Examination content

Concepts and representations of boundedness, monotonicity, periodicity and parity of functions

Properties and figures of basic elementary functions of sex inverse function, composite function and implicit function

The establishment of function relation in the simple application of elementary function: the limit of sequence and function

The definition of limit and the left and right limits of its property function are infinitesimal.

Four operational limits of size comparison limits Two criteria for the existence of operational limits: Simplicity

Two important limits of bounded criterion and compression criterion (omitted)

The concept of continuous function, the types of discontinuous points of function, and the continuous closed domain of elementary function

Properties of Intermittent Continuous Functions (Maximum Theorem, Minimum Theorem and Intermediate Theorem)

Examination requirements

1. Understand the concept of function, perform symbolic operation of function, and establish simple application problems.

Functional relations in problems.

2. Understand the parity, monotonicity, periodicity and boundedness of functions.

3. Understand the concept of composite function and the concepts of inverse function and implicit function.

4. Master the nature and graphics of basic elementary functions.

5. Understand the concepts of limit, left and right limit of function and function limit.

The relationship between existence and left and right limits.

6. Master the nature of limit and four algorithms.

7. Understand the two criteria for the existence of limit, and use them to find and master the limit.

The solution of two important limits.

8. To understand the concepts of infinitesimal, infinitesimal and infinitesimal order, we use equivalent nothing.

The poor seek the limit.

9. If you understand the concept of functional continuity, you will distinguish the types of functional discontinuity.

10. Understand the continuity of elementary functions and the properties of continuous functions on closed intervals (most

Maximum theorem, minimum theorem and intermediate value theorem), and will apply these properties.

Second, the differential calculus of unary function

Examination content

The concepts of derivative and differential, the geometric meaning and physical meaning of derivative can be

Relationship between conductivity and continuity: tangent and normal of plane curve and its equation base

The derivative of this elementary function and four operations of differential inverse function and compound function.

The concept of higher derivative of function differential method determined by implicit function and parametric equation

The invariant differential of the first differential form of the gate derivative of some simple functions is close.

Application of Rolle Theorem in Quasi-calculation: Determination of Lagrangian Median

Cauchy Mean Value Theorem Taylor Theorem L'H?pital (L'

Extreme value of hospital regular function and its solution: increase and decrease of function and concavity of function diagram

The inflection point of convex function graph and its solution asymptote depicts the graph of function

Solution of maximum and minimum of shape function and its simple application in circular arc differential curvature

Concept of approximate solution of curvature radius equation and bisection tangent method

Examination requirements

1. Understand the concepts of derivative and differential. Understand the geometric meaning of derivative and find the plane.

In order to understand the physical meaning of derivatives, the tangent equation and normal equation of curves should be described by derivatives.

Some physical quantities. Understand the relationship between differentiability and continuity of functions.

2. Master the four algorithms of derivative and the derivative method of compound function, and master the foundation.

Derivative formula of elementary function. Four Algorithms and First-order Differential Forms of Understanding Differential

Invariance of differential and its application in approximate calculation.

3. Understand the concept of higher derivative. If you master the derivative method of elementary function, you can score.

The first and second derivatives of the segment function, and will find the "first derivative" of some simple functions.

4. Find the first and second derivatives of implicit function and function determined by parametric equation.

Number, will find the derivative of the inverse function.

5. Understand Rolle theorem and Lagrange mean value theorem, and Cauchy mean value theorem and.

Taylor theorem, and will use them to solve some simple problems.

6. Understand the concept of extreme value of function, and master monotonicity and summation of function through derivative.

Function extreme value method will find the maximum and minimum value of function rescue and its simple application.

7. We can judge the concavity and convexity of the negative form of the function by the derivative and find the inflection point of the function graph.

I will find horizontal, vertical and oblique asymptotes, and I will draw the graph of the function.

8. Master the method of using L'H?pital's law to find the limit of indefinite form.

9. Understand the concepts of curvature and radius of curvature, and calculate curvature and radius of curvature.

10. Understand the dichotomy and tangent method for finding approximate solutions of equations.

3. Integral calculus of unary function

Examination content

Concepts of Primitive Function and Indefinite Integral Basic Properties of Indefinite Integral

The concept and properties of formula definite integral: integral mean value theorem; Variable upper bound definite integral and its application

Derivative Newton-Leibniz (Newton-Leibniz magic formula indefinite integral sum

Substitution integration method of integral and rational expressions of partial rational function and trigonometric function integral

And the concept of integral generalized integral of simple function and the approximation of calculating definite integral.

Application of definite integral in calculation method

Examination requirements

1. Understand the concepts of original function and indefinite integral and definite integral. understand

Integral mean value theorem.

2. Master the basic formula of indefinite integral and the properties of indefinite integral and definite integral.

Non-commutative integral method and integration by parts.

3. Can find the product of rational function, rational formula of trigonometric function and simple meta-function.

Points.

4. Understand the function of variable upper bound definite integral as its upper limit and its derivative theorem, and master it.

Newton-Leibniz formula.

5. Understand the concept of generalized integral and calculate generalized integral.

6. Understand the approximate calculation method of definite integral.

7. Master the expression and calculation of some geometric and physical quantities in definite integral (plane figure)

Area, arc length of plane curve, volume of rotator, lateral area, parallel cross-sectional area.

For the known solid volume, variable force, work, gravity, pressure and function average. ).

Fourth, ordinary differential equations

Examination content

Concept of solution of ordinary differential equation, general solution, initial condition and special solution of differential equation.

Reducible height of first-order linear differential equation of homogeneous equation with separable variables

Properties and structure theorems of solutions of second order linear differential equations with constant coefficients

Some homogeneous linear differential equations with constant coefficients above second order

Some Simplifications of Second Order Non-homogeneous Linear Differential Equations with Constant Coefficients

Single application

Examination requirements

1. Understand the concepts of differential equations and their solutions, general solutions, initial conditions and special solutions.

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

3. The following equations will be solved by order reduction method: (omitted)

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 know the solution of some higher-order linear differential equations.

Second order homogeneous linear differential equation with constant coefficients.

6. We will find that the free term is polynomial, exponential function, sine function and cosine function, thus

Special solution and general solution of second order non-homogeneous linear differential equation with constant coefficients and its sum and product

Solution.

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