A, function, limit, continuous assessment content

The concepts and representations of boundedness, monotonicity, periodicity and parity of functions, the properties of composite functions, inverse functions, piecewise functions and implicit functions, the establishment of functional relationships of graphic elementary functions, the definitions of sequence limits and function limits, the definitions of left and right limits of property functions, the concepts and relationships between infinitesimal and infinitesimal, and the four operational limits of infinitesimal comparison limits have two important limits: monotone boundedness criterion and pinch criterion.

Concept of Function Continuity Types of Discontinuous Points of Function Continuity of Elementary Function Test Requirements for Properties of Continuous Functions on Closed Interval

1. Understand the concept of function, master the expression 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 function left limit and right limit, 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. Understand the concept of function continuity (including left continuity and right continuity) and 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, value and minimum theorem, intermediate value theorem), and apply these properties.

Second, the examination content of differential calculus of unary function

The relationship between the geometric meaning of derivative and differential concept and the derivability and continuity of physical meaning function; Four operations of tangent, normal derivative and differential of plane curve: derivative of basic elementary function; Difference method; Inverse function; Implicit function; And the invariant differential mean value theorem of the first-order differential form of the function determined by the parametric equation; Hospital rules; Concave-convex, inflection point and asymptotic curve of extreme function graph; Describe the value of the function graph and the conceptual curvature of the minimum arc differential curvature.

Examination requirements

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.

6. Master the method of finding the limit of infinitive with L'H?pital's law.

7. Understand the concept of extreme value of function, master the method of judging monotonicity of function and finding extreme value of function with derivative, and master the method of finding value and minimum value of function and its application.

202 1 Postgraduate Mathematics (2) The contents of the examination outline are here, so everyone should review them carefully. More about the skills of preparing for the postgraduate entrance examination, preparing for the dry goods, news information, results inquiry, entrance of printing the admission ticket, printing time of the admission ticket, etc. Bian Xiao will continue to update. I wish all candidates can pass the exam smoothly. Be admitted to an ideal university.