collection concept

Intervals and Neighborhoods

The concept of function

Parity

Monotonicity

cyclical

Boundedness

Basic elementary functions, elementary functions

hyperbolic function

Simple interest and compound interest

Demand function, supply function and market equilibrium

Cost function, revenue function and profit function

definition

nature

The limit of a function when the independent variable tends to infinity

The limit of a function when the independent variable tends to a finite value

nature

infinitesimal

properties of infinitesimals

gigantic

four arithmetic rules

The limit of composite functions

limit existence criterion

Two important limits

Extreme application - continuous compound interest

Function continuity concept

The operation rules of continuous functions and the continuity of elementary functions

function break point

Properties of continuous functions on closed intervals

3 examples of concepts introduced

Definition of derivative

Left and right derivatives

derivative of function

The geometric meaning of derivatives

Four Arithmetic Rules for Derivatives

Derivative Rules for Composite Functions

The derivation rule for inverse functions

Derivative table (derivative formulas of constants and basic elementary functions)

Derivation rules for implicit functions

Logarithmic derivation

Derivatives of parametric functions

concept

calculate

The geometric significance of differentials and its application in approximate calculations

concept

calculate

Examples of definite integral problems

Definition of definite integral

The geometric meaning of definite integrals

Properties of definite integrals

Functions of the upper limit of integration and their derivatives

Basic formulas of calculus

substitution method

Integration by parts

microelement method of definite integrals

area of ​​plane figure

The volume of the body of revolution

Examples of the application of definite integrals in economics - finding the total function from the marginal function

Anomalous integrals over infinite intervals

Anomalous integrals of integrands with infinite discontinuities

The concept of primitive functions and indefinite integrals

subtopic

The first type of substitution method (differentiation method)

The second type of substitution method

Rolle's theorem

Lagrange's mean value theorem

Cauchy's mean value theorem

Taylor's mean value theorem

0/0 type and infinite/infinite type infinitive limits

Other types of infinitive limits

Monotonicity

Concave-convexity and inflection point

extreme value of function

Maximum and minimum values

function graphing

optimal value problem

marginal analysis

Elasticity analysis