Numerical Methods Test Problems at Undergraduate Level

tomcenjerrym
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Can anyone here give me the examples of most test problems of Numerical Methods in the Mid and End of semester at undergraduate level?

What is the most test problems of Numerical Methods in the mid and end of semester at undergraduate level that probably must come out in the test?

I am taking Numerical Methods and Finite Element Method course on this semester.

As I was read here that Numerical Methods for Partial Differential Equation is the fundamental of the Finite Element Method, then I guess I should start to learn numerical methods first from here.

Btw, there are Numerical METHODS & Numerical ANALYSIS and Finite Element METHODS & Finite Element ANALYSIS. ANALYSIS & METHOD, what is the difference?
 
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I'd say Newton, Runge-Kutta and maybe simplex.
 

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