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Fundamentals of Advanced Mathematics(Ⅱ)

样章
作者：
马知恩　王绵森　Fred Brauer
定价：
36.20元
ISBN：
978-7-04-017794-7
版面字数：
520.000千字
开本：
16开
全书页数：
453页
装帧形式：
平装
重点项目：
暂无
出版时间：
2006-01-15
物料号：
17794-00
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
暂无
  • 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
    • 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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