1. limit method: the limit method is one of the most basic methods in mathematical analysis, and the properties of the function are studied by solving the limit of the function at a certain point. Limit method can be used to solve derivative, integral and series problems.
2. Differential method: Differential method is a method to study the rate of change of function, and the law of change of function is studied by solving the derivative of function at a certain point. Differential method can be used to solve optimization problems, curve fitting problems and dynamics problems.
3. Integration method: Integration method is a method to study the cumulative effect of functions, which is studied by solving the definite integral or indefinite integral of functions in a certain interval. Integral method can be used to solve problems such as area, volume and mass.
4. Taylor expansion method: Taylor expansion method is a method that approximates a complex function to a simple function, and studies the properties of the function by solving the Taylor series of the function at a certain point. Taylor expansion method can be used to solve the approximation and error estimation of complex functions.
5. Series method: Series method is a method to study infinite series and infinite series. It studies the properties of infinite sequence and infinite series by solving the sum of them. Series method can be used to solve numerical approximation problems and probability theory problems.