I. Function, Limit and Continuity

1. Understand the concept of function, master the representation of function, and establish the functional relationship of application problems.

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

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

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

5. Understand the concept of limit, the concepts of left limit and right limit of function and the relationship between the existence of function limit and left limit and right limit.

6. Master the nature of limit and four algorithms.

7. Master two criteria for the existence of limit, and use them to find the limit, and master the method of using two important limits to find the limit.

8. Understand the concepts of infinitesimal and infinitesimal, master the comparison method of infinitesimal, and find the limit with equivalent infinitesimal.

9. Understanding the concept of function continuity (including left continuity and right continuity) will distinguish the types of function discontinuity points.

10. Understand the properties of continuous function and continuity of elementary function, understand the properties of continuous function on closed interval (boundedness, maximum theorem, mean value theorem), and apply these properties.

Second, the differential calculus of unary function

1. Understand the concepts of derivative and differential, understand the relationship between derivative and differential, understand the geometric meaning of derivative, find the tangent equation and normal equation of plane curve, understand the physical meaning of derivative, describe some physical quantities with derivative, and understand the relationship between function derivability and continuity.

2. Master the four algorithms of derivative and the derivative rule of compound function, and master the derivative formula of basic elementary function. Knowing the four algorithms of differential and the invariance of first-order differential form, we can find the differential of function.

3. If you understand the concept of higher derivative, you will find the higher derivative of simple function.

4. We can find the derivative of piecewise function, implicit function, function determined by parametric equation and inverse function.

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

3. Integral calculus of unary function

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

2. Master the basic formula of indefinite integral, the properties of indefinite integral and definite integral and the mean value theorem of definite integral, and master the integration methods of method of substitution and integration by parts.

3. Know the integral of rational function, rational trigonometric function and simple unreasonable function.

4. Understand the function of the upper limit of integral, find its derivative and master Newton-Leibniz formula.

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

6. Master the expression and calculation of some geometric physical quantities (the area of a plane figure, the arc length of a plane curve, the volume and lateral area of a rotating body, the area of a parallel section, the volume, work, gravity, pressure, center of mass, centroid, etc. of a known solid. ) and definite integral to find the average value of the function.

Four, multivariate function calculus

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

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.