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Since mathematical models express our understanding of how nature behaves, we use them to validate our understanding of the fundamentals about systems (which could be processes, equipment, procedures, devices, or products). Also, when validated, the model is useful for engineering applications related to diagnosis, design, and optimization.

First, we postulate a mechanism, then derive a model grounded in that mechanistic understanding. If the model does not fit the data, our understanding of the mechanism was wrong or incomplete. Patterns in the residuals can guide model...

An Application–Oriented Introduction to Essential Optimization Concepts and Best Practices

Optimization is an inherent human tendency that gained new life after the advent of calculus; now, as the world grows increasingly reliant on complex systems, optimization has become both more important and more challenging than ever before. Engineering Optimization provides a practically–focused introduction to modern engineering optimization best practices, covering fundamental analytical and numerical techniques throughout each stage of the optimization process....