We covered a lot of material in this chapter. Sage makes it fast and easy to do tedious symbolic tasks like computing integrals and Laplace transforms for complicated functions. In fact, the hardest part is making sure that you have defined your functions and expressions correctly.
Specifically, we covered:
Working with symbolic expressions
Manipulating symbolic expressions to put them in the form you want
Performing basic calculus operations like computing limits, derivatives, and integrals
Finding series representations, and computing their sums
Computing Laplace transforms
Finding exact solutions to ordinary differential equations
Sage has powerful symbolic capabilities. However, many real-world problems simply don't have analytical solutions. In other cases, Sage might not be able to find an analytical solution, even when it exists—software is never perfect! Some symbolic operations may consume so much memory or CPU time that they become impractical. Integrals, systems of equations,...