Part 1
Chapter 1 Vector Space
1.1 n-space R^n
1.2 Coordinate space and cross product of vectors
1.3 Polar and Spherical Coordinates

Chapter 2 Multivariable Functions
2.1 Multivariable functions and graphs
2.2 Limits of functions and continuous functions
2.3 Maximum and Minimum Theorem
Appendix n-dimensional Euclidean space

Chapter 3 Partial Derivatives and Directional Differentiation
3.1 Directional Differentiation and Gradient Vector
3.2 Differentiability
3.3 Chain Law

Chapter 4 Maximum and Minimum Values
4.1 Higher-order differentiation and higher-order derivatives
4.2 Extreme values ​​and thresholds
4.3 Hessian matrix
4.4 Lagrange multiplier method

Chapter 5 Differentiation of Multivariable Vector Functions
5.1 Multivariate vector functions
5.2 Jacobian Matrices and Jacobian Determinants
5.3 Chain rule for vector functions
5.4 Mean Value Theorem
5.5 Inverse function theorem
5.6 Implicit Function Theorem

Chapter 6 Divergent functions and curls of vector fields
6.1 Various vector fields
6.2 Vector fields and gradients
6.3 Vector fields and divergent functions
6.4 Curl of vector fields
supplement

Part 2
Chapter 7 Multiple Integrals
7.1 Riemann integral
7.2 Basic properties of integration
7.3 Integration of continuous functions
7.4 Fubini's theorem

Chapter 8 Substitution Integrals
8.1 Variable conversion formula
8.2 Conversion formulas between coordinate systems

Chapter 9 Line Integrals
9.1 Line integral of a function
9.2 Line integral of a vector field
9.3 Gradient vector field
9.4 Existence of potential functions

Chapter 10 Area Integrals
10.1 Parameterized surfaces
10.2 Plane
10.3 Area of ​​a surface
10.4 Surface integral of a function
10.5 Surface integral of a vector field

Part 3
Chapter 11: Boundaries and Directionality
11.1 Fragrance
11.2 Boundaries and the Fragrance of Boundaries

Chapter 12 Line Integrals and Area Integrals
12.1 Green's Theorem
12.2 Stokes' theorem

Chapter 13 Area and Volume Integrals
13.1 Divergence theorem for plane vector fields
13.2 Divergence theorem of space vector fields

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