Help with 1D Stress FE Model Analysis

[Jonny6001]

Hello, I am reading a book about finite elements with regards to stress analysis. I'm pretty sure the book is full of mistakes, which makes following and doing the examples fairly difficult.
I have posted a 1D analysis from the book, I'm not even sure how he comes up with some of the numbers in the calculations.

I do understand the method but what hasn't exactly "clicked" is the sign convention or the displacement of each node equating to the change in element length. The author has (u1-u2), then on the last element he switches to (u4-u3), is there a reason for this or is it because u4 is the last node?

Would someone mind having a really quick look at the images I posted to give their oppinion. But definitely his answers do not satisfy the simulataneous equations.

Thanks a lot for your time.

http://img2.imageshack.us/img2/3816/scan0001xo.jpg
http://img203.imageshack.us/img203/8407/scan0002r.jpg
http://img242.imageshack.us/img242/3311/scan0003e.jpg
http://img43.imageshack.us/img43/5510/scan0004al.jpg

I'm sorry, I've posted this in the general maths forum too but thinking about it, I think this area is more relevant.

 

[darkside00]

looks right to me. The author is specifying 4 nodes for his approximation.
u1 being the fixed end, u2 and u3 averaged in between, and u4 being the free end. Really, you can use as much nodes as you want, the more nodes, the more accurate. Although, The more nodes, the more stiffness k to calculate and a larger matrix to solve.
Also, your calculating with the element (eg. u2-u1), not the single node position

 

[Jonny6001]

i understand that,but how can his answers be correct if they don't satisfy the simultaneous equations?