This is from last year, and it should not change much this year (it will come out around 10 every year).

First of all, calculus

I. Function, Limit and Continuity

Examination content

Concept and expression of function: boundedness, monotonicity, periodicity and parity of function, inverse function, composite function, implicit function and piecewise function, as well as the concepts of sequence limit and left and right limit of function limit of graphic elementary function, the concepts of infinitesimal and infinitesimal, the basic properties of infinitesimal relationship and the comparison limit of order, four operations, two important limit functions, the concepts of continuity and discontinuity, and the properties of continuous function on the closed interval of elementary function.

Examination requirements

1. Understand the concept of function and master the representation of function. Deeply understand the boundedness, monotonicity, periodicity and parity of functions.

3. Understand the concepts of compound function, inverse function, implicit function and piecewise function.

4。 Master the nature and graphics of basic elementary functions and understand the concept of elementary functions.

5. The functional relationship in simple application problems will be established.

6. Understand the concepts of sequence limit and function limit (including left and right limits).

7. Understand the concept and basic properties of infinitesimal and master the comparison method of infinitesimal order. Understand the concept of infinity and its relationship with infinitesimal.

8. Understand the nature of limit and two criteria for the existence of limit (monotone bounded sequence has limit and pinch theorem), and master four algorithms of limit, and two important limits will be applied.

9. Understand the concept of function continuity (including left continuity and right continuity).

10. Understand the properties of continuous functions and the continuity of elementary functions, and understand the properties of continuous functions on closed intervals (boundedness, maximum theorem and mean value theorem) and their simple applications.

Second, the differential calculus of unary function

Examination content

The relationship between derivability and continuity of derivative concept function; Four operations of derivative; The concept and algorithm of derivative differentiation of higher derivative of basic elementary function: Hospital Law; The concavity and convexity of the extremum function graph of monotone function: inflection point; And the maximum and minimum values of the asymptote function graph.

Examination requirements

1。 Understand the concept of derivative and the relationship between derivability and continuity, and understand the geometric and economic significance of derivative (including the concepts of margin and elasticity).

2. Master the derivation formula of basic elementary functions, the four operation rules of derivatives and the derivation rules of compound functions; Master the derivative method and logarithmic derivative method of inverse function and implicit function.

3. In order to understand the concept of higher derivative, we can find the second and third derivatives and n-order derivatives of simpler functions.

4. Understand the concept of differential, the relationship between derivative and differential, and the invariance of first-order differential form: master differential method.

5. Understand the conditions and conclusions of Rolle Theorem (ROl 1e), Lagrange Mean Value Theorem (kgrange) and Oluc Mean Value Theorem, and master the simple applications of these three theorems.

6. Will use the Lobida rule to find the limit.

7. Master the method of judging monotonicity of function and its application, and master the solution of extreme value, maximum value and minimum value (including solving simple application problems).

8. Master the judgment method of curve convexity and inflection point and the solution method of curve asymptote.

9. Master the basic steps and methods of drawing functions, and be able to draw some simple functions.

3. Integral calculus of unary function

Examination content

The concept of original function and indefinite integral The basic properties of indefinite integral The concept and basic properties of indefinite integral The integral mean value theorem of partial definite integral The function defined by variable upper limit definite integral and its derivative Newton-Leibniz formula The concept of partial generalized integral and the application of calculating definite integral.

Examination requirements

1. Understand the concepts of original function and indefinite integral, and master the basic properties and basic integral formula of indefinite integral; Master the substitution integral method and integration by parts for calculating indefinite integral.

2. Understand the concept and basic properties of definite integral. Master Newton-Leibniz formula, substitution integral method of definite integral and partial integral. Will find the derivative of variable upper bound definite integral.

3. I will use definite integral to calculate the area of plane figure and the volume of rotator, and I will use definite integral to solve some simple economic application problems.

4. Understand the concept of convergence and divergence of generalized integral, master the basic method of calculating generalized integral, and understand the conditions of convergence and divergence of generalized integral.

Four, multivariate function calculus

Examination content

The concept of multivariate function, the geometric meaning of binary function, the limit and continuity of binary function, the properties of binary continuous function in bounded closed region (maximum theorem), the concept and calculation of partial derivative of multivariate composite function, the basic properties and calculation of simple double integral of high-order partial derivative fully differential multivariate function

Examination requirements

1. Understand the concept of multivariate function, and understand the representation and geometric meaning of binary function.

2. Understand the intuitive meaning of limit and continuity of binary function.

3. Understand the concepts of partial derivative and total differential of multivariate function, master the solution of partial derivative and total differential of compound function, and use the derivative rule of implicit function.

4. Understand the concepts of multivariate function extremum and conditional extremum/master the necessary conditions for the existence of multivariate function extremum, and understand the sufficient conditions for the existence of binary function extremum. Will find the extreme value of binary function. Lagrange multiplier method will be used to find conditional extremum. Can find the maximum and minimum of simple multivariate function, and can 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). Will calculate simple double integrals on unbounded regions.

Five, infinite series

Examination content

The concept of convergence and divergence of constant series, basic properties and necessary conditions for convergence, the concept of convergence of geometric series and convergence of positive series, the absolute convergence and conditional convergence of arbitrary series, the Leibniz theorem, the concept of convergence radius, convergence region (referring to open interval) and the basic properties of power series sum function in convergence interval, the solution of simple power series sum function and the power series expansion of elementary function

Examination requirements

1. Understand the concepts of convergence and divergence of series and sum of convergent series.

2. Master the necessary conditions of series convergence and the basic properties of convergent series. Master the conditions of convergence and divergence of geometric series and p series. Master the comparison discrimination method and D'Alembert (ratio) discrimination method of positive series.

3. Understand the concepts of absolute convergence and conditional convergence of arbitrary series, master Leibniz discriminant method of staggered series, and master the discriminant method of absolute convergence and conditional convergence.

4. Will find the convergence radius and convergence domain of power series.

5. Understand the basic properties of power series in convergence domain (continuity of sum function, item-by-item differentiation, item-by-item integration), and we will find some simple sum functions of power series.

6. Master the expansions of (abbreviated) power rank numbers, and use these expansions to indirectly expand some simple functions into power series.

Six, ordinary differential equation and envy equation

Examination content

Concept of differential equation solution, general solution, initial condition and special solution of differential equation with separable variables, second-order homogeneous linear equation with constant coefficient and simple non-homogeneous linear equation, general solution and simple application of first-order linear difference equation with constant coefficient.

Examination requirements

1. Understand the concepts of order, general solution, initial condition and special solution of differential equations.

2. Master the solutions of equations with separable variables, homogeneous equations and first-order linear equations.

3. Polynomial, exponential function, sine function, cosine function and their sum and product can be used to solve the second-order homogeneous linear equation with constant coefficients and the second-order inhomogeneous linear differential equation with constant coefficients.

4. Understand the concepts of difference and difference equation and their general and special solutions.

5. Master the solution method of the first-order linear difference equation with constant coefficients.

6. Will apply differential equations and difference equations to solve some simple economic application problems.