First, we will briefly discuss the various mathematical components that may occur in a scientific computation problem. We will also look for possible methods of solving problems. However, in this discussion, we will not look into the details of any method. In the later part, we will discuss the Python APIs relevant to these concepts.
The most common mathematical component that arises in most applications of scientific computing and applied mathematics is the system of linear algebraic equations. Generally, this system may occur due to approximations of nonlinear equations by linear equations or differential equations by algebraic equations.
A system of linear equations is a collection of simultaneous linear equations involving a set of variables, like this for example:
2 x1 + 1 x2 + 1 x3 = 1 1 x1 - 2 x2 - 1 x3 = 2 1 x1 + 1 x2 + 2 x3 = 2
This is a system of three linear equations with three unknown...