Calculus（2）/普通高等教育“十一五”國(guó)家級(jí)規(guī)劃教材簡(jiǎn)介，目錄書(shū)摘
2019-10-17 09:45
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Calculus（2）/普通高等教育“十一五”國(guó)家級(jí)規(guī)劃教材
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內(nèi)容簡(jiǎn)介: 《普通高等教育“十一五”國(guó)家級(jí)規(guī)劃教材：Calculus（2）》是英文版大學(xué)數(shù)學(xué)微積分教材，分為上、下兩冊(cè)。上冊(cè)為單變量微積分學(xué)，包括函數(shù)、極限和連續(xù)、導(dǎo)數(shù)、中值定理及導(dǎo)數(shù)的應(yīng)用以及一元函數(shù)積分學(xué)等內(nèi)容；下冊(cè)為多變量微積分學(xué)，包括空間解析幾何及向量代數(shù)、多元函數(shù)微分學(xué)、重積分、線積分與面積分、級(jí)數(shù)及微分方程初步等內(nèi)容。本書(shū)由兩位國(guó)內(nèi)作者和一位外籍教授共同完成，在內(nèi)容體系安排上與國(guó)內(nèi)主要微積分教材一致，同時(shí)也充分參考和借鑒了國(guó)外尤其是北美一些大學(xué)微積分教材的諸多特點(diǎn)，內(nèi)容深入淺出，語(yǔ)言簡(jiǎn)潔通俗。本書(shū)適合作為大學(xué)本科生一學(xué)年微積分教學(xué)的教材，也可作為非英語(yǔ)教學(xué)的參考書(shū)。
目錄:CHAPTER 5 Vectors and the Geometry of Space
5.1 Vectors
5.1.1 Concepts of Vectors
5. 1.2 Linear Operations Involving Vectors
5.1.3 Coordinate Systems in Three-Dimensional Space
5.1.4 Representing Vectors Using Coordinates
5.1.5 Lengths, Direction Angles and Projections of Vectors
5.2 Dot Product, Cross Product and Scalar Triple Product
5.2. 1 The Dot Product
5.2.2 The Cross Product
5.2.3 Scalar Triple Product
5.3 Equations of Planes and Lines
5.3. 1 Planes
5.3.2 Lines
5.4 Surfaces In Space
5.4. 1 Surfaces and Equations
5.4.2 Cylinder
5.4.3 Surface of Revolution
5.4.4 Quadric Surfaces
5.5 Curves in Space
5.5.1 General Equations of Curves in the Space
5.5.2 Parametric Equations of Curves in the Space
5.5.3 Parametric Equations of Surfaces in the Space
5.5.4 Projections of Curves in the Space
5.6 Exercises
5.6. 1 Vectors
5.6.2 Planes and Lines in Space
5.6.3 Surfaces and Curves in Space
5.6.4 Questions to Guide Your Revision
CHAPTER 6 Functions of Several Variables
6.1 Functions of Several Variables
6.1.1 Definition
6. l. 2 Limits
6.1.3 Continuity
6.2 Partial Derivatives
6.2. 1 Definition
6.2.2 Partial Derivative of Higher Order
6.3 Total Differential
6.3. 1 Definition
6.3.2 The Total Differential Approximation
6.4 The Chain Rule
6.5 Implicit Differentiation
6.5. 1 Functions Defined by a Single Equation,.
6.5.2 Functions Defined Implicitly by System of Equations
6.6 Applications of the Differential Calculus
6.6.1 Tangent Lines and Normal Planes
6.6.2 Tangent Planes and Normal Lines for Surfaces
6.7 Directional Derivatives and Gradient Vectors
6.8 Maximum and Minimum
6.8.1 Extrema of Functions of Several Variables
6.8.2 Lagrange Multipliers
6.9 Additional Materials
6.9. 1 Taylors Theorem for Functions of Two Variables
6.9.2 Clairaut
6.9.3 Cobb-Douglas Production Function
6.10 Exercises
6.10.1 Functions of Several Variables t.
6.10.2 Applications of Partial Derivatives
6.10.3 Questions to Guide Your Revision
CHAPTER 7 Multiple Integrals
7.1 Definition and Properties
7.2 Iterated Integrals
7.2. 1 Iterated Integrals in Rectangular Coordinates
7.2.2 Change of Variables Formula for Double Integrals
7.3 Triple Integrals
7.3.1 Triple Integrals in Reetangular Coordinates
7.3.2 Change of Variables in Triple Integrals
7.4 The Area of a Surface
……
CHAPTER 8 Line and Surface Integrals
CHAPTER 9 Infinite Sequences,Series and Approximations
CHAPTER 10 Introduction to Ordinary Differential Equation
Answers
Reterence Books
5.1 Vectors
5.1.1 Concepts of Vectors
5. 1.2 Linear Operations Involving Vectors
5.1.3 Coordinate Systems in Three-Dimensional Space
5.1.4 Representing Vectors Using Coordinates
5.1.5 Lengths, Direction Angles and Projections of Vectors
5.2 Dot Product, Cross Product and Scalar Triple Product
5.2. 1 The Dot Product
5.2.2 The Cross Product
5.2.3 Scalar Triple Product
5.3 Equations of Planes and Lines
5.3. 1 Planes
5.3.2 Lines
5.4 Surfaces In Space
5.4. 1 Surfaces and Equations
5.4.2 Cylinder
5.4.3 Surface of Revolution
5.4.4 Quadric Surfaces
5.5 Curves in Space
5.5.1 General Equations of Curves in the Space
5.5.2 Parametric Equations of Curves in the Space
5.5.3 Parametric Equations of Surfaces in the Space
5.5.4 Projections of Curves in the Space
5.6 Exercises
5.6. 1 Vectors
5.6.2 Planes and Lines in Space
5.6.3 Surfaces and Curves in Space
5.6.4 Questions to Guide Your Revision
CHAPTER 6 Functions of Several Variables
6.1 Functions of Several Variables
6.1.1 Definition
6. l. 2 Limits
6.1.3 Continuity
6.2 Partial Derivatives
6.2. 1 Definition
6.2.2 Partial Derivative of Higher Order
6.3 Total Differential
6.3. 1 Definition
6.3.2 The Total Differential Approximation
6.4 The Chain Rule
6.5 Implicit Differentiation
6.5. 1 Functions Defined by a Single Equation,.
6.5.2 Functions Defined Implicitly by System of Equations
6.6 Applications of the Differential Calculus
6.6.1 Tangent Lines and Normal Planes
6.6.2 Tangent Planes and Normal Lines for Surfaces
6.7 Directional Derivatives and Gradient Vectors
6.8 Maximum and Minimum
6.8.1 Extrema of Functions of Several Variables
6.8.2 Lagrange Multipliers
6.9 Additional Materials
6.9. 1 Taylors Theorem for Functions of Two Variables
6.9.2 Clairaut
6.9.3 Cobb-Douglas Production Function
6.10 Exercises
6.10.1 Functions of Several Variables t.
6.10.2 Applications of Partial Derivatives
6.10.3 Questions to Guide Your Revision
CHAPTER 7 Multiple Integrals
7.1 Definition and Properties
7.2 Iterated Integrals
7.2. 1 Iterated Integrals in Rectangular Coordinates
7.2.2 Change of Variables Formula for Double Integrals
7.3 Triple Integrals
7.3.1 Triple Integrals in Reetangular Coordinates
7.3.2 Change of Variables in Triple Integrals
7.4 The Area of a Surface
……
CHAPTER 8 Line and Surface Integrals
CHAPTER 9 Infinite Sequences,Series and Approximations
CHAPTER 10 Introduction to Ordinary Differential Equation
Answers
Reterence Books
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