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Python Numerics and Computations

This GitHub repository comprises a set of Python scripts addressing a diverse range of problems in numerical computing. Whether you are getting started with Python programming or delving into advanced numerical methods, this repository serves as a comprehensive resource.

Topics Covered:

Python Basics:

  • Introduction to Python: Einführung in Python
  • Data Types: Datentypen
  • Functions: Funktionen
  • Programs: Programme

Numerical Fundamentals:

  • Computer Arithmetic: Rechnerarithmetik
  • Machine Numbers:
    • Floating-point and Fixed-point Numbers: Gleitpunkt- und Festpunktzahlen
    • Single-precision, Double-precision, IEEE Formats: single-precision, double-precision, IEEE Formate
  • Approximation and Rounding Errors: Approximations- und Rundungsfehler
  • Conditioning: Konditionierung

Numerical Problem Solving:

  • Numerical Solution of Root-finding Problems: Numerische Lösung von Nullstellenproblemen
    • Fixed-point Iterations: Fixpunktiterationen
    • Newton's Method: Newton-Verfahren
  • Numerical Solution of Linear Systems of Equations: Numerische Lösung linearer Gleichungssysteme
    • Gaussian Algorithm with Error Propagation and Pivoting: Gauss-Algorithmus mit Fehlerfortpflanzung und Pivotisierung
    • Matrix Triangularization: Dreieckszerlegung von Matrizen
    • Error Analysis and Complexity Estimation: Fehlerrechnung und Aufwandabschätzung
    • Iterative Methods: Jacobi / Gauss-Seidel: Iterative Verfahren

Advanced Topics:

  • Introduction to Complex Numbers: Einführung in die komplexen Zahlen
  • Numerical Computation of Eigenvalues and Eigenvectors: Numerische Berechnung von Eigenwerten und Eigenvektoren