Learning Numerical Analysis for Physics Problems

[pc2-brazil]

Good afternoon,

I'm willing to study (teach myself) http://en.wikipedia.org/wiki/Numerical_analysis" , which I find very interesting, and which seems to be very useful for solving Physics problems (specifically, the motion of celestial bodies).
I have a background in Calculus (basically Limits, Derivatives and Integrals), but all my knowledge is self-taught.
My plan is to understand Numerical Analysis, specially Numerical Integration and Numerical Ordinary Differential Equations.
My question is: what background in Mathematics should I have in order to start doing this? In what sequence does it normally appear in courses?

 

[marcusl]

Well, usually you have already studied differential equations (DE's), multivariable calculus, and linear algebra. The first and last are obviously prerequisites to numerical methods for DE's.

Start your home-study program with numerical differentiation, since you know some calculus. I recommend Hamming's book "Numerical Methods for Scientists and Engineers" because it is clearly written, slow-paced, and application-oriented rather than math oriented. Integration is presented towards the end, so you may need to flip back to pick up the required introductory material.

 

[pc2-brazil]

Well, usually you have already studied differential equations (DE's), multivariable calculus, and linear algebra. The first and last are obviously prerequisites to numerical methods for DE's.

Start your home-study program with numerical differentiation, since you know some calculus. I recommend Hamming's book "Numerical Methods for Scientists and Engineers" because it is clearly written, slow-paced, and application-oriented rather than math oriented. Integration is presented towards the end, so you may need to flip back to pick up the required introductory material.

Thank you for your answer.
I found one exemplar of this book online, in a library here in Brazil, for a very cheap price. But it's a 1962 edition. Is it good?
Another question: What is the relation between Numerical Analysis and Perturbation Theory? Is the latter a subset of the former?