calculus
I. Function, Limit and Continuity
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 Functions Continuity of Elementary Functions Properties of Continuous Functions on Closed Interval
Second, the differential calculus of unary function
The relationship between the geometric meaning of derivative and differential concepts and the derivability and continuity of economic significance function; Four operations of tangent, normal derivative and differential of plane curve; Differential method of derivative of basic elementary function: differential method of higher derivative of inverse function and implicit function; Invariant differential mean value theorem in first-order differential form; Lobida law; Discrimination of monotonicity of function; The concavity and convexity of extreme function graph: inflection point; And the maximum and minimum values of the asymptote function graph.
3. Integral calculus of unary function
The concept of original function and indefinite integral The concept and basic properties of definite integral formula The function of upper limit of definite integral and its derivative Newton-Leibniz formula The substitution integration method of indefinite integral and definite integral and the application of partial integral Abnormal (generalized) integral definite integral.
Four, multivariate function calculus
The concept of multivariate function, the geometric meaning of binary function, the concept of limit and continuity of binary function, the concept and calculation of partial derivative of multivariate function in bounded closed region, the derivative method of multivariate composite function and the derivative method of implicit function.
The concept and basic properties of extreme value and conditional extreme value, maximum value and minimum value double integral of second-order partial derivative fully differential multivariate function and the calculation of simple abnormal double integral on unbounded domain
Verb (abbreviation of verb) ordinary differential equation
Basic concepts of ordinary differential equations, separable variable differential equations, homogeneous differential equations, first-order linear differential equations