微积分

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

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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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