Course Template
Numerical Integration & Differentiation in Applications (5 Modules)
Numerical Integration and Differentiation with Python.
Educational Objective
This course template conveys central procedures of numerical integration and numerical differentiation through concrete application problems from measurement data and function models. It builds professional competencies in the selection, implementation, and evaluation of numerical methods, particularly in comparing different approximation procedures and their error characteristics. The template combines mathematical modeling with clearly structured algorithmic implementation in Python and makes visible how data, formulas, and implementation condition each other. Professionally, it is to be assigned to the area of numerical methods, data-oriented analysis, and application-related modeling.
Competency Focus
- Implementation of Trapezoidal Rule, Simpson’s Rule, Gauss-Legendre Quadrature, and Adaptive Trapezoidal Rule for Numerical Integration
- Numerical Derivation of Discrete Data with Forward, Backward, and Central Difference
- Error analysis and step size studies for evaluating accuracy and method selection
- Processing and evaluation of CSV data from measurement files with pandas and NumPy
- Comparison of own implementations with reference values or library functions
- Visualization of error trends, measurement series, and numerical results with Matplotlib
- Interpretation of numerical results in application contexts such as distance, energy, and work
Structure of the modules
Distance from sensor data: Trapez rule
This module introduces numerical integration of discrete measurement data using the trapezoidal rule to calculate a distance from velocity values.
Simpson's Rule: Energy from Power-Time Series
This module deepens the integration of equidistant time series using Simpson's rule and orders the results methodically through a comparison of methods.
Gauss Quadrature: Error vs. Nodes
This module expands the method canon with the Gauss-Legendre quadrature and focuses on the connection between node number and approximation error.
Numerical Derivative: Error vs Step Size h
This module deals with the numerical differentiation of discrete data and makes the effects of different difference procedures and step sizes visible.
Adaptive Trapez Rule: Work from Force Curve
This module introduces adaptive refinement strategies and connects accuracy requirements with effort and convergence behavior of numerical integration.
The clearly structured modules create transparent learning objectives and can be easily integrated into existing lesson plans for data analysis and numerics.
Test the template in your own teaching and adapt the modules specifically to your group and subject-specific focal points.