The last example shows the potential of combining numerical algorithms with symbolic calculations, allowing us thereby to

• Validate and verify our algorithms.
• Including concepts like unit testing, one has the possibility to test and validate several or all parts of the code.
• Validation and verification are then included naturally.
• The above example allows you to test the mathematical error of the algorithm for the trapezoidal rule by changing the number of integration points. You get trained from day one to think error analysis.