| 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 Multiplicative 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(1ine) 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 Chapter 6 The Multivariable Differential Calculus and its Applications 6.1 Limits and Continuity of Multivariable 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 Multivariable 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 Multivariable 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 Multivariable 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 Taylors Formula for Functions of Two Variables 6.5.1 Taylors formula for functions of two variables …… Chapter 7 The Integral Calculus of Multivariable Scalar Functions and Its Applications Chapter 8 The Integral Calculus of Multivariable Vectorvalued Functions and its Applecations in the Theory of Fields Chapter 9 Linear Ordinary Differential Equations Appendix A Basic Properties of Matrices and Determinants Appendix B Answers and Hints for Exercises |
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