MATH128 Lecture Notes - Lecture 10: Differential Equation, Delaware Route 1
Document Summary
Differential equation is equation involving an unknown function and one or more derivatives of that function, and possibly the underlying independent variable. Order of de is the order of the highest derivative. Solution of de is a function that solves the de for all underlying independent variables in some interval. Solution to a de is a family of functions. Initial-value problems provide (a,f(a)) value that the solving function must satisfy: thus we find a specific, unique solution to ivp, direction fields, euler"s method this approximates numerical solution to any first-order de. Specify step size create chart depicting x, y, and other derivatives yn+1 = yn + f(xn,yn) x where y = f(x,y: no systematic technique works to solve all de, three useful techniques we will study.
