Computer History Museum - A visit

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As a child, I used to imagine that when I grow up I will work in a bookstore. I will sell books and in spare time read all the books. Whenever I get a chance to visit a big bookstore or Library, I feel as If I have entered heaven, my spine is thrilled with electric spikes.
This August, I got a chance to visit San Jose (Was there to attend an international conference ASONAM 2016 in San Francisco). Feeling a bit adventurous I tried Airbnb for the first time and stayed with Venna, a very sweet lady. When we reached, she suggested that since I am into computers I should visit Computer History Museum, I accepted her suggestion and am very happy that I did. The museum kindled the child in me, and once again I was back to childhood (not that I have really grown old), seeing the Babbage difference engine, the PDP-1, the Jacquard loom, I was transcended into a new world. The museum showcased the history of computers bringing them back to life through their gigantic exhibits. The exhibition Rev…

Solving Differential Equations:One step Methods

A lot of problems in science and engineering involve solving differential equations pendulums, RLC circuits, diffusion and so on. An ordinary differential equation can be expressed as: 
Generally solution of this equation is of the form:

Here 'phi' is the increment function or slope and h is the step size.  Thus, an estimate of slope is used to extrapolate the new value y(i+1) when the previous value y(i) is known, over a distance h.  The methods which are based on above equation are called one step methods. They all only differ by the definition of increment function.
Solved Example:
Calculate y(2) for in the interval t=[0,2]. Given y(0)=1, for


Solution:
Consider h=1, here
Using Euler Method:


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