Math 209 Lecture 3 - Numerical methods for solving ODEs part 1

In this lecture, we spend a large chunk of time going over HW problems regarding integration review, solving ODEs and money applications of first order ODEs--like compound interest. We then move on to numerical methods. Many times we cannot solve an ODE outright, but what we can do is approximate the value of a solution at a given point. We look to numerical methods to do this. The first one we will cover is Euler's Method, but to do that, we will need the aid of the linear approximation formula--which the text calls theorem 3.1. We explain where this formula comes from, and use it to make some numerical approximations of irrational numbers. Next time, we will turn this power towards making approximations of solutions to ODEs.