From 67897f3485c6d4f7e24426c2592e5f5cd0127c3f Mon Sep 17 00:00:00 2001 From: Claudio Maggioni Date: Thu, 19 Mar 2020 12:00:00 +0100 Subject: [PATCH] hw2 done up to ex3 --- hw2/assignment2.m | 36 ++++++++++++++++++++++++++++++++++++ hw2/assignment2.pdf | Bin 0 -> 16607 bytes hw2/hw2.pdf | Bin 88652 -> 91315 bytes hw2/hw2.tex | 7 +++++++ 4 files changed, 43 insertions(+) create mode 100644 hw2/assignment2.m create mode 100644 hw2/assignment2.pdf diff --git a/hw2/assignment2.m b/hw2/assignment2.m new file mode 100644 index 0000000..c6a59a4 --- /dev/null +++ b/hw2/assignment2.m @@ -0,0 +1,36 @@ +%% Assignment 2 +% Name: Claudio Maggioni +% +% Date: 19/3/2019 +% +% This is a template file for the first assignment to get started with running +% and publishing code in Matlab. Each problem has its own section (delineated +% by |%%|) and can be run in isolation by clicking into the particular section +% and pressing |Ctrl| + |Enter| (evaluate current section). +% +% To generate a pdf for submission in your current directory, use the following +% three lines of code at the command window: +% +% >> options.format = 'pdf'; options.outputDir = pwd; publish('assignment2.m', options) +% + +%% Problem 3 + +syms x; + +f = exp(x); +df = diff(f); +x_0 = 1; +err = zeros(10, 1); +h = zeros(10, 1); + +for i = 1:10 + h(i) = 10^(-i); + err(i) = abs(subs(df,x,x_0) - my_diff(f, x, x_0, h(i))); +end + +loglog(h, err) + +function approx = my_diff(f, x, x_0, h) + approx = (subs(f,x,x_0 + h) - subs(f, x, x_0)) / h; +end \ No newline at end of file diff --git a/hw2/assignment2.pdf b/hw2/assignment2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..671c3a782d1f61a7384a756c701910085aa42dba GIT binary patch literal 16607 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$h$ is exponentially nearer to 0), but at $10^{-9}$ this trend almost becomes the opposite due to loss of significant +digits when subtracting from $e^{x+h}$ $e^x$ and amplifiying this error by effectively multiplying that with exponentially +increasing powers of 10. \end{document}