Which book on Numerical Analysis should I use?

[pc2-brazil]

Good evening,

I have a background on one-variable Calculus and I am currently self-studying Calculus from Leithold's "The Calculus with Analytic Geometry". When I finish the part about infinite series, I plan to start studying Numerical Analysis.
I would like to ask what book on Numerical Analysis I should use.
Hamming's "Numerical Methods for Scientists and Engineers" seems to be highly regarded, but I don't know what is the necessary mathematical background for reading it. Probability seems to be also necessary for understanding its content. I don't find anywhere in the Internet information about prerequisites for reading this book.
My question is, basically: what book could suit my needs? Is there any more mathematics knowledge necessary for studying Numerical Analysis?

Thank you in advance.

 

[qspeechc]

I am not familiar with Hamming, but it is so cheap and the rating is so high I'd say get it anyway. Even if you are not ready now you will be shortly. Dover books are generally reliable.
A book I used for numerical analysis, though it was not the required book for the course, was Hildebrand "Introduction to Numerical Analysis", which can get quite detailed, but I think it is a good book nonetheless.
You can probably get a few Dover books cheaply.

 

[pc2-brazil]

I am not familiar with Hamming, but it is so cheap and the rating is so high I'd say get it anyway. Even if you are not ready now you will be shortly. Dover books are generally reliable.
A book I used for numerical analysis, though it was not the required book for the course, was Hildebrand "Introduction to Numerical Analysis", which can get quite detailed, but I think it is a good book nonetheless.
You can probably get a few Dover books cheaply.

Thank you for the suggestion. There are good reviews of this book at Amazon.
But I have doubts about what are the prerequisites for reading books on Numerical Analysis. It seems to require Probability as a prerequisite (because all the books seem to use probability distribution when talking about approximation and error). Also, I gave a look at this book in Google Books and, in the introduction, there is a part where it mentions "Weierstrass theorem", which seems to be a theorem from advanced Calculus (Mathematical Analysis?). I'm not sure whether the author assumes that the reader already knows these theorems or if they are introduced in Numerical Analysis.
So, I would like to know exactly what I should be familiar with before starting to study Numerical Analysis.

 

[qspeechc]

Let me expand on what I said earlier.

Generally at this level numerical analysis books require: calculus of one variable, sometimes vector calculus; a lot about series (series exapnsions etc.), which you do in calculus anyway; probability (sometimes).

Sometimes the books develop the concepts like probability, in other words teach it to you, sometimes not. It doesn't matter. You already know single-variable calculus, which is most of the prerequisites. In a short while you will know vector calculus. The essentials of probability you can pick up on your own in a relatively short time. Therefore you have most of the background needed already. That is why I said "Even if you are not ready now you will be shortly."

Go ahead and get Hamming, is my suggestion.

 

[pc2-brazil]

Let me expand on what I said earlier.

Generally at this level numerical analysis books require: calculus of one variable, sometimes vector calculus; a lot about series (series exapnsions etc.), which you do in calculus anyway; probability (sometimes).

Sometimes the books develop the concepts like probability, in other words teach it to you, sometimes not. It doesn't matter. You already know single-variable calculus, which is most of the prerequisites. In a short while you will know vector calculus. The essentials of probability you can pick up on your own in a relatively short time. Therefore you have most of the background needed already. That is why I said "Even if you are not ready now you will be shortly."

Go ahead and get Hamming, is my suggestion.

Thank you for the clarification.
So, I think I will get Hamming and/or Hildebrand's book.
By the way, I'm not very familiar with Dover publications, but I have one book from it ("Fundamentals of Astrodynamics") which I find very good.

 

[qspeechc]

Oh goodness, I forgot to add the most important things. Numerical methods is almost entirely about differential equations, so will need to know about those too, which means you need to know some linear algebra as well. I can't believe I forgot those! Sorry about that...

 

[pc2-brazil]

Oh goodness, I forgot to add the most important things. Numerical methods is almost entirely about differential equations, so will need to know about those too, which means you need to know some linear algebra as well. I can't believe I forgot those! Sorry about that...

No problem, I'm aware of the fact that Linear Algebra and differential equations are important.
I will get to differential equations at the end of the Calculus book. But I tend to think that differential equations are more important when the discussion of numerical integration and differentiation arises, isn't it?
I think Linear Algebra it shouldn't cause me much trouble, because I'm already familiar with matrices, determinants and systems of linear equations (mostly from high-school mathematics).

 

[qspeechc]

No problem, I'm aware of the fact that Linear Algebra and differential equations are important.
I will get to differential equations at the end of the Calculus book.

Usually calculus books say very little about differential equations, only for the simplest seperable equations, which is a small part of (ordinary, meaning there are no partial derivatives) differential equations so you may want to study them anyway. Most differential equations books cover linear algebra as well, so that should be fine.

But I tend to think that differential equations are more important when the discussion of numerical integration and differentiation arises, isn't it?

Numerical methods for differential equations is numerical integration, more or less, for what is solving a differential equation but integration (in a sense)? The problems of numerically differentiating and integrating are different problems anyway, that of numerical solutions to differential equations is a very large one.