Using computerized mathematical modeling and numerical analysis techniques to analyze and solve problems in the science and engineering domains is called scientific computing. Scientific problems include problems from various branches of science, such as earth science, space science, social science, life science, physical science, and formal science. These branches cover almost all the science domains that exist, from traditional science to modern engineering science, such as computer science. Engineering problems include problems from civil and electrical to (the latest) biomedical engineering.
In this chapter, we will cover the following topics:
Fundamentals of scientific computing
The flow of the scientific computation process
Examples from scientific and engineering domains
The strategy to solve complex problems
Approximation, errors, and related terms
Concepts of error analysis
Computer arithmetic and floating-point numbers
A background of Python
Why choose Python for scientific computing?
Mathematical modeling refers to modeling activity that involves mathematical terms to represent the behavior of devices, objects, phenomena, and concepts. Generally, it helps in better understanding of the behavior or observations of a concept, a device, or objects. It may help explain the observation and possibly prediction of some future behavior, or results that are yet to be observed or measured. Numerical analysis is an area of computer science and mathematics that designs, analyzes, and finally implements algorithms to numerically solve problems of natural sciences (for example, physics, biology, and earth science), social sciences (for example, economics, psychology, sociology, and political science), engineering, medicine, and business. There is a package and workflow named Python Dynamics (PyDy) that is used to study multibody dynamics. It is a workflow and a software package developed on top of the SymPy mechanics package. PyDy extends SymPy and facilitates the simulation of multibody dynamics.