Chapter 1 Function, Limit and Continuity
Equivalent infinitesimal substitution, Lobida rule, Taylor expansion
Find the limit of a function
The concept of function continuity and the types of function discontinuity points
Judging the continuity of function and the type of discontinuity
Chapter two? Differential calculus of univariate function
The definition of derivative, the relationship between derivability and continuity
By defining the relationship between derivative, derivative and continuity of a point.
Monotonicity of function, extreme value of function
The monotonicity and extremum of functions are discussed.
The Properties of Continuous Functions on Closed Interval, Rolle Theorem, Lagrange Mean Value Theorem, Cauchy Mean Value Theorem and Taylor Theorem Differential Mean Value Theorem and Their Applications
Chapter three? Integral calculus of unary function
Integral upper bound function and its derivative
Variable limit integral derivative problem
Integral of rational function, rational formula of trigonometric function and simple unreasonable function
Calculate indefinite integral and definite integral of integrand which are rational function, rational trigonometric function and simple irrational function.
Chapter IV Multivariate Function Calculus
The existence of implicit function, partial derivative and total differential and the causal relationship between them.
Discussion on the existence and continuity of function limit at one point, the existence of partial derivative, the existence of total differential and the continuity of partial derivative, and the causal relationship between them
The Concept, Properties and Calculation of Double Integral
Calculation and application of double integral
Chapter five? ordinary differential equation
Simple application of first-order linear differential equation, homogeneous equation and differential equation, using differential equation to solve some application problems
Linear algebra test site:
The first chapter determinant
Operation of determinant
Calculating determinant of abstract matrix
Chapter two? matrix
matrix operation
Find the higher idempotent element of matrix
Elementary transformation of matrix, elementary matrix
Proof proposition related to elementary transformation
Chapter III Carrier
Properties and discrimination of linear correlation and uncorrelation of vector groups
Linear correlation of vector groups
Linear combination and linear representation
It is determine whether that quantity can be linearly represen by a vector group.
Chapter IV Linear Equations
Solution of basic solution system and general solution of homogeneous linear equations
Find the basic solution system and general solution of homogeneous linear equations
Chapter V Eigenvalues and Eigenvectors of Matrices
The properties of eigenvalues and eigenvectors of real symmetric matrices are transformed into diagonal matrix methods.
Concepts and properties of similarity transformation and similarity matrix
Judgment and inverse problem of similarity matrix
Chapter six? square
The concept of quadratic form
Find the matrix and rank of quadratic form
The concept of contract transformation and contract matrix
Two forms and structures of mathematics:
(1) Full marks of test papers and test time
1. The full mark of the test paper is 150.
2. Examination time 180 minutes.
(2) the way to answer questions
1. The answer is closed.
2. written test.
(C) the content structure of the test paper
1. Advanced Mathematics 78%
2. Linear Algebra 22%
(D) the structure of the test questions
1. The question structure of the test paper is:
8 multiple-choice questions, each with 4 points and ***32 points.
2.6 fill in the blanks with small questions, with 4 points for each question and * * 24 points.
3. Answer (including proof questions) 9 small questions, ***94 points.
Data link: Baidu Encyclopedia-Postgraduate Mathematics II