Overview of integral part of mathematical ternary function;
1. Understand the concepts of original function and indefinite integral, master the basic properties and basic integral formula of indefinite integral, and master the substitution integral method and integration by parts of indefinite integral.
2. Understand the concept and basic properties of definite integral, understand the mean value theorem of definite integral, understand the function of upper limit of integral and find its derivative, and master Newton-Leibniz formula, method of substitution and integration by parts of definite integral.
3. Will use definite integral to calculate the area of plane figure, the volume of rotating body and the average value of function, and will use definite integral to solve simple economic application problems.
4. Understand the concept of generalized integral and calculate generalized integral.
Overview of infinite series:
1. Understand the convergence and divergence of series. The concept of the sum of convergent series.
2. Understand the basic properties of series and the necessary conditions of convergence and divergence of series, master the conditions of convergence and divergence of geometric series and series, and master the comparative judgment method and ratio judgment method of convergence and divergence of positive series.
3. Understand the concepts of absolute convergence and conditional convergence of arbitrary series and the relationship between absolute convergence and convergence, and understand Leibniz discriminant method of staggered series.
4. Will find the convergence radius, convergence interval and convergence domain of power series.
5. Knowing the basic properties of power series in its convergence interval (continuity of sum function, item-by-item derivation, item-by-item integration), we can find the sum function of simple power series in its convergence interval.
6. Understand the Maclaurin expansion of power x, sin x, cos x, ln( 1+x) and E (1+x).
To sum up, unbounded function of integral, improper integral and trial-and-error method will all be tested.