MIME 260 Lecture : Lecture 3

• School: McGill University
• Department: Mining & Materials Engineering
• Course: MIME 260
• Professor: Mihriban. O. Pekguleryuz

Document Summary

In today"s lecture we start our discussion of rst order ordinary di erential equations. We rst focus on geometric methods to understand solutions and then solve analytically for solutions of separable rst order equations. We start by studying rst order equations in normal form, Of course if f (y, t) = f (t), then the problem we are solving is to nd the antiderivative of y (t). As long as f (t) is a continuous function we know that the solution to the problem can be found by integration, y (t) = f (y, t) (1. 1) y(t) = z f (t) dt. This we know from the fundamental theorem of calculus. Integrating both sides we nd, y (t) = sin t y(t) = cos t + c. Integration introduces the arbitary constant c. we call cos t + c the general solution of the ordinary di erential equation.