Level from elementary school to university

Original article: zhidao.baidu.com/question/103431256.html

There is a difference between a series and a series.

The following are some differences:

IAt the beginning of elementary school, we came into contact with the series-number pattern-number law:

A regular number is a series. Such as even number and prime number.

Number arrangement: Number in sequence

Ascending Order: increasing/ascending order, for example, 3, 7, 11, 15 ....

Sort in descending order: decreasing/descending order, such as: 55, 50, 45, 40 ....

Alphabetic arrangement: alphabetical order, for example, a, B, c, d ,.....

II,What high school students are exposed to is the real series: series or progression.

They only have access to two simplest series:

Arithmetic deviation sequence: AP = arithmetic progression/series, with common difference [tolerances]

Proportional series: Gp = geometric progression/series with common ratio [public ratio]

III,Chinese universities and federated countries begin to study in high school -- Series

Before learning the series, first learn a function sequence, and then officially start learning the series ),

Compared with AP and GP in high school, there are roughly several changes:

1,Transition from number to function ):

Each item (term: Term) is determined by a function rather than a simple public ratio or a tolerances.

2,Transition from limited (definite/finite) to unlimited (indefinite/infinite ).

3,With limit ).

4,Use the summation symbol sigama -- Σ (sigama Notation ).

5,After learning calculus (calculus), I started to learn the mclulin series maclaurin's series,

Expand any function near zero (expansion), that is, if X is near zero.

Only explicit function (explicit) differentiation (differentiation) is not enough, and there must be an implicit number

(Implicit function.

6,Then there is the Taylor's series, which is an arbitrary function expanded near any point of interest.

7,Then there is the Fourier series, which has two basic features:

First, unlike the above two types of expansion, it uses integration knowledge;

Second, the above two types are expanded into an algebraic series (Algebraic series), and now expanded into a triangle

Trigonometrical series ). At this time, you are about to graduate from college.

8,The series of high school students do not need to discuss convergence or divergence.

Consider the convergence radius or convergence domain ).