Complete set of definite integral formulas for postgraduate mathematics
The core content of calculus in postgraduate mathematics;
First, the concepts of partial derivative and total differential of multivariate functions (mainly binary and ternary)
Second, the calculation of partial derivative and total differential, especially the second-order partial derivative of composite function and the partial derivative of implicit function.
Third, directional derivative and gradient (only mathematics 1 is required)
Fourth, the application of multivariate function differentiation in geometry (mathematics only)
5. Extreme value and conditional extreme value of multivariate function.
Frequently asked questions are:
1. Find the partial derivative and total differential of binary and ternary functions.
2. Find the first and second partial derivatives of implicit function.
3. Find the directional derivatives and gradients of binary and ternary functions.
4. Find the tangent and normal plane equation of space curve and tangent and normal plane equation of surface.
5. The application of extreme value of multivariate function in geometry, physics and economy.
The fourth problem is the combination of differential calculus of multivariate functions with vector algebra and spatial analytic geometry in the previous chapter, which should be reviewed together.
Extreme application problems need to use knowledge from other fields, especially in economics, and involve some concepts and laws in economics, so readers should pay attention to them when reviewing. The differential calculus of unary function occupies a very important position in calculus, with many contents and far-reaching influence, which will be involved in most chapters later.
To sum up, there are four parts:
1. The concept part focuses on the definition of derivative and differential. In particular, the derivative will be used to define the differentiability, higher derivative, derivability and continuity of the lecture segmentation function at the boundary point.
2. The operation part focuses on the derivative and differential formulas of basic elementary functions, the derivative and differential formulas of four operations, and the derivative formulas of functions determined by inverse functions, implicit functions and parametric equations.
3. In the theoretical part, Rolle theorem, Lagrange mean value theorem and Cauchy mean value theorem are mainly introduced.
4. The application part focuses on learning the properties of function (including monotonicity and extremum of function, convexity and inflection point of function graph, asymptote), the application of maximum value, finding the limit by using Roda's law, and the application of derivative in economic field, such as "elasticity" and "margin".