AP calculus ab is the basic part of mathematical analysis, but it does not include fitting transcendental functions with polynomial series, such as Taylor series and its special case McLaughlin series.

These methods of fitting transcendental functions with algebraic functions need to be mastered in bc.

I. * * * Identical parts:

I. Functions, graphs and limit functions, images and limits

A. graphic image analysis

B. Function limit (including unilateral limit) Function limit (including left and right limit)

C asymptomatic asymptote of unbounded behavior and its properties

Continuity as a property of a function, the function is continuous.

Two. outgrowth

A. the concept of derivative

B. Derive at one point

C. derivative as a function

The second derivative of d

E. Application of derivatives

F. Calculation of derivative

(derivative of product, derivative of quotient, derivative of composite function, derivative of implicit function)

Three. Integral integral

A. the definition and properties of definite integrals, concepts and properties

B. Application of integral

C. Basic theorem of calculus

D. Differential integration technique

(Inverse function direct integration method, variable substitution method)

E. Application of differential integral

(Applying initial conditions to solve kinematic problems)

Solve separable differential equations, especially the laws of exponential decay and exponential growth.

F. numerical approximation and numerical calculation of definite integral

(Riemann method-definition method, rectangle method, trapezoid method, left end point method, right end point method, midpoint method)

Second, the different parts (BC special exam):

Four. Polynomial approximation and series polynomial approximation and series

A. the concept of series (convergence and divergence)

B. Constant series

Others include:

Geometric series, harmonic series, generalized integral, McLaughlin series, Taylor series, Lagrange error calculation

In fact, from the learning point of view, if you have an introduction to calculus, it is not difficult to learn the basic knowledge of series on this basis.