2017年5月13日土曜日

学習環境

数学読本〈4〉数列の極限,順列/順列・組合せ/確率/関数の極限と微分法(松坂 和夫(著)、岩波書店)の第17章(関数の変化をとらえる - 関数の極限と微分法)、17.1(関数と極限)、極限の応用問題、問10.を取り組んでみる。


  1. x 2 2hx+ h 2 + y 2 2hy+ h 2 =1 x 2 2hx+2 h 2 +1 x 2 2hy1=0 x+hy=0 y 2 = x 2 2hx+ h 2 1 x 2 = x 2 2hx+ h 2 2 x 2 2hx+ h 2 1=0 x= h± h 2 2( h 2 1 ) 2 = h± 2 h 2 2 y=x+h= h 2 h 2 2 ( h± h 2 2( h 2 1 ) 2 , h 2 h 2 2 ) h0 ( ± 2 2 , 2 2 ) =( ± 1 2 , 1 2 )

コード(Emacs)

Python 3

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

from sympy import Symbol, solve, Limit, pprint

x = Symbol('x')
y = Symbol('y')
h = Symbol('h')

expr1 = x ** 2 + y ** 2 - 1
expr2 = (x - h) ** 2 + (y - h) ** 2 - 1

for i, (x, y) in enumerate(solve((expr1, expr2), x, y)):
    print('{}.'.format(i + 1))
    print('x = ')
    pprint(Limit(x, h, 0).doit())
    print('y = ')
    pprint(Limit(y, h, 0).doit())

入出力結果(Terminal, IPython)

$ ./sample10.py
1.
x = 
-√2 
────
 2  
y = 
√2
──
2 
2.
x = 
√2
──
2 
y = 
-√2 
────
 2
$

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
<label for="x1">x1 = </label>
<input id="x1" type="number" value="-2">
<label for="x2">x2 = </label>
<input id="x2" type="number" value="2">
<label for="h0">h = </label>
<input id="h0" type="number" 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="sample10.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_x1 = document.querySelector('#x1'),
    input_x2 = document.querySelector('#x2'),
    input_h = document.querySelector('#h0'),
    inputs = [input_x1, input_x2, input_h],
    p = (x) => pre0.textContent += x + '\n';

let draw = () => {
    pre0.textContent = '';

    let x1 = parseFloat(input_x1.value),
        x2 = parseFloat(input_x2.value),
        h = parseFloat(input_h.value);

    if (h === 0) {
        return 0;
    }
    let points = [[0, 0], [h, h]];
    
    let xscale = d3.scaleLinear()
        .domain([x1, x2])
        .range([padding, width - padding]);
    let ys = points.map((a) => a[1]);
    let yscale = d3.scaleLinear()
        .domain([x1, x2])
        .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', xscale(1) - xscale(0))
        .attr('fill', 'rgba(0, 0, 0, 0)')
        .attr('stroke', (d, i) => i === 0 ? '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();





















 
						

0 コメント:

コメントを投稿

Comments on Google+: