Merge branch 'main' into 7-solve-problem-7

latex/assignment_1.tex

@@ -84,84 +84,22 @@
     
 \textit{https://github.uio.no/FYS3150-G2-2023/Project-1}
     
-\section*{Problem 1}
+\input{problems/problem1}
 
-% Do the double integral
+\input{problems/problem2}
-\begin{align*}
-    u(x) &= \int \int \frac{d^2 u}{dx^2} dx^2\\
-         &= \int \int -100 e^{-10x} dx^2 \\
-         &= \int \frac{-100 e^{-10x}}{-10} + c_1 dx \\
-         &= \int 10 e^{-10x} + c_1 dx \\
-         &= \frac{10 e^{-10x}}{-10} + c_1 x + c_2 \\
-         &= -e^{-10x} + c_1 x + c_2
-\end{align*}
 
-Using the boundary conditions, we can find $c_1$ and $c_2$ as shown below:
+\input{problems/problem3}
 
-\begin{align*}
+\input{problems/problem4}
-    u(0) &= 0 \\
-    -e^{-10 \cdot 0} + c_1 \cdot 0 + c_2 &= 0 \\
-    -1 + c_2 &= 0 \\
-    c_2 &= 1
-\end{align*}
 
-\begin{align*}
+\input{problems/problem5}
-    u(1) &= 0 \\
-    -e^{-10 \cdot 1} + c_1 \cdot 1 + c_2 &= 0 \\
-    -e^{-10} + c_1 + c_2 &= 0 \\
-    c_1 &= e^{-10} - c_2\\
-    c_1 &= e^{-10} - 1\\
-\end{align*}
 
-Using the values that we found for $c_1$ and $c_2$, we get
+\input{problems/problem6}
 
-\begin{align*}
+\input{problems/problem7}
-    u(x) &= -e^{-10x} + (e^{-10} - 1) x + 1 \\
-         &= 1 - (1 - e^{-10}) - e^{-10x}
-\end{align*}
 
-\section*{Problem 2}
+\input{problems/problem8}
 
-% Write which .cpp/.hpp/.py (using a link?) files are relevant for this and show the plot generated.
+\input{problems/problem9}
-
-\section*{Problem 3}
-
-% Show how it's derived and where we found the derivation.
-
-\section*{Problem 4}
-
-% Show that each iteration of the discretized version naturally creates a matrix equation.
-
-\section*{Problem 5}
-
-\subsection*{a)}
-
-\subsection*{b)}
-
-\section*{Problem 6}
-
-\subsection*{a)}
-
-% Use Gaussian elimination, and then use backwards substitution to solve the equation
-
-\subsection*{b)}
-
-% Figure it out
-
-\section*{Problem 7}
-
-% Link to relevant files on gh and possibly add some comments
-
-\section*{Problem 8}
-
-%link to relvant files and show plots
-
-\section*{Problem 9}
-
-% Show the algorithm, then calculate FLOPs, then link to relevant files
-
-\section*{Problem 10}
-
-% Time and show result, and link to relevant files
 
 \end{document}

latex/problems/problem1.tex

@@ -0,0 +1,35 @@
+\section*{Problem 1}
+
+% Do the double integral
+\begin{align*}
+    u(x) &= \int \int \frac{d^2 u}{dx^2} dx^2\\
+         &= \int \int -100 e^{-10x} dx^2 \\
+         &= \int \frac{-100 e^{-10x}}{-10} + c_1 dx \\
+         &= \int 10 e^{-10x} + c_1 dx \\
+         &= \frac{10 e^{-10x}}{-10} + c_1 x + c_2 \\
+         &= -e^{-10x} + c_1 x + c_2
+\end{align*}
+
+Using the boundary conditions, we can find $c_1$ and $c_2$ as shown below:
+
+\begin{align*}
+    u(0) &= 0 \\
+    -e^{-10 \cdot 0} + c_1 \cdot 0 + c_2 &= 0 \\
+    -1 + c_2 &= 0 \\
+    c_2 &= 1
+\end{align*}
+
+\begin{align*}
+    u(1) &= 0 \\
+    -e^{-10 \cdot 1} + c_1 \cdot 1 + c_2 &= 0 \\
+    -e^{-10} + c_1 + c_2 &= 0 \\
+    c_1 &= e^{-10} - c_2\\
+    c_1 &= e^{-10} - 1\\
+\end{align*}
+
+Using the values that we found for $c_1$ and $c_2$, we get
+
+\begin{align*}
+    u(x) &= -e^{-10x} + (e^{-10} - 1) x + 1 \\
+         &= 1 - (1 - e^{-10}) - e^{-10x}
+\end{align*}

latex/problems/problem10.tex

@@ -0,0 +1,3 @@
+\section*{Problem 10}
+
+% Time and show result, and link to relevant files

latex/problems/problem2.tex

@@ -0,0 +1,3 @@
+\section*{Problem 2}
+
+% Write which .cpp/.hpp/.py (using a link?) files are relevant for this and show the plot generated.

latex/problems/problem3.tex

@@ -0,0 +1,4 @@
+
+\section*{Problem 3}
+
+% Show how it's derived and where we found the derivation.

latex/problems/problem4.tex

@@ -0,0 +1,3 @@
+\section*{Problem 4}
+
+% Show that each iteration of the discretized version naturally creates a matrix equation.

latex/problems/problem5.tex

@@ -0,0 +1,6 @@
+
+\section*{Problem 5}
+
+\subsection*{a)}
+
+\subsection*{b)}

latex/problems/problem6.tex

@@ -0,0 +1,9 @@
+\section*{Problem 6}
+
+\subsection*{a)}
+
+% Use Gaussian elimination, and then use backwards substitution to solve the equation
+
+\subsection*{b)}
+
+% Figure it out

latex/problems/problem7.tex

@@ -0,0 +1,3 @@
+\section*{Problem 7}
+
+% Link to relevant files on gh and possibly add some comments

latex/problems/problem8.tex

@@ -0,0 +1,3 @@
+\section*{Problem 8}
+
+%link to relvant files and show plots

latex/problems/problem9.tex

@@ -0,0 +1,3 @@
+\section*{Problem 9}
+
+% Show the algorithm, then calculate FLOPs, then link to relevant files