MindMap Gallery multivariable differential calculus
Sharing the knowledge points of multivariate differential calculus! The figure below includes basic concepts, principle test points, partial derivative calculation rules, applications in extreme values, knowledge expansion, etc. It is efficient in detecting leaks, clear and intuitive, and it is very easy to get high scores if you use it well!
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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.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
Multiple differentials
Basic concepts and principles test points
Basic theory
Theorem 1
Theorem 2
Limits of binary functions
continuous
Higher order partial derivatives, partial derivatives
Quanwei
Partial derivative calculation rules
Calculation rules for partial derivatives of composite functions
Theorem 1
Theorem 2
Calculation of partial derivative functions of implicit functions
determined by an equation Implicit function partial derivative calculation
determined by multiple equations Implicit function partial derivative calculation
Application in extreme values
unconditional extreme value
Extreme point and extreme point definition
unconditional extreme step
conditional extreme value
Knowledge expansion
Convert to the maximum value of a one-variable function
Lagrange multiplier method
Key question types
1. Limits of multivariate functions
2. The concept of multivariate differential calculus
3. Continuous, deflectable, differentiable and The relationship between partial derivatives of a continuous function
4. Find binary or multivariate partial derivatives
5. Deformation of partial derivative equations under transformation
6. Mixed problems of partial derivatives and differential equations
6. Conditional extreme values and unconditional extreme values of multivariate functions
differential equations
basic concept
Order, solution, special solution, general solution
Types and solutions of first-order differential equations
separable variable differential equations
Homogeneous differential equation
First-order homogeneous linear differential equation
First order non-uniformity
Reducible higher-order differential equations and their solutions
F=nth order of y
F=(x,y′,y")=0
F=(y,y′,y")=0
Theory of Higher Order Linear Differential Equations
Concepts and properties
concept
solution structure
solution
Second-order homogeneous solution with constant coefficients
Third-order homogeneous solution with constant coefficients
Method for finding non-homogeneous special solutions with second-order constant coefficients
Extension: Higher-order non-uniform solution method
Key question types
1. Standard, no specific type of first-order solution
2. Reducible higher-order differential equations
3.High-order constant coefficient linear differential equations
4. Transformation method to solve high-order differential equations
5. Differential equation synthesis problems
6.Physical applications of differential equations
double integral
Concepts, properties and calculations
concept
nature
Operation, area splitting
Integral mean value theorem
regional symmetry principle
Integration method
Cartesian coordinate method
Polar coordinate transformation
Key question types
1.Definition and basic properties
2. Change the order of points
3. Double integral calculation
4. Proof of double integral