This text provides a very simple, initial introduction to the complete scientificcomputing pipeline: models, discretization, algorithms, programming,verification, andvisualization. The pedagogical strategy is to use one case study - an ordinarydifferential equation describing exponential decay processes - to illustrate fundamentalconcepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus andsome very basic knowledge about computer programming. Contrary to similar textson numerical methods and programming, this text has a much stronger focus onimplementation and teaches testing and software engineering in particular.