A, function, limit, continuous assessment content

The concept and representation of function, boundedness, monotonicity, periodicity and parity of function, the properties of basic elementary functions of inverse function, piecewise function and implicit function, and the establishment of functional relationship of graphic elementary function.

Definitions and properties of sequence limit and function limit, left limit and right limit of function, concepts and relationships of infinitesimal and infinitesimal, properties of infinitesimal and four operational limits of infinitesimal, two important limits: monotone bounded 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 and master the expression of function, and you will 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 functions.

And the continuity of elementary functions, understand the properties of continuous functions on closed intervals (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. Mastering the four algorithms of derivative and the derivative rule of compound function, mastering the derivative formula of basic elementary function, and knowing the invariance of the four algorithms of differential and the first-order differential form, we can find the differential of function. Knowing the concept of higher derivative, we can 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's theorem, Lagrange's mean value theorem and Tylen's theorem, and understand and apply Cauchy's mean value theorem.

The contents of the 202 1 Postgraduate Mathematics (1) exam outline are here. More about the skills of preparing for the postgraduate entrance examination, preparing for the exam, news information, results inquiry, entrance of 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.