%% Lecture 13

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% HW 12 - a short one - due April 29
%
% Bring a copy to my office or leave it in my mailbox in Bryan Hall 509
%
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% Plan for the last lecture
%
% 1) Let's finish off ODE with an example
%
% 2) Example of debugging - recursion again
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% 3) Example of C programming - similarities and differences

% 4) Brief review of the course




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% ODE example from the textbook
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% Designing a safety bumper - see the picture
%
% The bumper is designed such that the force that the bumper
% applies to the car is a function of the velocity v and the
% displacement x of the front edge of the bumper based on

% F = K v^3 (x+1)^3
% where F = 30 s-kg/m^5, a constant
%
% A car of a mass m of 1500 kg hits the bumper at v = 90 km/h.
%
% Problem: Determine and plot the velocity of the car as a
% function of its position for 0 <= x <= 3 m.

% First problem solving - what do we need to have?
% We need a formula to relate velocity v and position x.

% Q: what is the independent variable? what is the dependent variable?
% Q: what is the boundary condition?  
% Q: what is the range of the dependent variable?