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"Three Outline of Postgraduate Mathematics" is the examination outline of Graduate Mathematics III (subject code 303), including calculus, linear algebra, probability theory and mathematical statistics. It is required to understand the concept and master the representation, so that the functional relationship of the application problem will be established.
Examination form
1, full marks in the test paper, and the test time.
The full mark of the test paper is 150, and the test time is 180 minutes.
Step 2 Answer method
The answer methods are closed book and written test.
Content structure of test paper
Calculus 60%
Linear algebra 20%
Probability theory and mathematical statistics 20%
Question structure of test paper
10 multiple-choice questions, with 5 points for each question and ***50 points.
Fill in the blanks with 6 small questions, with 5 points for each question and * * 30 points.
Answer (including proof questions) 6 small questions, ***70 points.
Function, limit, continuity
Examination requirements
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 limit function and left limit and right limit.
6. Understand the nature of limit and two criteria for the existence of limit, master four algorithms of limit, and master the method of finding limit by using two important limits.
7. Understand the concepts of infinitesimal and infinitesimal, master the comparison method of infinitesimal, and find the limit with equivalent infinitesimal.
8. Understanding the concept of function continuity (including left continuity and right continuity) will distinguish the types of function discontinuity points.
9. 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.