Examination contents-the concept of multivariate function, the geometric meaning of bivariate function, the limit and continuity of bivariate function, the properties of bivariate continuous function in bounded closed region, the derivation method of partial derivative and fully differential multivariate composite function and implicit function of multivariate function, the concepts, basic properties and calculation of extreme value and conditional extreme value, maximum value and minimum value of second-order partial derivative multivariate function.

Examination requirements

1. Understand the concept of multivariate function and the geometric meaning of bivariate function.

2. Understand the concepts of limit and continuity of binary function and the properties of binary continuous function in bounded closed region.

3. Knowing the concepts of partial derivative and total differential of multivariate function, we can find the first and second partial derivatives of multivariate composite function, total differential, existence theorem of implicit function and partial derivative of multivariate implicit function.

4. Understand the concepts of extreme value and conditional extreme value of multivariate function, master the necessary conditions of extreme value of multivariate function, understand the sufficient conditions of extreme value of binary function, find the extreme value of binary function, find the conditional extreme value by Lagrange multiplier method, find the maximum value and minimum value of simple multivariate function, and solve some simple application problems.

5. Understand the concept and basic properties of double integral, and master the calculation methods of double integral (rectangular coordinates and polar coordinates).

Verb (abbreviation of verb) ordinary differential equation

Examination contents-basic concepts of ordinary differential equations, differential equations with separable variables, homogeneous differential equations, first-order linear differential equations, reducible higher-order differential equations, properties of solutions and structural theorems of solutions, simple applications of second-order homogeneous linear differential equations with constant coefficients higher than second-order homogeneous linear differential equations with constant coefficients.

Examination requirements

1. Understand differential equations and their concepts such as order, solution, general solution, initial condition and special solution.

2. Mastering the solutions of differential equations with separable variables and first-order linear differential equations can solve homogeneous differential equations.

3. The following differential equations will be solved by order reduction method: and.

4. Understand the properties of the solution of the second-order linear differential equation and the structure theorem of the solution.

5. Master the solution of second-order homogeneous linear differential equations with constant coefficients, and be able to solve some homogeneous linear differential equations with constant coefficients higher than the second order.

6. Polynomials, exponential functions, sine functions, cosine functions and their sum and product can be used to solve second-order non-homogeneous linear differential equations with constant coefficients.

7. Can use differential equations to solve some simple application problems.

Directional derivative and gradient are not tested every year, but they have been tested in the last two years.