Euler, ODE1
CLEVE MOLER: Hello. I'm Cleve Moler, one of the founders and chief mathematician at the MathWorks. This series of videos is about solving ordinary differential equations in MATLAB. We can begin by recalling the definition of derivative. The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point. Our numerical approximations will rely upon the slope of the secant to the graph. That's a line through two points separated by a distance h. We'll have a lot to say about the step size h as we go along. What's important to realize is that as h goes to 0, the slope of the secant approaches the slope of tangent. The wiggly equals sign means approximately equal to. T0 is the point where we are finding the approximation. The value of the derivative at t0 is approximately equal to the slope of the secant. The slope of the secant is the change in the y value over the change in the t value. The change in y value is...