Examination content
The concept and expression of function: boundedness, monotonicity, periodicity and parity of function, properties of composite function, inverse function, piecewise function and implicit function, and the establishment of functional relationship of graphic elementary function. The definitions of sequence limit and function limit, the definition of left limit and right limit of property function, the concepts of infinitesimal and infinitesimal and their relationship, and the four operational limits of infinitesimal comparison limit. There are two important limits: monotone bounded criterion and pinch criterion;
Concept of Function Continuity Types of Discontinuous Points of Functions Continuity of Elementary Functions Properties of Continuous Functions on Closed Interval
Examination requirements
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, differential calculus of univariate function in MPA mathematical outline
Examination content
The relationship between the geometric meaning of derivative and differential concepts and the derivability and continuity of physical meaning function; Four operations of tangent, normal derivative and differential of plane curve; Derivative compound function, inverse function and implicit function of basic elementary function; And the invariant differential mean value theorem L'H?pital (L'Hospital) of the first differential form of the differential method of the function determined by the parameter equation. Discriminate the concavity and convexity, inflection point and asymptote of monotone extreme value function graph of regular function. Describe the maximum and minimum value of function graph. Concept of curvature circle and curvature radius 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 maximum and minimum value of function and its application.
Please pay attention to the announcement of 202 1 National Postgraduate Entrance Examination. That's all you have to read. You are worried about missing the exam registration, the printing time of the admission ticket, and the exam time. So why don't you start a global Ivy League? Free appointment SMS reminder? All right! Help you get the exam trends faster.