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RobinB27
2026-01-20 14:29:57 +01:00
parent 722ce04126 3c1cb6086c
commit d00ec94745
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4
semester3/numcs/numcs-summary.tex
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@@ -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/02_scipy.tex}
\input{parts/06_python/03_sympy.tex} \input{parts/06_python/03_sympy.tex}
\newsection
\section{Notes on the exam}
\input{parts/07_exam/00_intro.tex}
\end{document} \end{document}

9
semester3/numcs/parts/03_zeros/04_newton-one-d.tex
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@@ -23,9 +23,10 @@ falls $F(x^*) = 0$ und $F^(x^*) \neq 0$
\begin{code}{python} \begin{code}{python}
def newton_method(f, df, x: float, tol=1e-12, maxIter=100): def newton_method(f, df, x: float, tol=1e-12, maxIter=100):
""" Use Newton's method to find zeros, requires derivative of f """ """ Use Newton's method to find zeros, requires derivative of f """
iter = 0 k = 0
while (np.abs(df(x)) > tol and iter < maxIter): while (np.abs(f(x)) > tol and k < maxIter):
x -= f(x)/df(x); iter += 1 x -= f(x) / df(x)
k += 1
return x, iter return x, k
\end{code} \end{code}

7
semester3/numcs/parts/06_python/03_sympy-ex.py
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@@ -1,6 +1,6 @@
import sympy as sp import sympy as sp
a, b = (0, 1); a, b = (0, 1)
x, y = sp.symbols("x, y") # Create sympy symbols x, y = sp.symbols("x, y") # Create sympy symbols
f = x**2 + 3 * x - 2 # Create your function 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) # 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.hermite_poly(5) # Creates hermite poly of degree 5
sp.chebyshevt_poly(5) # Creates chebychev T (first kind) 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 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 # To print nicely rendered math expressions, you can use
sp.init_printing() sp.init_printing()

13
semester3/numcs/parts/07_exam/00_intro.tex Normal file
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@@ -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}.