Chapter 7 Spatial Analytic Geometry and Vector Algebra Section 1 Vector and Its Linear Operation Section 3 I Vector Concept 3 II. Linear operation exercise 7 of vector 3? The coordinates of 16 vector in the space Cartesian coordinate system Section 2 6 1. The coordinate representation of the space Cartesian coordinate system and the vector 6 2. Modulus, Direction Cosine and Projection of Vector 10 Exercise 7? 2 12 Multiplication of the vectors in the third quarter 13 I. Quantitative product of two vectors 13 II. Cross product of two vectors 15 * III. Mixed product of three vectors 17 Exercise 7? 3 18 The fourth section surface and its equation 18 I. The equation of the surface 18 II. Cylindrical surface 19 III. Revolving surface 2 1 IV. Common quadric surface 23 exercise 7? Section V Spatial Curve and Its Equation 26 Ⅰ. Equation 27 of Spatial Curve Ⅱ. Projection of space curve on coordinate plane 29 Exercise 7? 53 1 the plane of the sixth section and its equation 3 1 i. Equation 3 1 ii of the plane. The positional relationship between two planes. Distance from point to plane 35 Exercise 7? 635 Section 7 Space Straight Line and Its Equation 36 i. Equation 36 II of Straight Line. The positional relationship between straight line and straight line, straight line and plane 39 Ⅲ. Plane binding 4 1 exercise 7? 743 The fifth comprehensive exercise 45 The sixth differential of multivariate function Chapter 8 Differential of multivariate function 49 Section 1 Multivariate function, limit and continuity 49 I. Preparatory knowledge 49 II. The basic concept of multivariate function 5 1 III. The limit of multivariate function. Continuity of multivariate function 55 Exercise 8? 157 partial derivative in the second quarter 58 I. Concept and calculation of partial derivative 58 II. Higher-order partial derivative 60 exercise 8? 262 total differential in the third quarter and its application 62 i. total differential 63 II. Linearization of binary function 65 Exercise 8? The law of derivative of multivariate composite function in the fourth quarter 67 I. Chain law of derivative of multivariate composite function 67 II. Derivation of derivative of abstract composite function. Invariance of Total Differential Form 70 Exercise 8? 47 1 Section 5 Derivative Rule of Implicit Function 72 I. Existence Theorem of Unary Implicit Function and Derivative Formula of Implicit Function 72 II. Existence Theorem of Binary Implicit Function and Derivative Formula of Implicit Function 73 Exercise 8? 574 Section VI Geometric application of differential calculus of multivariate functions. Tangent plane and normal plane of space curve. Tangent and normal plane of space curve 77 Exercise 8? Section 7 directional derivative and gradient 79 i. directional derivative 80 II. Gradient 82 III. The concept of field 84 Exercise 8? 785 Section 8 Extreme value of multivariate function and its solution 85 I. Extreme value, maximum value and minimum value 85 II. Conditional Extreme Lagrange Multiplier Method 88 Exercise 8? 89 1 the sixth comprehensive exercise 92 the seventh multivariate function integral chapter 9 double integral 97 the concept and properties of double integral in the first section 97 I. The concept of double integral 97 II. The properties of double integral 100 exercise 9? 1 102 calculation of double integral in the second quarter 103 i. calculation of double integral with cartesian coordinates 103 ii. Calculating Double Integral in Polar Coordinates 109 Exercise 9? 2 1 1 1 Section III Triple Integral 1 12 The concept of triple integral 1 12 Second, calculate the triple integral1/kloc-using Cartesian coordinates. 3 1 19 The application of multiple integrals in the fourth quarter 120 I. Geometric application 120 II. Mass, centroid, moment, centroid 122 III. Moment of inertia 125 IV. Effective braking radius of automobile disc brake 127 exercise 9. 4 128 Chapter 10 Curve Integral and Surface Integral 130 Section 1 Arc-length curve integral 130 I. Concept and properties of arc-length curve integral II. Calculation and application of arc-length curve integral13/exercise 10? 1 135 Curve integration of coordinates in the second quarter 135 I. Concept of curve integration of coordinates 136 II. Curve integral calculation of coordinate 138 III. The connection between two kinds of curve integrals 140 exercises 10? 2 14 1 Section 3 Green's formula and its application 142 I. Green's formula 142 II. Green's formula. Curve integral has nothing to do with path 146 exercise 10? 3 150 The surface integral of the fourth quarter area 15 1 1. The concept of the surface integral of the area 15 1 2. Calculation and application of area integral 152 exercise 10? 4 158 Section 5 Surface Integral of Coordinate 159 I. Concept of Surface Integral of Coordinate 159 II. Calculation exercise of coordinate 162 surface integral 10? 5 165 Section VI Gauss Formula Flux and Divergence 165 1. Gauss formula 166 2. The condition of integrating zero along any closed surface 169 3. Flux and divergence 169 exercise 10? 6 17 1 Section VII Flow and Curvature of Stokes Formula Ring 172 I. Stokes Formula 172 II. Conditions for spatial curve integration independent of path 175 III. Circulation and Curvature 176 Exercise 10? 7 178 Seventh Comprehensive Exercise 179 Chapter VIII Infinite Series XI Infinite Series 185 Concept and Properties of Constant Series in Section 1/Concept of KLOC-0/85 I Constant Series/Basic Properties of KLOC-0/85 II Infinite Series 189 Exercise/KLOC-. 1 193 convergence method of positive series in the second quarter 193 I. Basic theorem of positive series 194 II. Convergence law of positive series 194 exercises 1 1? 220 1 Section III General Constant Series 202 I. Staggered Series and Its Convergence Method 202 II. Convergence of General Constant Series Absolute Convergence and Conditional Convergence 204 Exercise 1 1? 3206 Four-quarter power series 206 I. General concept of function term series 206 II. Power series and its convergence. Four operations of power series 2 12 IV. Derivative and Integral of Power Series 2 14 Exercise 1 1? 42 16 The function in the fifth section is expanded into power series 2 16 I and Taylor series 2 16 II. The method of expanding a function into a power series 2 18 III. Application of power series 222 exercise 1 1 5225 Section 6 Fourier Series 226 1. Orthogonality of trigonometric series and trigonometric function system. A function with a period of 2π is expanded into a Fourier series of 227 3. Sine series and cosine series 23 1 exercises 1 1? 6233 Section 7 Fourier Series of General Periodic Function 233 Exercise 1 1? 7237 Article 8 Comprehensive Exercise 238 Answer 240