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Your professional code is 070502, and you want to take advanced mathematics.

Outline of advanced mathematics for postgraduate entrance examination

The first unit function, limit and continuity

The concept and representation of function; Boundedness, monotonicity, periodicity and parity of functions; Inverse function, composite function, implicit function, piecewise function; Properties and graphs of basic elementary functions; The simple application of elementary function and the establishment of function relationship: the definition and properties of sequence limit and function limit; the left and right limits of function; Infinitely small; Infinity; Infinitesimal comparison; Four operations of limit; Two criteria for the existence of limit; Monotone bounded criterion and pinch criterion; Two important limitations:

lim(sinx/x)= 1，lim( 1+ 1/x)x=e

x→0 x→∞

The concept of function continuity: the types of function discontinuity points; Continuity of elementary function; Properties of Continuous Functions on Closed Interval (Maximum Theorem and Minimum Theorem)

Unit 2 Differential calculus of univariate function

The concepts of derivative and differential; Geometric meaning and physical meaning of derivative; The relationship between differentiability and continuity of functions; Tangents and normals of plane curves; Derivative of basic elementary function; Four operations of derivative and differential; Differential method of functions determined by inverse function, composite function, implicit function and parametric equation; The concept of higher derivative; Derivatives of some simple functions; Invariance of first-order differential form; The application of differential in approximate calculation: Rolle theorem, Larenger mean value theorem, Cauchy mean value theorem, Taylor theorem, Lobida rule.

Function extremum and its solution, function increase and decrease and determination of concavity of function graph, inflection point and its solution of function graph, asymptote, description of function graph, solution of function maximum and minimum and its simple application.

Unit 3 Integral calculus of univariate function

Concepts of primitive function and indefinite integral, basic properties of indefinite integral, basic integral formula, concept and properties of definite integral, integral mean value theorem, variable upper bound definite integral and its derivatives, Newton-Leibniz formula, substitution integral method and partial integral of indefinite integral and definite integral, rational formula of rational function and trigonometric function, integral of simple and unreasonable function, concept and calculation of generalized integral, application of definite integral and approximate calculation method.

Unit 4 Ordinary differential equations

Concept of ordinary differential equation, solution, general solution, initial condition and special solution of differential equation; Variable separable equation, first-order linear differential equation, homogeneous equation, Bernoulli equation, reducible higher-order differential equation (y' = f (x), y' = f (x, y'), y "= f (y, y "))；); Properties of solutions of linear differential equations and structural theorems of solutions: second-order homogeneous linear differential equations with constant coefficients; Simple second-order non-homogeneous linear differential equation with constant coefficients.

Unit 5 Differential calculus of multivariate functions

The concept of vector, the concepts and solutions of surface equation, plane equation and straight line equation, the distance from point to point, the distance between straight line and plane, and the cylinder whose generatrix is parallel to the coordinate axis.

The concept of multivariate function, the concept of limit and continuity of binary function, the properties of continuous function on bounded closed field, partial derivative; The concept of total differential, compound function, derivative of implicit function, second-order partial derivative, the concept of extreme value of multivariate function, the necessary condition of extreme value of multivariate function, and the solution of extreme value.

Unit 6 Integral calculus of multivariate functions

The concept of double integral, the properties of double integral, the calculation of double integral (rectangular coordinates, polar coordinates), the concepts of two kinds of curve integral, and the geometric application of double integral.

Unit 7 Power Function

The concept of convergence and divergence of constant series, the concept of sum of convergent power series, the basic properties of convergence and the necessary conditions of convergence; Geometric series and p series; Leibniz theorem of comparative convergence, ratio convergence, root convergence and staggered series of positive terms; Absolute convergence and conditional convergence, convergence domain of function term series and the concept of sum function; Convergence radius, convergence interval and convergence domain of power series, basic properties of power series in its convergence interval, and solution of simple power series sum function.