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11章(積分の計算)、3(三角関数の積分)、練習問題20.を取り組んでみる。
コード(Emacs)
Python 3
#!/usr/bin/env python3 from sympy import pprint, symbols, pi, sin, cos, Integral, Function, plot x, a, b, c = symbols('x, a, b, c') for f in [sin(x), cos(x)]: I1 = Integral(f, (x, a + 2 * pi, b + 2 * pi)) I2 = Integral(f, (x, a, b)) I3 = Integral(f, (x, -pi + c, pi + c)) I4 = Integral(f, (x, -pi, pi)) for t in [I1, I2, I1.doit(), I1.doit() == I2.doit(), I3, I4, I3.doit(), I3.doit() == I4.doit()]: pprint(t) print() p = plot(sin(x), cos(x), legend=True, show=False) for i, color in enumerate(['red', 'green']): p[i].line_color = color p.save('sample26.svg')
入出力結果(Terminal, Jupyter(IPython))
$ ./sample26.py b + 2⋅π ⌠ ⎮ sin(x) dx ⌡ a + 2⋅π b ⌠ ⎮ sin(x) dx ⌡ a cos(a) - cos(b) True c + π ⌠ ⎮ sin(x) dx ⌡ c - π π ⌠ ⎮ sin(x) dx ⌡ -π 0 True b + 2⋅π ⌠ ⎮ cos(x) dx ⌡ a + 2⋅π b ⌠ ⎮ cos(x) dx ⌡ a -sin(a) + sin(b) True c + π ⌠ ⎮ cos(x) dx ⌡ c - π π ⌠ ⎮ cos(x) dx ⌡ -π 0 True $
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="-10"> <label for="x2">x2 = </label> <input id="x2" type="number" value="10"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="-10"> <label for="y2">y2 = </label> <input id="y2" type="number" value="10"> <br> <label for="a0">a = </label> <input id="a0" type="number" min="1" value="-1"> <label for="b0">b = </label> <input id="b0" type="number" min="1" value="2"> <label for="c0">c = </label> <input id="c0" type="number" min="1" value="3"> <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="sample26.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_a0 = document.querySelector('#a0'), input_b0 = document.querySelector('#b0'), input_c0 = document.querySelector('#c0'), inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2, input_a0, input_a0, input_c0], p = (x) => pre0.textContent += x + '\n'; let fns = [[(x) => Math.sin(x), 'red'], [(x) => Math.cos(x), 'green']]; 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), a0 = parseFloat(input_a0.value), b0 = parseFloat(input_b0.value), c0 = parseFloat(input_c0.value); if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) { return; } let points = [], lines = [[a0 + 2 * Math.PI, y1, a0 + 2 * Math.PI, y2, 'blue'], [b0 + 2 * Math.PI, y1, b0 + 2 * Math.PI, y2, 'blue'], [a0, y1, a0, y2, 'orange'], [b0, y1, b0, y2, 'orange'], [-Math.PI + c0, y1, -Math.PI + c0, y2, 'brown'], [Math.PI + c0, y1, Math.PI + c0, y2, 'brown'], [-Math.PI, y1, -Math.PI, y2, 'skyblue'], [Math.PI, y1, Math.PI, y2, 'skyblue']]; fns .forEach((o) => { let [f, color] = o; for (let x = x1; x <= x2; x += dx) { let y = f(x); points.push([x, y, 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].forEach((fs) => p(fs.join('\n'))); }; inputs.forEach((input) => input.onchange = draw); btn0.onclick = draw; btn1.onclick = () => pre0.textContent = ''; draw();
1 コメント :
感謝您提供的有用且非常有用的信息。非常有趣。我喜歡您分享的所有內容,並欣賞您的美麗創作。感謝您與大家分享。我了解您的一切。 它很棒而且很棒。
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