Algorithms, variables, and control flow

Algorithms and Variables

An algorithm is a finite sequence of unambiguous steps that solves a problem, automating calculations from numerical integration to simulations.

A variable stores a value in RAM and can be updated anytime. Always initialise variables before use; uninitialised variables cause the most bugs in scientific code.

The CPU executes instructions sequentially or in parallel, while RAM holds active data and secondary storage persists data after power-off.

Control Flow and Pitfalls

Control flow structures dictate the order of execution. A conditional executes code when a condition is true, while a loop repeats a block of code.

For example, Euler numerical integration updates position and velocity over time steps: $x = x + v \times \text{dt}$

Common pitfall: The computer executes exact instructions, never intended logic. Off-by-one errors in loops and boundary conditions are where intent and execution diverge most.