The three basic calculation mathematics of 1. high number must be calculated, and the calculation cornerstone of advanced mathematics is its three most basic calculations: seeking limit, seeking derivative and seeking integral. As long as mathematics exists, it is inevitable.
(1) limit calculation
Limit calculation often appears in all kinds of questions, except comprehensive questions and proof questions, which are rarely seen.
Is the most basic calculation.
In limit calculation, there are the following tests:
Method of substitution directly seeks the limit (that is, directly substituting the number), infinitesimal replacement seeks the limit (replacing simplification with equivalent infinitesimal), big head seeks the limit (fractional limit, numerator and denominator grasp the big head at the same time), important limit (a formula is really important), and L'H?pital seeks the limit (fractional derivative needs to be derived at the same time).
The calculation of limit mainly pays attention to two points, one is to choose the correct method according to the characteristics of limit, and the other is how to operate these methods, which needs to be remembered.
(2) Deduction and calculation
Derivative calculation, which some students have been exposed to in high school, is the most existent calculation in advanced mathematics.
In derivative calculation, there are the following tests:
The four operations of derivation (that is, the derivation of addition, subtraction, multiplication and division, which has a corresponding formula), the derivation of compound function (which is difficult to understand and easy to operate, so long as you know the formula, you are not afraid), and the derivation of implicit function (just follow the steps).
The soul of derivative calculation lies in the memory of derivative formula, and the derivation methods of various functions are different, which needs to be kept in mind.
(3) Integral calculation
Integral calculation is one of the most difficult calculations and the inverse process of derivative calculation. Many things are hard to go backwards, such as from simplicity to luxury, from luxury to simplicity.
In the integral calculation, there are the following tests:
Differential integration (in fact, it is the inverse process of derivative of composite function, but it is difficult to understand), radical substitution integration (it is correct to follow the steps), and partial integration (the formula is very simple to remember and the formula is also very simple).
The soul of integral calculation is the memory of formula, but the choice of method is also a big difficulty, and sometimes choice is more important than ability.
2. The application of limit and derivative. In the trilogy of science, definition, calculation and application, the definition is relatively less investigated, and the calculation is the most, followed by application.
Application of (1) limit
The necessary point of extreme application is the necessary and sufficient condition of infinitesimal comparison and continuity. Infinitesimal comparison is a pre-knowledge point for infinitesimal replacement to find the limit. There are often tests such as judging the comparison type (who runs faster) and finding the parameters of the known comparison type (that is, finding the unknown). The necessary and sufficient conditions for continuity are more specific, and generally only the continuous parameter problem (called continuous unknown) is investigated.
(2) the application of derivative
The application of derivatives must be learned. L'H?pital counts as one (mentioned above), and so does the extreme value of the function. The most basic problem of extreme value is to find the extreme value of a function (also follow the steps).
The above knowledge points are the knowledge points that college students must learn in advanced mathematics. Everyone must learn and use it flexibly!
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