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 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2部(微分と基本的な関数)、第7章(逆関数)、4(逆正接関数)、練習問題22.を取り組んでみる。
高さをy、時間をt、視角をθとする。
コード(Emacs)
Python 3
#!/usr/bin/env python3 from sympy import pprint, symbols, atan, Derivative y, t = symbols('y, t') θ = atan(y / 500) Dy = Derivative(θ, y, 1) Dt = Dy * 200 for t in [Dy, Dy.doit(), Dt, Dt.doit(), Dt.subs({y: 1000}).doit()]: pprint(t) print()
入出力結果(Terminal, Jupyter(IPython))
$ ./sample22.py d ⎛ ⎛ y ⎞⎞ ──⎜atan⎜───⎟⎟ dy⎝ ⎝500⎠⎠ 1 ──────────────── ⎛ 2 ⎞ ⎜ y ⎟ 500⋅⎜────── + 1⎟ ⎝250000 ⎠ d ⎛ ⎛ y ⎞⎞ 200⋅──⎜atan⎜───⎟⎟ dy⎝ ⎝500⎠⎠ 2 ────────────── ⎛ 2 ⎞ ⎜ y ⎟ 5⋅⎜────── + 1⎟ ⎝250000 ⎠ 2/25 $
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="0.1"> <br> <label for="x1">x1 = </label> <input id="x1" type="number" value="0"> <label for="x2">x2 = </label> <input id="x2" type="number" value="1500"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="0"> <label for="y2">y2 = </label> <input id="y2" type="number" value="1500"> <br> <label for="θ0">θ = </label> <input id="θ0" type="number" min="0" step="0.01" 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="sample22.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_θ0 = document.querySelector('#θ0'), inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2, input_θ0], 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), θ0 = parseFloat(input_θ0.value); if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) { return; } let points = [], lines = [[500, y1, 500, y2, 'red'], [x1, 1000, x2, 1000, 'blue'], [0, 0, 500, 500 * Math.tan(θ0), 'green']], fns = [], 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]); } }); 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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