MindMap Gallery Differentiation method of multivariate functions and its applications
Differential method of multivariate functions and its applications: basic concepts of multivariate functions: plane point set, n-dimensional space, concept of multivariate functions, limits of multivariate functions, continuity of multivariate functions.
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This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
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Differentiation method of multivariate functions and its applications
Basic concepts of multivariate functions
Plane point set, n-dimensional space
n-dimensional space
Area
One-dimensional
two-dimensional
three dimensional
The concept of multivariate functions
n-ary function
binary function
ternary function
Limits of multivariate functions
definition
double limit
Determine that the double limit does not exist
Find the double limit
Continuity of multivariate functions
definition
theorem
Partial derivative
The definition and calculation method of partial derivatives
Partial derivatives of multivariate functions at a point
Partial derivative with respect to x
Partial derivative with respect to y
Partial derivatives of multivariate functions
Partial derivative with respect to x
Partial derivative with respect to y
Calculation of partial derivatives
Find the partial derivative function
The difference between the notation of a function of one variable and the notation of a partial derivative
Find the partial derivative at a point
definition
seek descendants first
Seek first and seek later
The geometric significance of partial derivatives of binary functions
Higher order partial derivatives
theorem
Total differential
definition
differentiable conditions
Necessary conditions for differentiability
sufficient conditions for differentiability
necessary and sufficient conditions for being differentiable
Calculation of total differentials
The function is differentiable, and the partial derivatives have a continuous relationship with the function
Derivative Rules for Multivariate Composite Functions
Chain derivation rule for multivariate composite functions
total derivative formula
When there are more than two intermediate variables
The case where the intermediate variable is a multivariate function
Total Differentials of Multivariable Composite Functions
total differential form invariance
Derivative formula of implicit function
case of an equation
Implicit function existence theorem
Implicit function derivation method
The case of the system of equations
Extreme values of multivariate functions and their methods of finding them
extreme value problem
optimal value problem
Extreme values of multivariate functions
unconditional extreme value
Definition of extreme value
Necessary conditions for extreme values
Sufficient conditions for extreme values of binary functions
Steps to find the extreme value of a binary function (unconditional)
conditional extreme value
Methods for finding conditional extreme values
substitution method
Lagrange multiplier method
promotion
best value
Find the maximum value of a multivariate function on a bounded closed region D
Find the best value for practical problems