By now we have learned enough about using Python to make it a powerful graphing calculator. You should be able to use it to easily put numbers into symbolic solutions you find by hand. Notice that once you solve a problem once symbolically, and have Python enter the numbers, many other problems are as simple as changing the inputs in your python code. The more we learn about physics the more we learn that many problems are just the same problem with different words and numbers.
We have also learned to use Python to make plots. Plotting is a great tool for visualizing problems, but it can also be used to solve problems. Consider when we saw two moving objects with different position vs time graphs, and we wanted to find the time that they are at the same location. Or consider when we wanted to determine the highest point of a projectile, and its horizontal displacement at that moment. Both of these are problems where graphing can be a useful tool.
In addition to these, we have also seen other powerful applications such as numerical differentiation or Euler's method. Though these examples are designed to expose you to more powerful numerical methods that you may see more in the future, you may choose to use them to solve physics problems that are interesting to you. Euler's method is one that allows us to apply our constant acceleration physics to problems where the acceleration is no longer constant, enabling us to tackle more realistic problems.
For the remainder of this unit, we will direct our focus to new mathematical tools that will allow us to solve similar types of problems in more difficult settings. As our focus shifts, we will spend less of our focus on new Python skills. However, though our focus is shifting, don't feel that Python will be any less useful to us. Continue to use Python as your calculator for problems.
From here on there will be less included Python code as calculator work for the worked examples. However, we will still give advanced numerical methods examples as they are appropriate.