连环画教科书，电子版微积分

       2018年7月14日，我们发表“00后大学生喜欢电子版微积分教材”，

理由是；电子版微积分是连环画教科书，风格新颖，内思想深刻，容有趣。

比如：打开电子版微积分教科书，找到第七章第一节定位在第1张示意图 Figure 7.1.1上，让其占据整个视频，排除一切干扰因，以便仔细“读图”，牢记相关符号的含义。          。                                                                                                           

    顾名思义，所谓连环画教课书是指：

Figure 1.1.1；Figure 1.1.2；Figure 1.1.3；Figure 1.1.4，….

Figure 2.1.1；Figure 2.1.2；Figure 2.1.3；Figure 2.1.4，….

…  …  … …

  连环画教课书各章节的示意图。环环相扣，配备说明，突出主题。

比如，学习第七章三角函数，目光顺着Figure 7.1.1；Figure 7.1.2；Figure 7.1.3；Figure 7.1.4，…….顺序“读”

下去，开动脑筋，前后联系，抓住主题，必有收获。

如此这般，00后大学生怎么会不喜欢电子版微积分教课书呢？                                                                           

袁萌  陈启清   2月27日

附件：Figure 7.1.4说明文字

Arc lengths（弧长） are used to measure angles. Two units of measurement for angles

are radians (best for mathematics) and degrees (used in everyday life).

DEFINITION

Let P and Q be two points on the unit circle. The measure of the angle L POQ

~ in radians is fhe length of the arc PQ. A degree is defined as

1 o = n/180 radians,

whence the measure of L POQ in degrees is 180/n times the length of PQ.

Approximately, 1 o ~ 0.01745 radians,

1 radian ~ 57°18' = (5ngt.

A complete revolution is 360° or 2n radians. A straight angle is 180° or n radians. A

right angle is 90° or n/2 radians.

It is convenient to take the point (1, 0) as a starting point and measure arc

length around the unit circle in a counterclockwise direction. Imagine a particle

which moves with speed one counterclockwise around the circle and is at the point

( 1, 0) at time t = 0. It will complete a revolution once every 2n units of time. Thus if the

particle is at the point P at time t, it will also be at P at all the times t + 2kn, k an

integer. Another way to think of the process is to take a copy of the real line, place the

origin at the point (1, 0), and wrap the line around the circle infinitely many times with

the positive direction going counterclockwise. Then each point on the circle will

correspond to an infinite family of real numbers spaced 2n apart (Figure 7.1.5) .

•• • ' - 7r, 1T' 311'"' ••• ••• • - 271", 0, 271", •••

•••, -180°, 180°, 540°, ..• •••• -360°, 0°, 360°, ...

1r Jrr 7rr

... , 2'2'T''''

Figure 7.1.5 .... -90°, 270°, 630° ....

368 7 TRIGONOMETRIC FUNCTIONS

The Greek letters e (theta) and¢ (phi) are often used as variables for angles

or circular arc lengths.

DEFINITION

Let P(x, y) be the point at counterclockll'ise distance 0 around the unit circle

starting _li-om (1, 0). X is cal/ed the cosine of(} and J' the sine of tJ,

X= COS 8, )' = sin e.

Figure 7.1.6

Cos 8·and sin 8 are shown in Figure 7.1.6. Geometrically, if 0 is between 0

and n/2 so that the point P(x, y) is in the first quadrant, then the radius OP is the

hypotenuse of a right triangle with a vertical side sin 0 and horizontal side cos 0. By

Theorem 1, sin 8 and cos 0 are real functions defined on the whole real line. We

write sin" 0 for (sin 0)", and cos" 8 for (cos 8)". By definition (cos 8, sin 8) = (x, y) is a

point on the unit circle x 2 + y 2 = 1, so we always have

sin 2 e + cos2 0 = I.

Also, -