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 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3章(微分係数、導関数)、補充問題 41-50.を取り組んでみる。
dydx=14x−34+32x−14y−(2+2·23)=(14·18+32·12)(x−16)y−18=(132+34)(x−16)y−18=2532(x−16)
dydx=6x2y−(28+3)=32(x−12)y−268=32(x−12)
dydx=(x−3)(x−4)+(x−1)(x−4)+(x−1)(x−3)y+12=(12+4+3)xy+12=19x
dydx=4x+5y−17=13(x−2)
dydx=2x(2x+3)+(x2+1)2y−10=14(x−1)
コード(Emacs)
HTML5
<div id="graph0"></div> <pre id="output0"></pre> <label for="r0">r = </label> <input id="r0" type="number" min="0" value="1"> <label for="dx">dx = </label> <input id="dx" type="number" min="0" step="0.01" value="0.01"> <label for="n0">n = </label> <input id="n0" type="number" min="41" max="50" step="1" value="41"> <br> <label for="x1">x1 = </label> <input id="x1" type="number" value="0"> <label for="x2">x2 = </label> <input id="x2" type="number" value="20"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="0"> <label for="y2">y2 = </label> <input id="y2" type="number" value="20"> <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="sample41.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_n = document.querySelector('#n0'), 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_n, input_x1, input_x2, input_y1, input_y2], p = (x) => pre0.textContent += x + '\n'; let f10 = (x) => x ** (1 / 4) + 2 * x ** (3 / 4), f11 = (x) => 25 / 32 * (x - 16) + 18, f20 = (x) => 2 * x ** 3 + 3, f21 = (x) => 3 / 2 * (x - 1 / 2) + 26 / 8, f30 = (x) => (x - 1) * (x - 3) * (x - 4), f31 = (x) => 19 * x - 12, f40 = (x) => 2 * x ** 2 + 5 * x - 1, f41 = (x) => 13 * (x - 2) + 17, f50 = (x) => (x ** 2 + 1) * (2 * x + 3), f51 = (x) => 14 * (x - 1) + 10, f60 = (x) => (x - 1) / (x + 5), f61 = (x) => 6 / 49 * (x - 2) + 1 / 7, f70 = (x) => x ** 2 / (x ** 3 + 1), f71 = (x) => - 4 / 27 * (x - 2) + 4 / 9, f80 = (x) => (x ** 2 + 1) / (x ** 3 + 1), f81 = (x) => - 8 / 37 * (x - 2) + 5 / 9, f90 = (x) => x ** 2 / (x ** 2 - 1), f91 = (x) => -4 / 9 * (x - 2) + 4 / 3, f00 = (x) => (x - 1) / (x ** 2 + 1), f01 = (x) => 1 / 2 *(x - 1) fns = [[f10, f11], [f20, f21], [f30, f31], [f40, f41], [f50, f51], [f60, f61], [f70, f71], [f80, f81], [f90, f91], [f00, f01]]; let draw = () => { pre0.textContent = ''; let r = parseFloat(input_r.value), dx = parseFloat(input_dx.value), n = parseInt(input_n.value, 10) - 41, 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 = [], [f0, f1] = fns[n]; for (let x = x1; x <= x2; x += dx) { points.push([x, f0(x)]); } let t = points.length; for (let x = x1; x <= x2; x += dx) { points.push([x, f1(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 < t ? 'green': 'blue'); svg.append('g') .attr('transform', `translate(0, ${yscale(0)})`) .call(xaxis); svg.append('g') .attr('transform', `translate(${xscale(0)}, 0)`) .call(yaxis); } inputs.forEach((input) => input.onchange = draw); btn0.onclick = draw; btn1.onclick = () => pre0.textContent = ''; draw();
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