## 2018年6月19日火曜日

### 数学 - Python - JavaScript - 解析学 - 積分 - 積分の計算 - 三角関数の積分(連続関数、周期関数、円周率)

1. $\begin{array}{}{\int }_{a+2\pi }^{b+2\pi }f\left(x\right)\mathrm{dx}\\ ={\int }_{a}^{b}f\left(x\right)\mathrm{dx}\end{array}$
$\begin{array}{}{\int }_{-\pi +c}^{\pi +c}f\\ ={\int }_{-\pi +c}^{-\pi }f+{\int }_{-\pi }^{\pi }f+{\int }_{\pi }^{\pi +c}f\\ ={\int }_{\left(\pi +c\right)}^{\pi }f+{\int }_{-\pi }^{\pi }f+{\int }_{\pi }^{\pi +c}f\\ ={\int }_{-\pi }^{\pi }f+{\int }_{\left(\pi +c\right)}^{\left(\pi +c\right)}f\\ ={\int }_{-\pi }^{\pi }f\end{array}$

コード(Emacs)

Python 3

#!/usr/bin/env python3
from sympy import pprint, symbols, pi, sin, cos, Integral, Function, plot

x, a, b, c = symbols('x, a, b, c')

for f in [sin(x), cos(x)]:
I1 = Integral(f, (x, a + 2 * pi, b + 2 * pi))
I2 = Integral(f, (x, a, b))
I3 = Integral(f, (x, -pi + c, pi + c))
I4 = Integral(f, (x, -pi, pi))

for t in [I1, I2, I1.doit(), I1.doit() == I2.doit(),
I3, I4, I3.doit(), I3.doit() == I4.doit()]:
pprint(t)
print()

p = plot(sin(x), cos(x), legend=True, show=False)
for i, color in enumerate(['red', 'green']):
p[i].line_color = color
p.save('sample26.svg')


$./sample26.py b + 2⋅π ⌠ ⎮ sin(x) dx ⌡ a + 2⋅π b ⌠ ⎮ sin(x) dx ⌡ a cos(a) - cos(b) True c + π ⌠ ⎮ sin(x) dx ⌡ c - π π ⌠ ⎮ sin(x) dx ⌡ -π 0 True b + 2⋅π ⌠ ⎮ cos(x) dx ⌡ a + 2⋅π b ⌠ ⎮ cos(x) dx ⌡ a -sin(a) + sin(b) True c + π ⌠ ⎮ cos(x) dx ⌡ c - π π ⌠ ⎮ cos(x) dx ⌡ -π 0 True$


HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
<label for="r0">r = </label>
<input id="r0" type="number" min="0" value="0.5">
<label for="dx">dx = </label>
<input id="dx" type="number" min="0" step="0.001" value="0.001">
<br>
<label for="x1">x1 = </label>
<input id="x1" type="number" value="-10">
<label for="x2">x2 = </label>
<input id="x2" type="number" value="10">
<br>
<label for="y1">y1 = </label>
<input id="y1" type="number" value="-10">
<label for="y2">y2 = </label>
<input id="y2" type="number" value="10">
<br>
<label for="a0">a = </label>
<input id="a0" type="number" min="1" value="-1">
<label for="b0">b = </label>
<input id="b0" type="number" min="1" value="2">
<label for="c0">c = </label>
<input id="c0" type="number" min="1" value="3">

<button id="draw0">draw</button>
<button id="clear0">clear</button>

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/d3/4.2.6/d3.min.js" integrity="sha256-5idA201uSwHAROtCops7codXJ0vja+6wbBrZdQ6ETQc=" crossorigin="anonymous"></script>

<script src="sample26.js"></script>


JavaScript

let div0 = document.querySelector('#graph0'),
pre0 = document.querySelector('#output0'),
width = 600,
height = 600,
btn0 = document.querySelector('#draw0'),
btn1 = document.querySelector('#clear0'),
input_r = document.querySelector('#r0'),
input_dx = document.querySelector('#dx'),
input_x1 = document.querySelector('#x1'),
input_x2 = document.querySelector('#x2'),
input_y1 = document.querySelector('#y1'),
input_y2 = document.querySelector('#y2'),
input_a0 = document.querySelector('#a0'),
input_b0 = document.querySelector('#b0'),
input_c0 = document.querySelector('#c0'),
inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2,
input_a0, input_a0, input_c0],
p = (x) => pre0.textContent += x + '\n';

let fns = [[(x) => Math.sin(x), 'red'],
[(x) => Math.cos(x), 'green']];

let draw = () => {
pre0.textContent = '';

let r = parseFloat(input_r.value),
dx = parseFloat(input_dx.value),
x1 = parseFloat(input_x1.value),
x2 = parseFloat(input_x2.value),
y1 = parseFloat(input_y1.value),
y2 = parseFloat(input_y2.value),
a0 = parseFloat(input_a0.value),
b0 = parseFloat(input_b0.value),
c0 = parseFloat(input_c0.value);

if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) {
return;
}

let points = [],
lines = [[a0 + 2 * Math.PI, y1, a0 + 2 * Math.PI, y2, 'blue'],
[b0 + 2 * Math.PI, y1, b0 + 2 * Math.PI, y2, 'blue'],
[a0, y1, a0, y2, 'orange'],
[b0, y1, b0, y2, 'orange'],
[-Math.PI + c0, y1, -Math.PI + c0, y2, 'brown'],
[Math.PI + c0, y1, Math.PI + c0, y2, 'brown'],
[-Math.PI, y1, -Math.PI, y2, 'skyblue'],
[Math.PI, y1, Math.PI, y2, 'skyblue']];

fns
.forEach((o) => {
let [f, color] = o;
for (let x = x1; x <= x2; x += dx) {
let y = f(x);

points.push([x, y, color]);
}
});

let xscale = d3.scaleLinear()
.domain([x1, x2])
let yscale = d3.scaleLinear()
.domain([y1, y2])

let xaxis = d3.axisBottom().scale(xscale);
let yaxis = d3.axisLeft().scale(yscale);
div0.innerHTML = '';
let svg = d3.select('#graph0')
.append('svg')
.attr('width', width)
.attr('height', height);

svg.selectAll('line')
.data([[x1, 0, x2, 0], [0, y1, 0, y2]].concat(lines))
.enter()
.append('line')
.attr('x1', (d) => xscale(d[0]))
.attr('y1', (d) => yscale(d[1]))
.attr('x2', (d) => xscale(d[2]))
.attr('y2', (d) => yscale(d[3]))
.attr('stroke', (d) => d[4] || 'black');

svg.selectAll('circle')
.data(points)
.enter()
.append('circle')
.attr('cx', (d) => xscale(d[0]))
.attr('cy', (d) => yscale(d[1]))
.attr('r', r)
.attr('fill', (d) => d[2] || 'green');

svg.append('g')
.attr('transform', translate(0, ${height - padding})) .call(xaxis); svg.append('g') .attr('transform', translate(${padding}, 0))
.call(yaxis);

[fns].forEach((fs) => p(fs.join('\n')));
};

inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();


#### 1 コメント :

รัตนาวดี ภูมิวรรณさんのコメント...

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