In this chapter, we will cover the following topics:

- Finding the root of a mathematical function
- Minimizing a mathematical function
- Fitting a function to data with nonlinear least squares
- Finding the equilibrium state of a physical system by minimizing its potential energy

**Mathematical optimization** is a wide area of applied mathematics. It consists of finding the best solution to a given problem. Many real-world problems can be expressed in an optimization framework. What is the shortest path on the road from point A to point B? What is the best strategy to solve a puzzle? What is the most energy-efficient shape of a car (automotive aerodynamics)? Mathematical optimization is relevant in many domains including ...

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