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2 changes: 1 addition & 1 deletion Project.toml
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name = "NumericalAnalysis"
uuid = "fb18ad0a-c577-441c-b4b0-b42a431f6d4f"
authors = ["Zhuofei Zhou"]
version = "0.2.0"
version = "0.3.0"

[deps]
Conda = "8f4d0f93-b110-5947-807f-2305c1781a2d"
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3 changes: 3 additions & 0 deletions README.md
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Expand Up @@ -51,6 +51,9 @@ Now,just have some Methods here
- Newton_cotes
- Romberg
- Gaussian_Quad
- Mutiple Integrals
- SimpsonDoubleIntegral
- GaussianDoubleIntegral
more information in Docs.

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4 changes: 2 additions & 2 deletions docs/build/index.html
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · NumericalAnalysis.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit">NumericalAnalysis.jl</span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Basic"><span>Basic</span></a></li></ul></li><li><span class="tocitem">Functions</span><ul><li><a class="tocitem" href="m/basic/">Basic function</a></li><li><a class="tocitem" href="m/SEq1/">SEq in one variable</a></li><li><a class="tocitem" href="m/Polynomial/">Interpolation and the Lagrange Polynomial</a></li><li><a class="tocitem" href="m/NCalculus/">Numerical Differentiation and Integration</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/ZhouZhuofei/NumericalAnalysis.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Numerical-Analysis"><a class="docs-heading-anchor" href="#Numerical-Analysis">Numerical Analysis</a><a id="Numerical-Analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Numerical-Analysis" title="Permalink"></a></h1><hr/><p><a href="https://coveralls.io/github/ZhouZhuofei/NumericalAnalysis.jl?branch=master"><img src="https://coveralls.io/repos/github/ZhouZhuofei/NumericalAnalysis.jl/badge.svg?branch=master" alt="Coverage"/></a> <a href="https://codecov.io/gh/ZhouZhuofei/NumericalAnalysis.jl"><img src="https://codecov.io/gh/ZhouZhuofei/NumericalAnalysis.jl/branch/master/graph/badge.svg" alt="codecov"/></a> <a href="https://github.com/ZhouZhuofei/NumericalAnalysis.jl/blob/master/LICENSE"><img src="https://img.shields.io/badge/license-MIT-brightgreen.svg?style=flat" alt="License"/></a></p><hr/><p>It&#39;s a julia package for Numerical Analysis.</p><p>Now, i just write a little function in it. I am a beginner of Julia and numerical analysis, there may be many problems, 👏 to discuss with me.🤣</p><hr/><h2 id="Basic"><a class="docs-heading-anchor" href="#Basic">Basic</a><a id="Basic-1"></a><a class="docs-heading-anchor-permalink" href="#Basic" title="Permalink"></a></h2><p>here are some function:</p><p>Now, i just write some functions:</p><ul><li>Basic<ul><li>N the derivative, use ForwardDiff packageto calculate <span>$\frac{dy}{dx}$</span>, then recursive to get Nth derivative.(emmm, I feel a bit slow)</li><li>Taylor Polynomial, get the value nth Taylor Ploynomial.</li></ul></li><li>Solutions for equation in one Variable<ul><li>Bisection function, find root</li><li>fixed_point function.</li><li>Newton&#39;s Method</li><li>The Secant Method</li><li>The False Position Method</li><li>Modified Newton&#39;s Method</li><li>Müller’s Method</li></ul></li><li>Interpolation and the Lagrange Polynomial<ul><li>nth Larange interpolating polynomial</li><li>Neville’s Iterated Interpolation</li><li>Newton’s Divided-Difference Formula</li><li>Natural Cubic Spline</li><li>Clamped Cubic Spline</li></ul></li><li>Numerical Differentiation and integration<ul><li>Differentiation<ul><li>Three-Point and Five-Point formula</li></ul></li><li>Integration<ul><li>Trapezoidal Rule</li><li>Simpson&#39;s Rule</li><li>Newton_Cotes</li><li>Romberg</li><li>Gaussian_Quad</li></ul></li></ul></li></ul><hr/><hr/><ul><li>NthDerivative(f, x, n)</li></ul><pre><code class="language-julia">using NumericalAnalysis
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · NumericalAnalysis.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit">NumericalAnalysis.jl</span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Basic"><span>Basic</span></a></li></ul></li><li><span class="tocitem">Functions</span><ul><li><a class="tocitem" href="m/basic/">Basic function</a></li><li><a class="tocitem" href="m/SEq1/">SEq in one variable</a></li><li><a class="tocitem" href="m/Polynomial/">Interpolation and the Lagrange Polynomial</a></li><li><a class="tocitem" href="m/NCalculus/">Numerical Differentiation and Integration</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/ZhouZhuofei/NumericalAnalysis.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Numerical-Analysis"><a class="docs-heading-anchor" href="#Numerical-Analysis">Numerical Analysis</a><a id="Numerical-Analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Numerical-Analysis" title="Permalink"></a></h1><hr/><p><a href="https://coveralls.io/github/ZhouZhuofei/NumericalAnalysis.jl?branch=master"><img src="https://coveralls.io/repos/github/ZhouZhuofei/NumericalAnalysis.jl/badge.svg?branch=master" alt="Coverage"/></a> <a href="https://codecov.io/gh/ZhouZhuofei/NumericalAnalysis.jl"><img src="https://codecov.io/gh/ZhouZhuofei/NumericalAnalysis.jl/branch/master/graph/badge.svg" alt="codecov"/></a> <a href="https://github.com/ZhouZhuofei/NumericalAnalysis.jl/blob/master/LICENSE"><img src="https://img.shields.io/badge/license-MIT-brightgreen.svg?style=flat" alt="License"/></a></p><hr/><p>It&#39;s a julia package for Numerical Analysis.</p><p>Now, i just write a little function in it. I am a beginner of Julia and numerical analysis, there may be many problems, 👏 to discuss with me.🤣</p><hr/><h2 id="Basic"><a class="docs-heading-anchor" href="#Basic">Basic</a><a id="Basic-1"></a><a class="docs-heading-anchor-permalink" href="#Basic" title="Permalink"></a></h2><p>here are some function:</p><p>Now, i just write some functions:</p><ul><li>Basic<ul><li>N the derivative, use ForwardDiff packageto calculate <span>$\frac{dy}{dx}$</span>, then recursive to get Nth derivative.(emmm, I feel a bit slow)</li><li>Taylor Polynomial, get the value nth Taylor Ploynomial.</li></ul></li><li>Solutions for equation in one Variable<ul><li>Bisection function, find root</li><li>fixed_point function.</li><li>Newton&#39;s Method</li><li>The Secant Method</li><li>The False Position Method</li><li>Modified Newton&#39;s Method</li><li>Müller’s Method</li></ul></li><li>Interpolation and the Lagrange Polynomial<ul><li>nth Larange interpolating polynomial</li><li>Neville’s Iterated Interpolation</li><li>Newton’s Divided-Difference Formula</li><li>Natural Cubic Spline</li><li>Clamped Cubic Spline</li></ul></li><li>Numerical Differentiation and integration<ul><li>Differentiation<ul><li>Three-Point and Five-Point formula</li></ul></li><li>Integration<ul><li>Trapezoidal Rule</li><li>Simpson&#39;s Rule</li><li>Newton_Cotes</li><li>Romberg</li><li>Gaussian_Quad</li></ul></li><li>Mutiple Integrals<ul><li>SimpsonDoubleIntegral</li><li>GaussianDoubleIntegral</li></ul></li></ul></li></ul><hr/><hr/><ul><li>NthDerivative(f, x, n)</li></ul><pre><code class="language-julia">using NumericalAnalysis
NthDerivative(x-&gt;x^3, 4, 4) # 0</code></pre><pre class="documenter-example-output">0</pre><pre><code class="language-julia">NthDerivative(x-&gt;x^3, 4, 2) # 24</code></pre><pre class="documenter-example-output">24</pre><pre><code class="language-julia">NthDerivative(cos, 1, 5) # NthDerivative(cos, 1, 5)</code></pre><pre class="documenter-example-output">-0.8414709848078965</pre><hr/><ul><li>TaylorPolynomials(f, x, x₀, n)</li></ul><pre><code class="language-julia">TaylorPolynomials(cos, 0.1, 0, 6) # TaylorPolynomials(cos, 0.1, 0, 6)</code></pre><pre class="documenter-example-output">0.9950041652777778</pre><pre><code class="language-julia">TaylorPolynomials(x-&gt;x^3, 1.1, 1, 6) #1.331000..</code></pre><pre class="documenter-example-output">1.3310000000000004</pre><hr/><ul><li>Bisection(f, a, b)</li></ul><pre><code class="language-julia">using NumericalAnalysis: SEq1
SEq1.Bisection(sin, π/2, 3π/2)</code></pre><pre class="documenter-example-output">3.14159274721655</pre><pre><code class="language-julia">SEq1.Bisection(x-&gt;x-1, 0, 3π/2, output_seq=true)</code></pre><pre class="documenter-example-output">26-element Array{Any,1}:
[2.356194490192345, 1.3561944901923448]
Expand All @@ -21,4 +21,4 @@
[0.9999994915241543, -5.084758456508354e-7]
[0.9999997724044256, -2.2759557438689626e-7]
[0.9999999128445612, -8.71554387549267e-8]
[0.9999999830646291, -1.6935370883430778e-8]</pre></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="m/basic/">Basic function »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 22 October 2020 15:54">Thursday 22 October 2020</span>. Using Julia version 1.5.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
[0.9999999830646291, -1.6935370883430778e-8]</pre></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="m/basic/">Basic function »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Friday 30 October 2020 18:03">Friday 30 October 2020</span>. Using Julia version 1.5.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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