Practical Mathematical Modeling

No model is perfect! Models are only approximations to reality, and as such, models always present deviations (or error) from reality. However, such deviation or error does not necessarily imply that the model is wrong. It simply indicates that the model is incomplete. Even the properties of those deviations provide valuable information about the system being modeled. This book presents mathematical modeling from a practical perspective, where error is an important part of the model, and plays a key role in the continuous improvement of the models. Under this perspective, models are tools that help us understand our reality. This approach also integrates all different types of mathematical models into a single theoretical framework. Various step-by-step examples are included to illustrate the basic concepts presented. All calculations are performed in R language, and the corresponding codes are included.