From 77175d47c03713dc371d624d097aa7b35f2c1593 Mon Sep 17 00:00:00 2001
From: Isabel Slingerland <I.C.Slingerland-1@student.tudelft.nl>
Date: Tue, 1 Oct 2024 14:54:12 +0200
Subject: [PATCH] fixed the issue example TSE
---
book/numerical_methods/4-taylor-series-expansion.ipynb | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/book/numerical_methods/4-taylor-series-expansion.ipynb b/book/numerical_methods/4-taylor-series-expansion.ipynb
index 04cc4a84..0b63ba1f 100644
--- a/book/numerical_methods/4-taylor-series-expansion.ipynb
+++ b/book/numerical_methods/4-taylor-series-expansion.ipynb
@@ -78,7 +78,7 @@
"Note that $x$ and $\\Delta x$ can be written interchangeably when $x_i=0$ as $\\Delta x=x-x_i$. If this would not be the case, for example if $x_i=\\pi$ the result is completely different.\n",
"\n",
"```\n",
- "Compute the TSE polynomial truncated until $\\mathcal{O}(\\Delta x)^6$ for $f(x)=\\sin(x)$ around $x_i=\\pi$\n",
+ "Compute the TSE polynomial truncated until $\\mathcal{O}(\\Delta x)^6$ for $f(x)=\\sin(x)$ around $x_i=\\frac{\\pi}{2}$\n",
"\n",
"```{admonition} Solution\n",
":class: tip, dropdown\n",
@@ -86,9 +86,9 @@
"Applying the definition of TSE:\n",
"\n",
"\n",
- "$$\\sin(x) \\approx \\sin(x_i+\\Delta x) \\approx \\sin(\\pi) + (x-\\pi)\\cos(\\pi) - \\frac{(x-\\pi)^2}{2}\\sin(\\pi) - \\frac{(x-\\pi)^3}{6}\\cos(\\pi) + \\frac{(x-\\pi)^4}{24}\\sin(\\pi) + \\frac{(x-\\pi)^5}{120}\\cos(\\pi) +\\mathcal{O}(\\Delta x)^6$$\n",
+ "$$\\sin(x) \\approx \\sin(x_i+\\Delta x) \\approx \\sin(\\frac{\\pi}{2}) + (x-\\frac{\\pi}{2})\\cos(\\frac{\\pi}{2}) - \\frac{(x-\\frac{\\pi}{2})^2}{2}\\sin(\\frac{\\pi}{2}) - \\frac{(x-\\frac{\\pi}{2})^3}{6}\\cos(\\frac{\\pi}{2}) + \\frac{(x-\\frac{\\pi}{2})^4}{24}\\sin(\\frac{\\pi}{2}) + \\frac{(x-\\frac{\\pi}{2})^5}{120}\\cos(\\frac{\\pi}{2}) +\\mathcal{O}(\\Delta x)^6$$\n",
"\n",
- "$$\\sin(x) \\approx \\sin(x_i+\\Delta x) \\approx 1 - \\frac{(x-\\pi)^2}{2} + \\frac{(x-\\pi)^4}{24} \\text{ with an error } \\mathcal{O}(\\Delta x)^6$$\n",
+ "$$\\sin(x) \\approx \\sin(x_i+\\Delta x) \\approx 1 - \\frac{(x-\\frac{\\pi}{2})^2}{2} + \\frac{(x-\\frac{\\pi}{2})^4}{24} \\text{ with an error } \\mathcal{O}(\\Delta x)^6$$\n",
"\n",
"```\n",
"\n",
--
GitLab