What is Numerical Analysis?

[Jin314159]

I'll be taking Numerical Analysis in the fall and I honestly have no idea what it's about. Can anyone tell me what the main topics in Numerical Analysis Are?

Thanks.

[ahrkron]

It probably refers to the study of methods to numerically solve math problems (I say "probably" because some times different universities emphasize different aspects of a course, and because I haven't looked too hard for a "stadard" definition).

The type of things that it may cover: methods for finding solutions to simultaneous equations, roots of functions, maximization tools, numerical solution of partial differential equations, numerical integration, Monte Carlo methods, sampling.

Sometimes people call all of this "numerical methods", and reserve the name "numerical analysis" for a course more focused on convergence, accuracy and complexity of the algorithms involved.

[fourier jr]

I haven't taken these courses since I'm more into pure math; here are the calendar entries though:
(part 1, sept-dec)
An introduction to selected topics in Numerical Analysis. Typical areas covered: error analysis, roots of equations, systems of linear equations, linear programming, interpolation, numerical integration, and ordinary differential equations.

(part 2, jan-apr)
An introduction to selected topics in Numerical Analysis. Typical areas covered: ordinary differential equations, numerical differentiation, approximation of functions, iterative methods for linear equations, eigenvalues and eigenvectors, systems of nonlinear equations, boundary-value problems and partial differential equations.

http://web.uvic.ca/calendar2004/CDs/CSC/349A.html
http://web.uvic.ca/calendar2004/CDs/CSC/349B.html

If you've done 1st-year calculus, you've already seen at least one numerical method I think. I remember rectangular, trapezoidal & Simpson's approximation of definite integrals. That's pretty much what 'numerical methods' is all about; once you've failed to find an exact solution (3.1415926535... vs. Pi) you use a numerical method to find a solution that's 'close enough' to be useful. Or maybe a numerical solution would be faster or easier to deal with than finding an exact solution. Anyway, that's what numerical methods do, as far as I know.

[Jin314159]

Much thanks to Fourier and Ahrkron. I looked at course description for the Numerical Analysis that I will be taking and this is what it says:

"Programming for numerical calculations, round-off error, approximation and interpolation, numerical quadrature, and solution of ordinary differential equations. Practice on the computer."

Sounds interesting.

[HallsofIvy]

While a large part of the course will be about learning and possibly "implementing" algorithms (the "easy" part), some of it will no doubt concern accuracy and stability of the methods.