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)
- Nebo(Windows アプリ)
- iPad Pro + Apple Pencil
- MyScript Nebo(iPad アプリ)
- 参考書籍
解析入門 原書第3版 (S.ラング(著)、松坂 和夫(翻訳)、片山 孝次(翻訳)、岩波書店)の第3部(積分)、第10章(積分の性質)、2(積分の性質)、6、7、8、9.を取り組んでみる。
コード(Emacs)
Python 3
#!/usr/bin/env python3
from sympy import pprint, symbols, sin, cos, exp, pi, Integral, plot
x = symbols('x', real=True)
fs = [(sin(x) + cos(x), (-pi, pi)),
(2 * x ** 5, (-1, 1)),
(exp(x), (-1, 2)),
(4 * x ** 2, (-1, 3))]
for i, (f, (a, b)) in enumerate(fs, 6):
print(f'{i}.')
I = Integral(f, (x, a, b))
for t in [I, I.doit()]:
pprint(t)
print()
print()
p = plot(*[f for f, _ in fs], ylim=(-5, 5), show=False, legend=True)
for i, color in enumerate(['red', 'green', 'blue', 'orange']):
p[i].line_color = color
p.save('sample6.svg')
入出力結果(Terminal, Jupyter(IPython))
$ ./sample6.py 6. π ⌠ ⎮ (sin(x) + cos(x)) dx ⌡ -π 0 7. 1 ⌠ ⎮ 5 ⎮ 2⋅x dx ⌡ -1 0 8. 2 ⌠ ⎮ x ⎮ ℯ dx ⌡ -1 -1 2 - ℯ + ℯ 9. 3 ⌠ ⎮ 2 ⎮ 4⋅x dx ⌡ -1 112/3 $
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="-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="sample6.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 fns = [[(x) => Math.sin(x) + Math.cos(x), 'red'],
[(x) => 2 * x ** 5, 'green'],
[(x) => Math.exp(x), 'blue'],
[(x) => 4 * x ** 2, 'orange']];
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 = [[-Math.PI, y1, -Math.PI, y2, 'red'],
[Math.PI, y1, Math.PI, y2, 'red'],
[-1, y1, -1, y2, 'green'],
[1, y1, 1, y2, 'green'],
[-1, y1, -1, y2, 'blue'],
[2, y1, 2, y2, 'blue'],
[-1, y1, -1, y2, 'orange'],
[3, y1, 3, y2, 'orange']],
fns1 = [],
fns2 = [];
fns
.forEach((o) => {
let [f, color] = o;
for (let x = x1; x <= x2; x += dx) {
let y = f(x);
points.push([x, y, color]);
}
});
fns1
.forEach((o) => {
let [f, color] = o;
lines.push([x1, f(x1), x2, f(x2), color]);
});
fns2
.forEach((o) => {
let [f, color] = o;
for (let x = x1; x <= x2; x += dx0) {
let g = f(x);
lines.push([x1, g(x1), x2, g(x2), 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('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, fns1, fns2].forEach((fs) => p(fs.join('\n')));
};
inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();
.
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