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+\documentclass[12pt,a4paper,pdftex]{exam}
+
+\usepackage[german]{babel}
+\usepackage{natbib}
+\usepackage{graphicx}
+\usepackage[small]{caption}
+\usepackage{sidecap}
+\usepackage{pslatex}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\setlength{\marginparwidth}{2cm}
+\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref}
+
+%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry}
+\pagestyle{headandfoot}
+\header{{\bfseries\large Exercise 2}}{{\bfseries\large Vectors}}{{\bfseries\large 18. Oktober, 2017}}
+\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email:
+  jan.grewe@uni-tuebingen.de}
+\runningfooter{}{\thepage}{}
+
+\setlength{\baselineskip}{15pt}
+\setlength{\parindent}{0.0cm}
+\setlength{\parskip}{0.3cm}
+\renewcommand{\baselinestretch}{1.15}
+
+\newcommand{\code}[1]{\texttt{#1}}
+\renewcommand{\solutiontitle}{\noindent\textbf{Solutions:}\par\noindent}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+\begin{document}
+\vspace*{-6.5ex}
+\begin{center}
+  \textbf{\Large Introduction to Scientific Computing}\\[1ex]
+         {\large Jan Grewe, Jan Benda}\\[-3ex]
+         Neuroethology \hfill --- \hfill Institute for Neurobiology \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\
+\end{center}
+
+The exercises are meant for self-monitoring and revision of the lecture
+topic. You should try to solve them on your own. Your solution should
+be submitted as a single script (m-file) in the Ilias system. Each
+task should be solved in its own ``cell''. Each cell must be
+executable on its own. The file should be named according to the following pattern:
+``variables\_datatypes\_\{lastname\}.m'' benannt werden
+(e.g. variables\_datentypes\_mueller.m).
+
+\begin{questions}
+  \question Create vector with the following contents:
+  \begin{parts}
+    \part Integer numbers ranging from 1 to 10.
+    \begin{solution}
+      \code{a = 1:10;}
+    \end{solution}
+    \part Integer numbers in the range 0 to 20 in steps of 2.
+    \begin{solution}
+      \code{a = 0:2:20;}
+    \end{solution}
+    \part \textbf{Descending} values ranging from 100 to 0.
+    \begin{solution}
+      \code{a = 100:-1:0;}
+    \end{solution}
+    \part In 10 steps from 0 to 1.
+    \begin{solution}
+      \code{a = 0:0.1:1;}
+    \end{solution}
+    \part In 11 steps from 0 to 1.
+    \begin{solution}
+      \code{a = 0:1/11:1;}
+    \end{solution}
+    \part In 50 steps from 0 to $2\pi$ ($\pi$ is known in Matlab as the constant
+    \code{pi}).
+    \begin{solution}
+      \code{a = 0:2*pi/50:2*pi;}
+    \end{solution}
+  \end{parts}
+
+  \question Calculations with vectors:
+  \begin{parts}
+    \part Create a vector \code{x = [3 2 6 8];}
+    \part What is the size of this vector? Use the functions  \code{size} and \code{length}. What is the difference between them?
+    \begin{solution}
+      \code{x = [3 2 6 8];
+        \\ disp(length(x));\\ 4\\ disp(size(x))\\ 1 4}
+    \end{solution}
+    \part What changes in \code{size} and \code{length} when you transpose the vector.
+    \begin{solution}
+      The length does not change, the size is inverted.
+    \end{solution}
+    \part Add 5 to each element of \verb+x+.
+    \begin{solution}
+      \code{disp(x + 5)}
+    \end{solution}
+    \part Multiply each element of \code{x} with 2;
+    \begin{solution}
+      \code{disp(x * 2)}
+    \end{solution}
+    \part Create a second vector (\verb+y = [4 1 3 5];+).
+    Make sure that \code{x} is in its original form.
+    \part Add both vectors \code{x + y}.
+    \begin{solution}
+      \code{y = [4 1 3 5]; \\disp(x + y)\\7     3     9    13}
+    \end{solution}
+    \part Subtract \code{y} from \code{x}.
+    \begin{solution}
+      \code{disp(x - y)\\-1     1     3    3}
+    \end{solution}
+    \part Multiply both vectors \code{x * y}.
+    \begin{solution}
+      \code{disp(x * y)\\Error using *. Inner matrix dimension must agree.}
+    \end{solution}
+    \part Explain the error message
+    \begin{solution}
+      * operator is the matrix multiplication. The inner dimensions must agree.\linebreak
+      \code{disp(size(x))\\1   4 \\disp(size(y)) \\ 1   4}\\
+      (m,n)*(n,o) w\"are ok.
+    \end{solution}
+    \part What needs to be done to make \code{mtimes} and 
+    \code{*} working?
+    \begin{solution}
+      y needs to be transposed: \code{x * y'}
+    \end{solution}
+    \part Multiply element-wise (\code{x .* y}) and assign the result to a new variable.
+    \begin{solution}
+      \code{z = x .* y;}
+    \end{solution}
+  \end{parts}
+
+  \question Creating vectors using helper functions:
+  \begin{parts}
+    \part Create a vector of the length 100 using the function
+    \code{ones} (see help). What is its purpose?
+    \begin{solution}
+      \code{ones(100,1)} creates a vector of the given size and fills it with 1.
+    \end{solution}
+    \part Create a vector of the length 100 using the function
+    \code{zeros} (see help). What is its purpose?
+    \begin{solution}
+      \code{zeros(100,1)} creates a vector of the given size and fills it with 0.
+    \end{solution}
+    \part Create a vector with 100 elements. All elements should have the value
+    4.5.
+    \begin{solution}
+      \code{ones(100, 1) * 4.5}
+    \end{solution}
+    \part Create a 100 element vector filled with random numbers (\code{rand},
+    see help).
+    \begin{solution}
+      \code{x = rand(100, 1)}
+    \end{solution}
+    \part Use the function \code{linspace} to create a 100 element vector with values between 0 and 1.
+    \begin{solution}
+      \code{x = linspace(0, 1, 100)}
+    \end{solution}
+  \end{parts}
+
+  \question Indexing in vectors:
+  \begin{parts}
+    \part Create a 100 element length vector with values ranging from 0 to 99.
+    \begin{solution}
+      \code{x = linspace(0, 99, 100);}
+    \end{solution}
+    \part Print the first, last, fifth, 24th and the second-to-last value.
+    \begin{solution}
+      \code{disp(x(1))\\ disp(x(end))\\ disp(x(5))\\ disp(x(24))\\ disp(x(end-1))}
+    \end{solution}
+    \part Print the first 10 values.
+    \begin{solution}
+      \code{x(1:10)}
+    \end{solution}
+    \part Print the last 10 values.
+    \begin{solution}
+      \code{disp(x(end-9:end))}
+    \end{solution}
+    \part Try to print the value at the zeroth position.
+    \begin{solution}
+      \code{x(0)\\ Subscript indices must either be real positive integers or logicals.}
+    \end{solution}
+    \part Try to access the value at the 110th position.
+    \begin{solution}
+      \code{x(110)\\ Index exceeds matrix dimensions.}
+    \end{solution}
+    \part Access the values at the positions 3, 15, and 42 with a single command.
+    \begin{solution}
+      \code{disp(x([3 15 42]))}
+    \end{solution}
+    \part Access 10 randomly selected values (used \verb+randi+ to create random indices).
+    \begin{solution}
+      \code{x(randi(100,10,1))}
+    \end{solution}
+  \end{parts}
+
+  \question Store some text in a valriable. The text should consist of at least two words (e.g. \code{x = 'some
+    text'}). Use indexing to print out the words individually.
+  \begin{solution}
+    \code{x = 'some text'; \\ disp(x(1:4))\\disp(x(6:end))}
+  \end{solution}
+
+\end{questions}
+
+\end{document}