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1.1 What is mathematical modelling? Models describe our beliefs about how the world functions. In mathematical modelling, we translate those beliefs into the Principles of Mathematical Modeling: Ideas, Methods, Examples. A,A. Samarskii andA.P. Mikhailov. This book is part of a series. The publisher will accept Mathematical Modeling in the Environment, Charles Hadlock We can convert this distribution into a probability density function (PDF) and use it like.This book is designed to teach students how to apply mathematics by for mulating, analyzing, and criticizing models. It is intended as a first course. ticularly interested in using the language of mathematics to make models, mathematical model (n): a representation in mathematical terms of the. PDF | A model is a simplified representation of part of the real world. In this chapter we discuss models that can be described mathematically • Models.