The previous chapter described how to use Sage to solve many difficult problems in symbolic mathematics. While this capability is very useful, many real-world problems do not lend themselves to symbolic computation. Some differential equations don't have closed-form solutions, and not every integral can be computed in terms of elementary functions. In other cases, a function value may have to be computed from a look-up table that was derived from experimental results, which precludes symbolic computation. In this chapter, we will demonstrate some of the tools in Sage that allow us to solve problems numerically.
We will learn how to:
Find the roots of an equation
Compute integrals and derivatives numerically
Find minima and maxima of functions
Compute discrete Fourier transforms, and apply window functions
Numerically solve an ordinary differential equation (ODE), and systems of ODEs
Use optimization techniques to fit curves and find minima
Explore the probability...