Fundamentals of Advanced Mathematics(Ⅱ)

作者：

马知恩　王绵森　Fred Brauer

定价：

36.20 元

版面字数：

520千字

开本：

16开

装帧形式：

平装

版次：

1

最新版次
印刷时间：

2023年

ISBN：

978-7-04-017794-7

物料号：

17794-00

出版时间：

2006-01-15

读者对象：

高等教育

一级分类：

数学与统计学类

二级分类：

理工类专业数学基础课

三级分类：

高等数学

册数：

暂无

目录
- Chapter 5 Vector Algebra and Analytic Geometry in Space
  - 5.1 Vectors and Their Linear Operations
    - 5.1.1 The concept of vector
    - 5.1.2 Linear operations on vectors
    - 5.1.3 Projection of vectors
    - 5.1.4 Rectangular coordinate systems in space and components of vectors
  - Exercises 5.1
  - 5.2 M ultiplicative Operations on Vectors
    - 5.2.1 The scalar product(dot product,inner product) of two vectors
    - 5.2.2 The vector product (cross product,outer product) of two vectors
    - 5.2.3 The mixed product of three vectors
  - Exercises 5.2
  - 5.3 Planes and Lines in Space
    - 5.3.1 Equations of planes
    - 5.3.2 Position relationships between two planes
    - 5.3.3 Equations of straight lines in space
    - 5.3.4 Position relationships between two lines
    - 5.3.5 Position relationships between a line and a plane
    - 5.3.6 Distance from a point to a plane (line)
  - Exercises 5.3
  - 5.4 Surfaces and Space Curves
    - 5.4.1 Equations of surfaces
    - 5.4.2 Quadric surfaces
    - 5.4.3 Equations of space curves
  - Exercises 5.4
- Chapter 6 The M ultivariable Differential Calculus and its Applications
  - 6.1 Limits and Continuity of M ultivariable Functions
    - 6.1.1 Primary knowledge of point sets in the space Rn
    - 6.1.2 The concept of a multivariable function
    - 6.1.3 Limit and continuity of multivariable functions
  - Exercises 6.1
  - 6.2 Partial Derivatives and Total Differentials of M ultivariable Functions
    - 6.2.1 Partial derivatives
    - 6.2.2 Total differentials
    - 6.2.3 Higher-order partial derivatives
    - 6.2.4 Directional derivatives and the gradient
  - Exercises 6.2
  - 6.3 Differentiation of M ultivariable Composite Functions and Implicit Functions
    - 6.3.1 Partial derivatives and total differentials of multivariable composite functions
    - 6.3.2 Differentiation of implicit functions defined by one equation
    - 6.3.3 Differentiation of implicit functions determined by more than one equation
  - Exercises 6.3
  - 6.4 Extreme Value Problems for M ultivariable Functions
    - 6.4.1 Unrestricted extreme values
    - 6.4.2 Global maxima and minima
    - 6.4.3 Extreme values with constraints; The method of Lagrange multipliers
  - Exercises 6.4
  - *6.5 Taylor's Formula for Functions of Two Variables
    - 6.5.1 Taylor's formula for functions of two variables
    - 6.5.2 Proof of the sufficient condition for extreme values of function of two variables
  - Exercises 6.5
  - 6.6 Derivatives and Differentials of Vector-valued Functions
    - 6.6.1 Derivatives and differentials of vector-valued functions of one variable
    - 6.6.2 Derivatives and differentials of vector-valued functions of two variables
    - 6.6.3 Rules for differential operations
  - Exercises 6.6
  - 6.7 Applications of Differential Calculus of M ultivariable Functions in Geometry
    - 6.7.1 Tangent line and normal plane to a space curve
    - 6.7.2 Arc length
    - 6.7.3 Tangent planes and normal lines of surfaces
    - 6.7.4 Curvature
    - *6.7.5 The Frenet frame
    - *6.7.6 Torsion
  - Exercises 6.7
  - Synthetic exercises
- Chapter 7 The Integral Calculus of M ultivariable Scalar Functions and Its Applications
  - 7.1 The Concept and Properties of the Integral of a M ultivariable Scalar Function
    - 7.1.1 Computation of mass of an object
    - 7.1.2 The concept of the integral of a multivariable scalar function
    - 7.1.3 Properties of integrals of multivariable scalar functions
  - Exercises 7.1
  - 7.2 Computation of Double Integrals
    - 7.2.1 Geometric meaning of the double integral
    - 7.2.2 Computation methods for double integrals in rectangular coordinates
    - 7.2.3 Computation of double integrals in polar coordinates
    - *7.2.4 Integration by substitution for double integrals in general
  - Exercises 7.2
  - 7.3 Computation of Triple Integrals
    - 7.3.1 Reduction of a triple integral to an iterated integral consisting of a single integral and a double integral
    - 7.3.2 Computation of triple integrals in cylindrical and spherical coordinates
    - *7.3.3 Computation of triple integrals by general substitutions
  - Exercises 7.3
  - 7.4 Applications of M ultiple Integrals
    - 7.4.1 The method of elements for multiple integrals
    - 7.4.2 Examples of applications
  - Exercises 7.4
  - 7.5 Line and Surface Integrals of the First Type
    - 7.5.1 Line integrals of the first type
    - 7.5.2 Surface integrals of the first type
  - Exercises 7.5
  - Synthetic exercises
- Chapter 8 The Integral Calculus of M ultivariable Vectorvalued Functions and its Applications in the Theory of Fields
  - 8.1 Line and Surface Integrals of the Second Type
    - 8.1.1 The concept of field
    - 8.1.2 Line integrals of the second type
    - 8.1.3 Surface integrals of the second type
  - Exercises 8.1
  - 8.2 The Relations Between Different Kinds of Integrals and their Applications to Fields
    - 8.2.1 Green's formula
    - 8.2.2 The conditions for a planar line integral to have independence of path
    - 8.2.3 Stokes'ormula and the curl of a vector
    - 8.2.4 Gauss'ormula and divergence
    - 8.2.5 Some important particular vector fields
  - Exercises 8.2
- Chapter 9 Linear Ordinary Differential Equations
  - 9.1 Linear Differential Equations of Higher Order
    - 9.1.1 Some examples of linear differential equation of higher order
    - 9.1.2 Structure of solutions of linear differential equations
    - 9.1.3 Solution of higher-order homogeneous linear differential equations with constant coefficients
    - 9.1.4 Solution of higher-order nonhomogeneous linear differential equations with constant coefficients
    - 9.1.5 Solution of higher-order linear differential equations with variable coefficients
  - Exercises 9.1
  - *9.2 Linear Systems of Differential Equations
    - 9.2.1 Basic concepts of linear systems of differential equations
    - 9.2.2 The structure of solutions of a linear system of equations
    - 9.2.3 Solution of a homogeneous system of linear equations with constant coefficients
    - 9.2.4 Solution of nonhomogeneous systems of linear equations with constant coefficients
    - 9.2.5 Some applications of systems of linear equations
  - *Exercises 9.2
  - Synthetic exercise
- Appendix A Basic Properties of M atrices and Determinants
  - A.1 M atrices
    - A.1.1 Elementary concepts of matrices
    - A.1.2 Operations on matrices
      - A.1.2.1 Linear operations on matrices
      - A.1.2.2 M ultiplication of matrices
      - A.1.2.3 Powers of a square matrix
      - A.1.2.4 Transpositions of matrices
    - A.1.3 Representation of the product of two matrices by rows(columns)
  - Exercises A.1
  - A.2 Determinants and Cramer's Rule
    - A.2.1 Definition and properties of determinants
    - A.2.2 Cramer's rule
  - Exercises A.2
- Appendix B Answers and Hints for Exercises

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