Chapter 7 Analytic Geometry in Space and Vector Algebra 1
7.1 Vector and their linear operations 1
7.2 Rectangular coordinate systems in space and components of vectors 6
7.3 The scalar product vector product mixed product 15
7.4 Planes and their equations 23
7.5 Straight lines in space and their equations 28
7.6 Surfaces and their equations 34
7.7 Space curves and their equations 39
7.8 Quadric surfaces 41
Chapter 8 The Multivariable Differential Calculus and its Applications 47
8.1 Basic concepts of multivariable functions 47
8.2 Limit and continuity for function of several variables 57
8.3 Partial derivatives and higher-order partial derivatives 63
8.4 Total differentials 71
8.5 Directional derivatives and the gradient 77
8.6 Differentiation of multivariable composite functions 84
8.7 Differentiation of implict functions 89
8.8 Applications of differential calculus of multivariable functions in geometry 100
8.9 Extreme value problems for multivariable functions 107
Chapter 9 Multiple Integrals 119
9.1 Double integral 119
9.2 Evaluation of a double integral by iterated integration 123
9.3 Change of variables in a double integral 132
9.4 Improper double integrals 140
9.5 Applications of double integrals 142
9.6 Extensions to higher dimensions 147
9.7 Change of variables in a triple integral 150
Chapter 10 Line Integrals and Surface Integrals 163
10.1 Line integrals with respect to arc lengths 163
10.2 Line integrals with respect to coordinates 169
10.3 Green's theorem,Path independence 174
10.4 Surface integrals with respect to surface areas 179
10.5 Surface integrals with respect to coordinates 183
10.6 The divergence theorem 186
10.7 Stokes theorem 192
Chapter 11 Differential Equations 199
11.1 Differential equations and their solutions 199
11.2 Separable equations 204
11.3 Linear first-order equations 209
11.4 Homogeneous equations 214
11.5 Exact equations 220
11.6 Reducible second-order equations 224
11.7 second-order linear equations 228
Answers 242