 Geometric meaning of the differential

2．4．3 Rules of operations on differentials

2．4．4 Application of the differential in approximate computation

Exercises 2．4

2．5 The Mean Value Theorem in Differential Calculus and L’Hospital’S Rules

2．5．1 Mean value theorems in differential calculus

2．5．2 L’Hospital’S rules

Exercises 2．5

2．6 Taylor’S Theorem and Its Applications

2．6．1 Taylor’S theorem

2．6．2 Maclaurin formulae for some elementary functions

2．6．3 Some applications of Taylor’S theorem

Exerc ises 2．6

2．7 Study of Properties of Functions

2．7．1 Monotonicity of functmns

2．7．2 Extreme values of functions

2．7．3 Global maxima and minima

2．7．4 Convexity of functmns

Exercises 2．7

Synthetic exerc ises

Chapter 3 The Integral Calculus and Its Applications

3．1 Concept and Properties of Definite Integrals

3．1．1 Examples of definite integral problems

3．1．2 The definition of definite integral

3．1．3 Properties of def'mite integrals

Exercises 3．1

3．2 The Newton-Leibniz Formula and the Fundamental Theorems of Calculus

3．2．1 Newton-Leibniz formula

3．2．2 Fundamental theorems of CalcUlus

Exercises 3．2

3．3 Indefinite Integrals and Integration

3．3．1 IndeKmite integrals

3．3．2 Integration by substitutions

3．3．3 Integration by parts

3．3．4 Quadrature problems for elementary fundamental functions

Exercises 3．3

3．4 Applications of Definite Integrals

3．4．1 Method of elements for setting up integral representations

3．4．2 Some examples on the applications of the defmite integral in geometry

3．4．3 Some examples of applications ofthe definite integralin physics

Exercises 3．4

3．5 Some Types of Simple Differential Equations

3．5．1 Some fundamental concepts

3．5．2 First order differential equations with variables separable

3．5．3 Linear equations offirst order

3．5．4 Equations of first order solvable by transformations of variables

3．5．5 Differential equations of second order solvable by reduced order

methods

3．5．6 Some examples of application of differential equations

Exertises 3．5

3．6 Improper Integrals

3．6．1 Integration on an infinite interval

3．6．2 Integrals of unbounded functions

Exercises 3．6

Chapter 4 Infinte Series

4．1 Series of Constant Terms

4．I．I Concepts and properties of series with constant terms

4．1．2 Convergence tests for series of positive terms

4．1．3 Series with variation of signs and tests for convergence

Exercises 4．1

4 2 Power Series

4．2．I Concepts of series of functions

4．2．2 Convergence of power series and operations on power series

4．2．3 Expansion of functions in power series

4．2．4 Some examples of applications of power series

4．2．5 Uniform convergence of series of functions

Exercises 4．2

4．3 Fourier Series

4．3．1 Periodic functions and trigonometric series

4．3．2 Orthogonality of the system of trigonometric functions and Fourier series

4．3．3 Fourier expansions of periodic functions

4．3．4 Fourier expansion of functions defined on the interval[O，l]

4．3．5 Complex form of Fourier series

Exercises 4．3

Synthetic exerc ises

Appendix Answers and Hints for Exercises~