Programming and Numerics

The course consists of two parts: Introduction to procedure-oriented programming in Python (2/3) and Numerics (1/3). The Python skills will be generally applicable to many different problems, but as soon as the level is high enough, most of the examples will be directed towards problem-solving in the Numerics domain.

Procedure-oriented programming:

• Variables and data types.
• Input and output.
• Control structures: Sequence, conditional program flow and repetitions.
• Structuring and modularisation of programs; functions and modules.
• Data structures: Lists, tables, text strings, sets, tuples and dictionaries.
• Persistent storage of data, file input and output, and exceptions.
• Recursion.
• Python as a programming environment.
• Computation of N-dimensional matrixes
• Plot of functions.

Numerics:

• Numeric Integration of Functions: Trapezoidal rule, Simpson's rule, Adaptive Simpson's rule
• Newton's method for finding zeros of a real-valued function
• Gaussian elimination for solving systems of linear equations
• Numerical solution of ordinary differential equations
• Fixed-point iteration

Knowledge: By the end of the course, the candidate can:

• explain central concepts and mechanisms of procedural programming
• derive the result of small programs and functions
• explain number representation, precision of calculations, and the workings of central numerical methods

Skills: By the end of the course, the candidate can:

• use relevant tools for editing and running Python code.
• use viable data structures, control structures and decomposition in functions and modules to make well-structured, working code.
• apply some central numerical methods to solve calculation problems, and import and use numerical library functions in Python.
• identify causes for errors and lack of precision in programs, and correct the errors.
• demonstrate and explain your own program code to others.

Lectures, exercise lectures, mandatory exercises.