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, Google Chrome...)用JavaScript Library: MathJax
- 参考書籍
解析入門〈1〉(松坂 和夫(著)、岩波書店)の第5章(各種の初等関数)、5.4(三角関数(続き)、逆三角関数)、問題8.を取り組んでみる。
コード(Emacs)
Python 3
#!/usr/bin/env python3 # -*- coding: utf-8 -*- from sympy import Symbol, symbols, sin, Limit, pprint, Derivative print('8.') x = Symbol('x', nonzero=True) m, n = symbols('m n', integer=True, positive=True) f = x ** m * sin(1 / x ** n) for i in range(3): fi = Derivative(f, x, i) pprint(fi) pprint(fi.doit())
入出力結果(Terminal, IPython)
$ ./sample8.py 8. m ⎛ -n⎞ x ⋅sin⎝x ⎠ m ⎛ -n⎞ x ⋅sin⎝x ⎠ d ⎛ m ⎛ -n⎞⎞ ──⎝x ⋅sin⎝x ⎠⎠ dx m ⎛ -n⎞ m -n ⎛ -n⎞ m⋅x ⋅sin⎝x ⎠ n⋅x ⋅x ⋅cos⎝x ⎠ ───────────── - ───────────────── x x 2 d ⎛ m ⎛ -n⎞⎞ ───⎝x ⋅sin⎝x ⎠⎠ 2 dx m ⎛ 2 ⎛ -n⎞ -n ⎛ -n⎞ ⎛ -n⎞ 2 -n ⎛ -n⎞ 2 -2⋅n x ⋅⎝m ⋅sin⎝x ⎠ - 2⋅m⋅n⋅x ⋅cos⎝x ⎠ - m⋅sin⎝x ⎠ + n ⋅x ⋅cos⎝x ⎠ - n ⋅x ⋅ ─────────────────────────────────────────────────────────────────────────────── 2 x ⎛ -n⎞ -n ⎛ -n⎞⎞ sin⎝x ⎠ + n⋅x ⋅cos⎝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="0.0001"> <br> <label for="x1">x1 = </label> <input id="x1" type="number" value="-1"> <label for="x2">x2 = </label> <input id="x2" type="number" value="1"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="-1"> <label for="y2">y2 = </label> <input id="y2" type="number" value="1"> <br> <label for="m0">m = </label> <input id="m0" type="number" min="1" step="1" value="1"> <label for="n0">n = </label> <input id="n0" type="number" min="1" step="1" value="1"> <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="sample8.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_m = document.querySelector('#m0'), input_n = document.querySelector('#n0'), inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2, input_m, input_n], p = (x) => pre0.textContent += x + '\n'; let f6 = (x) => x === 0 ? 0 : x * Math.sin(1 / x), f71 = (x) => x === 0 ? 0 : x ** 2 * Math.sin(1 / x), f72 = (x) => x === 0 ? 0 : 2 * x * Math.sin(1 / x) - Math.cos(1 / x); 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), m = parseInt(input_m.value, 10), n = parseInt(input_n.value, 10); if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) { return; } let points = [], f = (x) => x ** m * Math.sin(x ** -n), f1 = (x) => (m * x ** m * Math.sin(x ** -n) - n * x ** (m - n) * Math.cos(x ** -n)) / x, f2 = (x) => x ** m * (m ** 2 * Math.sin(x ** -n) - 2 * m * n * x ** -n * Math.cos(x ** -n) - m * Math.sin(x ** - n) + n ** 2 * x ** -n * Math.cos(x ** -n) - n ** 2 * x ** (-2 * n) * Math.sin(x ** -n) + n * x ** -n * Math.cos(x ** -n)) / x ** 2; for (let x = x1; x <= x2; x += dx) { if (x !== 0) { points.push([x, f(x)]); } } let t1 = points.length; for (let x = x1; x <= x2; x += dx) { if (x !== 0) { points.push([x, f1(x)]); } } let t2 = points.length; for (let x = x1; x <= x2; x += dx) { if (x !== 0) { points.push([x, f2(x)]); } } 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, i) => i < t1 ? 'red': i < t2 ? 'green' : 'blue'); svg.append('g') .attr('transform', `translate(0, ${yscale(0)})`) .call(xaxis); svg.append('g') .attr('transform', `translate(${xscale(0)}, 0)`) .call(yaxis); p(f6(0)); p(f71(0)); p(f72(0)); } inputs.forEach((input) => input.onchange = draw); btn0.onclick = draw; btn1.onclick = () => pre0.textContent = ''; draw();
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