[advanced mathematics] [6] differential calculus of multivariate functions

1. The basic concept of multivariate function

1.1 Plane point set

1.1.1 Inside point 、 External point 、 Boundary point 、 Get together

give an example

1.1.2 Plane point set

1.1.3 n Dimensional space

1.2 The concept of multivariate function

1.3 Limit of multivariate function

1.4 Continuity of multivariate functions

1.5 Properties of continuous multivariate functions on bounded closed domains

2. Partial derivative

2.1 Definition

2.2 Higher order partial derivative

3. Total differential

3.1 Definition

3.2 Theorem

Superposition theorem

4. Derivation rule of multivariate composite function

4.1 The case of univariate function and multivariate composite function

Total derivative

4.2 The combination of multivariate functions and multivariate functions

4.3 Other situations

5. Derivation formula of implicit function

5.1 The case of an equation

5.2 The case of equations

6. Geometric application of differential calculus of multivariate functions

6.1 Univariate vector valued functions and their derivatives

6.2 Derivative algorithm of vector valued function

6.2 Tangent and normal plane of space curve

6.3 The tangent plane and normal of the surface

7. Directional derivatives and gradients

7.1 Directional derivative

7.2 gradient

8. Extremum of multivariate function and its solution

8.1 Theorem

8.2 Conditional extremum

8.3 Lagrange multiplier method