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
数学読本〈5〉微分法の応用/積分法/積分法の応用/行列と行列式(松坂 和夫(著)、岩波書店)の第19章(細分による加法 - 積分法)、19.3(定積分の性質と計算)、置換積分法の応用(1) - 偶関数と奇関数、問29.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, plot, solve print('29.') x, c = symbols('x c') p = symbols('p', nonzero=True) f = (x - c) * (x ** 2 - p ** 2) try: I = Integral(f, (x, -p, p)) for g in [I, I.doit()]: pprint(g) pprint(solve(I.doit(), c, dict=True)) for i, c0 in enumerate([0, 1]): p = plot(f.subs({p: 1, c: c0}), show=False, legend=True) p.save(f'sample29_{i}.svg') except Exception as err: print(type(err), err)
入出力結果(Terminal, IPython)
$ ./sample29.py 29. p ⌠ ⎮ ⎛ 2 2⎞ ⎮ (-c + x)⋅⎝- p + x ⎠ dx ⌡ -p 3 4⋅c⋅p ────── 3 [{c: 0}] <class 'ValueError'> The same variable should be used in all univariate expressions being plotted. $
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"> <br> <label for="p0">p = </label> <input id="p0" type="number" value="1"> <label for="c0">c = </label> <input id="c0" 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="sample29.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'), input_p0 = document.querySelector('#p0'), input_c0 = document.querySelector('#c0'), inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2, input_p0, input_c0], 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 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), p0 = parseFloat(input_p0.value), c0 = parseFloat(input_c0.value); if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) { return; } let points = [], f = (x) => (x - c0) * (x ** 2 - p0 ** 2), lines = [[-p0, y1, -p0, y2, 'red'], [p0, y1, p0, y2, 'red']], fns = [[f, 'green']], fns1 = [], fns2 = []; 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]); } } }); fns1.forEach((o) => { let [fn, color] = o; lines.push([x1, fn(x1), x2, fn(x2), color]); }); fns2.forEach((o) => { let [fn, color] = o; for (let x = x1; x <= x2; x += dx0) { let g = fn(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'))); p(`S = ${4 / 3 * p0 ** 3 * c0}`); }; inputs.forEach((input) => input.onchange = draw); btn0.onclick = draw; btn1.onclick = () => pre0.textContent = ''; draw();
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