学習環境
- Surface 3 (4G LTE)、Surface 3 タイプ カバー、Surface ペン(端末)
- Windows 10 Pro (OS)
- 数式入力ソフト(TeX, MathML): MathType
- MathML対応ブラウザ: Firefox、Safari
- MathML非対応ブラウザ(Internet Explorer, Microsoft Edge, Google Chrome...)用JavaScript Library: MathJax
- 参考書籍
解析入門〈2〉(松坂 和夫(著)、岩波書店)の第8章(積分の計算)、8.1(不定積分の計算)、問題5.を取り組んでみる。
コード(Emacs)
Python 3
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
from sympy import pprint, symbols, Integral, sin, cos, tan
print('5.')
x = symbols('x')
fs = [tan(x) ** 3,
sin(x) ** 2 * cos(x) ** 2,
1 / (sin(x) ** 3 * cos(x) ** 3)]
for i, f in enumerate(fs, 1):
I = Integral(f, x)
pprint(I)
I = I.doit()
pprint(I)
pprint(I.factor())
pprint(I.expand())
入出力結果(Terminal, IPython)
$ ./sample5.py
5.
⌠
⎮ 3
⎮ tan (x) dx
⌡
⎛ 2 ⎞
log⎝sin (x) - 1⎠ 1
──────────────── - ─────────────
2 2
2⋅sin (x) - 2
⎛ 2 ⎞ 2 ⎛ 2 ⎞
log⎝sin (x) - 1⎠⋅sin (x) - log⎝sin (x) - 1⎠ - 1
───────────────────────────────────────────────
2⋅(sin(x) - 1)⋅(sin(x) + 1)
⎛ 2 ⎞
log⎝sin (x) - 1⎠ 1
──────────────── - ─────────────
2 2
2⋅sin (x) - 2
⌠
⎮ 2 2
⎮ sin (x)⋅cos (x) dx
⌡
x sin(2⋅x)⋅cos(2⋅x)
─ - ─────────────────
8 16
2⋅x - sin(2⋅x)⋅cos(2⋅x)
───────────────────────
16
x sin(2⋅x)⋅cos(2⋅x)
─ - ─────────────────
8 16
⌠
⎮ 1
⎮ ─────────────── dx
⎮ 3 3
⎮ sin (x)⋅cos (x)
⌡
2
2⋅sin (x) - 1 ⎛ 2 ⎞
- ───────────────────── - log⎝sin (x) - 1⎠ + 2⋅log(sin(x))
4 2
2⋅sin (x) - 2⋅sin (x)
⎛ 2 ⎞ 4 ⎛ 2 ⎞ 2 4
- 2⋅log⎝sin (x) - 1⎠⋅sin (x) + 2⋅log⎝sin (x) - 1⎠⋅sin (x) + 4⋅log(sin(x))⋅sin
──────────────────────────────────────────────────────────────────────────────
2
2⋅(sin(x) - 1)⋅(sin(x) + 1)⋅sin (x)
2 2
(x) - 4⋅log(sin(x))⋅sin (x) - 2⋅sin (x) + 1
───────────────────────────────────────────
2
⎛ 2 ⎞ 2⋅sin (x) 1
- log⎝sin (x) - 1⎠ + 2⋅log(sin(x)) - ───────────────────── + ─────────────────
4 2 4
2⋅sin (x) - 2⋅sin (x) 2⋅sin (x) - 2⋅sin
────
2
(x)
$
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="0.0001" value="0.001"> <br> <label for="x1">x1 = </label> <input id="x1" type="number" value="-5"> <label for="x2">x2 = </label> <input id="x2" type="number" value="5"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="-5"> <label for="y2">y2 = </label> <input id="y2" type="number" value="5"> <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="sample5.js"></script>
JavaScript
let div0 = document.querySelector('#graph0'),
pre0 = document.querySelector('#output0'),
width = 600,
height = 600,
padding = 50,
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'),
inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2],
p = (x) => pre0.textContent += x + '\n',
range = (start, end, step=1) => {
let res = [];
for (let i = start; i < end; i += step) {
res.push(i);
}
return res;
};
let f1 = (x) => Math.tan(x) ** 3,
f2 = (x) => Math.sin(x) ** 2 * Math.cos(x) ** 2,
f3 = (x) => 1 / (Math.sin(x) ** 3 * Math.cos(x) ** 3);
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);
if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) {
return;
}
let points = [],
lines = [],
fns = [[f1, 'red'],
[f2, 'green'],
[f3, 'blue']];
fns
.forEach((o) => {
let [fn, color] = o;
for (let x = x1; x <= x2; x += dx) {
let y = fn(x);
if (Math.abs(y) < Infinity) {
points.push([x, y, color]);
}
}
});
let xscale = d3.scaleLinear()
.domain([x1, x2])
.range([padding, width - padding]);
let yscale = d3.scaleLinear()
.domain([y1, y2])
.range([height - padding, padding]);
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('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.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.append('g')
.attr('transform', `translate(0, ${height - padding})`)
.call(xaxis);
svg.append('g')
.attr('transform', `translate(${padding}, 0)`)
.call(yaxis);
p(fns.join('\n'));
};
inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();
0 コメント:
コメントを投稿