Most phenomena involved in physical systems are governed by well-defined scientific laws. These laws correlate different properties and provide insights to the states of a system and processes it undergoes. Mathematical models can therefore be derived based on the laws, allowing scientists and engineers to explain what has happened or predict what will happen.

If a mathematical model is too complicated to solve, a computer will be needed.
Thus, we have a **computational model** that approximates the solution using some
numerical algorithms. Computational models are now increasingly important parts of
computer-aided design (CAD) packages, which are in the tool box of almost every engineer
whose job involves research and development (R&D). Computational models are often called
**numerical simulations**. So we will use the two terms interchangably.

Today's students need to have a fundamental understanding of what computational models are and how they can be used to accelerate R&D processes.