From 2765f4932063bf61c061f5736c9ac06cf9d4b0b6 Mon Sep 17 00:00:00 2001 From: Basil Feitknecht <114588139+bfeitknecht@users.noreply.github.com> Date: Sun, 18 Jan 2026 14:30:02 +0100 Subject: [PATCH 1/6] Fix Newton's Method The old one incorrectly uses the absolute value of the derivative --- semester3/numcs/parts/03_zeros/04_newton-one-d.tex | 11 +++++++---- 1 file changed, 7 insertions(+), 4 deletions(-) diff --git a/semester3/numcs/parts/03_zeros/04_newton-one-d.tex b/semester3/numcs/parts/03_zeros/04_newton-one-d.tex index 208c701..712e7cb 100644 --- a/semester3/numcs/parts/03_zeros/04_newton-one-d.tex +++ b/semester3/numcs/parts/03_zeros/04_newton-one-d.tex @@ -23,9 +23,12 @@ 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 + fx = f(x) + dfx = df(x) + while (np.abs(fx) > tol and k < maxIter): + x -= fx / dfx + k += 1 - return x, iter + return x, k \end{code} From 8d8fc8bf7b9bef7f25cad3afb411efd2aa5943ff Mon Sep 17 00:00:00 2001 From: Basil Feitknecht <114588139+bfeitknecht@users.noreply.github.com> Date: Sun, 18 Jan 2026 14:36:24 +0100 Subject: [PATCH 2/6] Fix my silly mistake (no reevaluation of functions) --- semester3/numcs/parts/03_zeros/04_newton-one-d.tex | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/semester3/numcs/parts/03_zeros/04_newton-one-d.tex b/semester3/numcs/parts/03_zeros/04_newton-one-d.tex index 712e7cb..3122c39 100644 --- a/semester3/numcs/parts/03_zeros/04_newton-one-d.tex +++ b/semester3/numcs/parts/03_zeros/04_newton-one-d.tex @@ -24,10 +24,8 @@ falls $F(x^*) = 0$ und $F^(x^*) \neq 0$ def newton_method(f, df, x: float, tol=1e-12, maxIter=100): """ Use Newton's method to find zeros, requires derivative of f """ k = 0 - fx = f(x) - dfx = df(x) - while (np.abs(fx) > tol and k < maxIter): - x -= fx / dfx + while (np.abs(f(x)) > tol and k < maxIter): + x -= f(x) / df(x) k += 1 return x, k From e0ccc4418d7babc3633b7cc056d58562f268e708 Mon Sep 17 00:00:00 2001 From: Basil Feitknecht <114588139+bfeitknecht@users.noreply.github.com> Date: Mon, 19 Jan 2026 00:36:02 +0100 Subject: [PATCH 3/6] Fix docstring From 26134eb63ddfa3fe8cc1019918b3fc881fb417a1 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Mon, 19 Jan 2026 07:05:39 +0100 Subject: [PATCH 4/6] [NumCS] Compile changes by @bfeitknecht --- semester3/numcs/numcs-summary.pdf | Bin 1468072 -> 1468152 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/semester3/numcs/numcs-summary.pdf b/semester3/numcs/numcs-summary.pdf index b0043dbb01e71a4f4d201b563e832df42d4c6541..7ba4c6910ff2ed51aa5a24c310ad30e450ec04eb 100644 GIT binary patch delta 83265 zcmV)JK)b)F%~|-(S+I5z0ZOxX5)2OnvxaQBlZPQHm%*A0Dzn=m778OBtxvws$|eh5 zb%j&+#FN7O;I1AHY=^(Hqqx`v=Rcu^^;^bWL-vJ76GxU>@V-vIaM6445 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+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() diff --git a/semester3/numcs/parts/07_exam/00_intro.tex b/semester3/numcs/parts/07_exam/00_intro.tex new file mode 100644 index 0000000..d2c895e --- /dev/null +++ b/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)) 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}. 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