| CHAPTER 5 Vectors and the Geometry of Space5.1 Vectors5.1.1 Concepts of Vectors5. 1.2 Linear Operations Involving Vectors5.1.3 Coordinate Systems in Three-Dimensional Space5.1.4 Representing Vectors Using Coordinates5.1.5 Lengths, Direction Angles and Projections of Vectors5.2 Dot Product, Cross Product and Scalar Triple Product5.2. 1 The Dot Product5.2.2 The Cross Product5.2.3 Scalar Triple Product5.3 Equations of Planes and Lines5.3. 1 Planes5.3.2 Lines5.4 Surfaces In Space5.4. 1 Surfaces and Equations5.4.2 Cylinder5.4.3 Surface of Revolution5.4.4 Quadric Surfaces5.5 Curves in Space5.5.1 General Equations of Curves in the Space5.5.2 Parametric Equations of Curves in the Space5.5.3 Parametric Equations of Surfaces in the Space5.5.4 Projections of Curves in the Space5.6 Exercises5.6. 1 Vectors5.6.2 Planes and Lines in Space 5.6.3 Surfaces and Curves in Space5.6.4 Questions to Guide Your Revision CHAPTER 6 Functions of Several Variables6.1 Functions of Several Variables6.1.1 Definition6. l. 2 Limits6.1.3 Continuity6.2 Partial Derivatives6.2. 1 Definition6.2.2 Partial Derivative of Higher Order6.3 Total Differential6.3. 1 Definition6.3.2 The Total Differential Approximation6.4 The Chain Rule6.5 Implicit Differentiation6.5. 1 Functions Defined by a Single Equation,.6.5.2 Functions Defined Implicitly by System of Equations6.6 Applications of the Differential Calculus6.6.1 Tangent Lines and Normal Planes6.6.2 Tangent Planes and Normal Lines for Surfaces6.7 Directional Derivatives and Gradient Vectors6.8 Maximum and Minimum6.8.1 Extrema of Functions of Several Variables6.8.2 Lagrange Multipliers6.9 Additional Materials6.9. 1 Taylor's Theorem for Functions of Two Variables6.9.2 Clairaut6.9.3 Cobb-Douglas Production Function6.10 Exercises6.10.1 Functions of Several Variables t.6.10.2 Applications of Partial Derivatives6.10.3 Questions to Guide Your RevisionCHAPTER 7 Multiple Integrals7.1 Definition and Properties7.2 Iterated Integrals7.2. 1 Iterated Integrals in Rectangular Coordinates7.2.2 Change of Variables Formula for Double Integrals7.3 Triple Integrals7.3.1 Triple Integrals in Reetangular Coordinates7.3.2 Change of Variables in Triple Integrals7.4 The Area of a Surface……CHAPTER 8 Line and Surface IntegralsCHAPTER 9 Infinite Sequences,Series and ApproximationsCHAPTER 10 Introduction to Ordinary Differential EquationAnswersReterence Books |
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