MATH 2243 Lecture Notes - Lecture 1: Ordinary Differential Equation
Document Summary
Differential equation- an equation with a derivative in it. Ordinary differential equation- a derivative where there is one unknown y(t), y" Partial differential equation- u(x,y,t) a differential equation with multiple variables. Systems of des- two or more differential equations to solve. Linear- derivatives of unknown functions only appear linearly in the de. A is 3rd order, b is 3rd order, c is 2nd order. A is linear, b is non-linear, and c is non-linear (xy) A is also a variable coefficient de (t^2) , while b is a constant coefficient de. There is an initial condition on the right side of the equation, the solution is one member of the family of curves. The solution to de we call integral curves. For any initial condition, we want to choose one of the integral curves as solutions to ivp. When that happens, we call integral curves general solutions. To a good approximation, mg: force due to gravity, g=9. 8 m/s .
