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
   6.1.2 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 Taylors 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
   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 Rectangular Coordinates
   7.3.2 Change of Variables in Triple Integrals
  7.4 The Area of a Surface
  7.5 Additional Materials
  7.6 Exercises
   7.6.1 Double Integrals
   7.6.2 Triple Integrals
   7.6.3 Applications of Multiple Integrals
   7.6.4 Questions to Guide Your Revision
 CHAPTER 8 Line and Surface Integrals
  8.1 Line Integrals
   8.1.1 Introduction
   8.1.2 Definition of the Line Integral with Respect to Arc Length
   8.1.3 Evaluating Line Integrals,∫Cf(x, y)ds,in R2
   8.1.4 Evaluating Line Integrals,∫Cf(x,y,z)ds,in R3
  8.2 Vector Fields，Work，and Flows
   8.2.1 Introduction
   8.2.2 The Line Integral of a Vector Field Along a Curve C
   8.2.3 Different Forms of the Line Integral Including ∫CF→·dr→
   8.2.4 Examples of Line Integrals
  8.3 Greens Theorem in R2
   8.3.1 The Circulation Curl Form of Greens Theorem
   8.3.2 The Divergence Flux Form of Greens Theorem
   8.3.3 Generalized Greens Theorem
  8.4 Path Independent Line Integrals and Conservative Fields
   8.4.1 Introduction
   8.4.2 Fundamental Results on Path Independent Line Integrals
  8.5 Surface Integrals
   8.5.1 Definition of Integration With Respect to Surface Area
   8.5.2 Evaluation of Surface Integrals
  8.6 Surface Integrals of Vector Fields
   8.6.1 Definition and Properties of Flux,SF→·N→dS
   8.6.2 Evaluating SF→·N→dS for a Surface z=z(x,y)
  8.7 The Divergence Theorem
   8.7.1 Introduction
   8.7.2 Physical interpretation of the Divergence SymbolQC@·F→(x,y,z)
  8.8 Stokes Theorem
  8.9 Additional Materials
   8.9.1 Green
   8.9.2 Gauss
   8.9.3 Stokes
  8.10 Exercises
   8.10.1 Line Integrals
   8.10.2 Surface Integrals
   8.10.3 Questions to Guide Your Revision
 CHAPTER 9 Infinite Sequences,Series and Approximations
  9.1 Infinite Sequences
  9.2 Infinite Series
   9.2.1 Definition of Infinite Series
   9.2.2 Properties of Convergent Series
  9.3 Tests for Convergence
   9.3.1 Series with Nonnegative Terms
   9.3.2 Series with Negative and Positive Terms
  9.4 Power Series and Taylor Series
   9.4.1 Power Series
   9.4.2 Working with Power Series
   9.4.3 Taylor Series
   9.4.4 Applications of Power Series
  9.5 Fourier Series
   9.5.1 Fourier Series Expansion with Period 2π
   9.5.2 Fourier Cosine and Sine Series with Period 2π
   9.5.3 The Fourier Series Expansion with Period 2l
   9.5.4 Fourier Series with Complex Terms
  9.6 Additional Materials
   9.6.1 Fourier
   9.6.2 Maclaurin
   9.6.3 Taylor
  9.7 Exercises
   9.7.1 Series with Constant Terms
   9.7.2 Power Series
   9.7.3 Fourier Series
   9.7.4 Questions to Guide Your Revision
 CHAPTER 10 Introduction to Ordinary Differential Equation
  10.1 Differential Equations and Mathematical Models
  10.2 Methods for Solving Ordinary Differential Equations
   10.2.1 Separable Equations
   10.2.2 Substitution Methods
   10.2.3 Exact Differential Equations
   10.2.4 Linear First Order Differential Equations and Integrating Factors
   10.2.5 Reducible Second Order Equations
   10.2.6 Linear Second Order Differential Equations
  10.3 Other Ways of Solving Differential Equations
   10.3.1 Power Series Method
   10.3.2 Direction Fields
   10.3.3 Numerical Approximation:Eulers Method
  10.4 Additional Materials
   10.4.1 Euler
   10.4.2 Bernoulli
   10.4.3 The Bernoulli Family
   10.4.4 Development of Calculus
  10.5 Exercises
   10.5.1 Introduction to Differential Equations
   10.5.2 First Order Differential Equation
   10.5.3 Second Order Differential Equation
   10.5.4 Questions to Guide Your Revision
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