prerequisites for numerical analysis

[Zeuge]

What material should one have a good background in before taking a numerical analysis course? My course catalog lists only multivariate and vector calculus. How useful is vector calculus in NA?

 

[pphan]

You should have been exposed to a little bit of programming and completed a couse in linear algebra, DE.

Edit: also, depend on your school , you should know Matlab or Maple.

 

[Jacek Podlewski]

I agree it depends on the school, I for example had a fully theoretical, proof-based numerical analysis course (and actually appreciate that fact a lot) and did the programming in other classes.

Every mathematician should have some basic vector calculs in his toolbox, however, it is mostly used in typically physical applications. There shouldn't be a problem if you don't do it before numerical analysis , unless your NA syllabus includes some methods for PDEs, which is very unlikely.

I'd suggest a solid review of linear algebra and calculus, as you might frequently use e.g. Taylor expantions or some non-trivial estimates for function values or sequences. Some basics of topology and functional analysis might help (ever heard of Banach's Fixed Point Theorem?).

 

[Zeuge]

It's a mix of proofs and computational work in Matlab. Can you guys recommend me a good introductory text on numerical analysis that uses matlab? Or even just an introductory matlab book would be appreciated.

 

[Daniel Duffy]

As @Jacek mentioned, linear algebra is needed.

These 2 books I recommend

Dahlquist and Bjorck "Numerical Methods" (Dover)
Bronson "Matrix Operations" (Schaum)

I reckon it would be easy to program these in Matlab (or they already exist in Matlab).

Have you seen the MIT videos on matrix algebra by Prof Gil Strang?

 

[Zeuge]

As @Jacek mentioned, linear algebra is needed.

These 2 books I recommend

Dahlquist and Bjorck "Numerical Methods" (Dover)
Bronson "Matrix Operations" (Schaum)

I reckon it would be easy to program these in Matlab (or they already exist in Matlab).

Have you seen the MIT videos on matrix algebra by Prof Gil Strang?

Thanks for the recommendations. This is the course description:

This course covers direct and iterative methods of solution of linear algebraic equations and eigenvalue problems. Topics include numerical differentiation and quadrature for functions of a single variable, approximation by polynomials and piece-wise polynomial functions, approximate solution of ordinary differential equations, and solution of nonlinear equations.

Do you think the MIT lectures would be of some use for this?

 

[MathFinCS]

Thanks for the recommendations. This is the course description:

This course covers direct and iterative methods of solution of linear algebraic equations and eigenvalue problems. Topics include numerical differentiation and quadrature for functions of a single variable, approximation by polynomials and piece-wise polynomial functions, approximate solution of ordinary differential equations, and solution of nonlinear equations.

Do you think the MIT lectures would be of some use for this?

MIT lectures are very useful. So is Strang's book. (to learn linear algebra).

 

[Zeuge]

I just had another quick question -- how useful is numerical analysis in areas of quant finance outside derivatives pricing?