Merge branch 'main' of https://github.com/janishutz/eth-summaries

semester3/numcs/numcs-summary.tex

@@ -224,4 +224,8 @@ Complete code (with many visualisations), also for topics not covered in this su
 \input{parts/06_python/02_scipy.tex}
 \input{parts/06_python/03_sympy.tex}
 
+\newsection
+\section{Notes on the exam}
+\input{parts/07_exam/00_intro.tex}
+
 \end{document}

semester3/numcs/parts/03_zeros/04_newton-one-d.tex

@@ -23,9 +23,10 @@ falls $F(x^*) = 0$ und $F^(x^*) \neq 0$
 \begin{code}{python}
 def newton_method(f, df, x: float, tol=1e-12, maxIter=100):
     """ Use Newton's method to find zeros, requires derivative of f """
-    iter = 0
-    while (np.abs(df(x)) > tol and iter < maxIter):
-        x -= f(x)/df(x); iter += 1
+    k = 0
+    while (np.abs(f(x)) > tol and k < maxIter):
+        x -= f(x) / df(x)
+        k += 1
     
-    return x, iter
+    return x, k
 \end{code}

semester3/numcs/parts/06_python/03_sympy-ex.py

@@ -1,6 +1,6 @@
 import sympy as sp
 
-a, b = (0, 1);
+a, b = (0, 1)
 x, y = sp.symbols("x, y")  # Create sympy symbols
 f = x**2 + 3 * x - 2  # Create your function
 # In the below, for 1D differentiation, we can omit the symbol and just use sp.diff(f)
@@ -13,5 +13,10 @@ roots = sp.roots(f)  # Computes the roots of function f analytically
 sp.hermite_poly(5)  # Creates hermite poly of degree 5
 sp.chebyshevt_poly(5)  # Creates chebychev T (first kind) poly of degree 5
 sp.chebyshevu_poly(5)  # Creates chebychev U (second kind) poly of degree 5
+system = [f + y, x**3 + 2 * y, 3 * y - 2 * x]  # A system of equations
+sp.solve(system)  # Solves a system of equations algebraically
+sp.nsolve(
+    system, [x, y], (0, 1)
+)  # Input the system, the variables to solve in and interval
 # To print nicely rendered math expressions, you can use
 sp.init_printing()

semester3/numcs/parts/07_exam/00_intro.tex

@@ -0,0 +1,13 @@
+A few example questions that might show up in the exam are:
+\begin{itemize}
+    \item Reused homework tasks from the Moodle Quizzes and Code Expert (e.g. the GPS task)
+    \item Reused tasks from the mock exam
+    \item Doing quadrature on an $\arctan$ function, for which you have to use Gauss-Newton quadrature
+\end{itemize}
+Knowing \texttt{sympy} and having read through the docs of it (at least partially) can help tremendously.
+Additionally, try to use the script with a horrible (i.e. slow and not context-aware (i.e. it start search from the start)) PDF reader to get used to that.
+You can get such a search function in a PDF reader by installing Firefox ESR 72 (on which to my knowledge, Safe Exam Browser is based).
+
+For the multiple-choice tasks, if applicable, use properties of the formulas
+(e.g. for the Radau quadrature, use the fact that one of the edges of the interval has to be included and the weight computation is different for it)
+or otherwise use the Jupyter notebook to run functions that are already implemented in the script, or better yet, \texttt{sympy}.