同济：004-5.初等函数

系统管理员 2021-11-04 14:26 335阅读 0赞

同济6版，P17

# 实行数学学过的函数：基本初等函数 #

![1525006-20190524095856384-761657437.png][]

# 1.初等函数定义： #

由常数和基本初等函数经过有限次四则运算和有限次函数复合步骤所构成并可用一个式子表示的函数，称初等函数。

例如：

![1525006-20190524100704910-1976491143.png][]

## 注意：分段函数一般不是实行函数，因为它一般不能用一个公式表示，但也有例外，如绝对值函数，它可用一个式子表示如下： ##

![1525006-20190524101104594-1941019348.png][]进度：19：06

## 2.指数函数分解成双曲函数： ##

--------------------

# #

![1525006-20190528100225630-1105744376.png][]

## **2.1双曲正弦+双曲余弦（**例：e^x分解：**）** ##

![1525006-20190528100850261-1304077249.png][]

## **a.双曲正弦写法：sinh x 或 sh x** ##

![1525006-20190528101039893-344193427.png][]

双曲正弦图像：

![1525006-20190528101308421-1570595158.png][]

![1525006-20190528101459475-2506309.png][]

##  b.双曲余弦： ##

![1525006-20190528102842943-555211290.png][]

**双曲余弦图像：**

**![1525006-20190528102930736-1421167365.png][]**

![1525006-20190528103012911-1903602119.png][]

c.综合：双曲正弦+双曲余弦

![1525006-20190528103115490-802351591.png][]

## 总结： ##

![1525006-20190528103201239-2080667341.png][]

## 双曲函数应用： ##

![1525006-20190528103304628-131692373.png][]

![1525006-20190528103333895-1248612527.png][]

![1525006-20190528103411205-298499467.png][]

# 2.2. 双曲正切 #

--------------------

![1525006-20190528103621905-486298308.png][]

图形：

![1525006-20190528103646832-130615200.png][]

# 2.3.双曲余切 #

--------------------

![1525006-20190528104039680-1271075182.png][]

### 图形： ###

![1525006-20190528104125860-1320577589.png][]

双曲函数 运算性质 与 三角函数 有很多类似或可比较的地方：

![1525006-20190528104526772-1239061513.png][]

![1525006-20190528105557504-15660853.png][]

(学习手册P23 表1.1.10)

# 3.反双曲函数(Inverse Hyperbolic Sine) #

--------------------

#  ![1525006-20190601090848005-1301103525.png][] #

(高数同济6 教材：p19，倒数第二行)

## 3.1反双曲余弦函数（Inverse Hyperbolic Cosine） ##

--------------------

## ![1525006-20190601092602227-119953701.png][] ##

（教材; p20）

图形：

![1525006-20190601092810164-1070577050.png][]

![1525006-20190601092850635-495568626.png][]

##  4.反双曲正切 ##

--------------------

## ![1525006-20190601092947443-1861869953.png][] ##

![1525006-20190601093008408-1235513006.png][]

http://xuxzmail.lofter.com/post/6f68e\_6364a21?act=qbbloglofter\_20150506\_01

转载于:https://www.cnblogs.com/chenxi188/p/10916427.html

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