Question on numerical analysis prerequisites

In summary, a lack of real analysis prior to NA might not be a problem, but not having it would prevent you from having a deeper understanding of the material.
  • #1
cue928
130
0
First of all, I apologize if this is in the wrong section. I would like to know what background is needed to be properly prepared for numerical analysis. I will have had calculus III (leaving C-4 left), ordinary differential equations. I'd be taking linear algebra concurrently.

Also, does one need analysis for mathematical probability? It's not explicitly listed as an option but I've glanced at the book and it appears to at least touch on measure spaces, which makes me think I'd be at a disadvantage for lacking analysis. Interestingly enough, even our class which teaches proof is not required for it either.

I ask on both of these because I don't think our prerequisites are properly lined out. I had to do a lot of extra work in ODE to make up for my lack of linear algebra. Thanks!
 
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  • #2
Unfortunately, there are many different topics that ma or may not be included in "numerical analysis" so it is very difficult to say what prerequites a particular numerical analysis course will require. It sounds to me like you have all of the basic ones but the best thing to do is to talk to the person who will be teaching the course.
 
  • #3
I was just surprised to look at the book and see topics from calculus IV, such as double integrals, partial derivatives, etc. I had to spend a ton of extra time in a previous class learning things that I should have learned prior to taking it if the prerequisites had been set up correctly, so my appetite to do that again is really pretty low.
 
  • #4
Well, NA does concern itself with making calculations and using algorithms to evaluate integrals and calculate derivatives. NA provides the computational tools for other branches of science and engineering to use to obtain useful results. Solving linear systems and solving differential equations also occur frequently, so you should know some of the basics about those branches of analysis for your NA courses, so that you can understand how the numerical techniques from the NA course are applied.
 
  • #5
Just from looking at the book, it looks like a fascinating subject. But my course load will be much heavier in the fall that it was for example when I took ODE, so I want to make sure that I have what I need, or close thereto, because I simply won't have the time to play catch-up on prior stuff.

Is a lack of real analysis prior to NA a serious problem or a bump in the road? Would it be something that's not critical, but not having it would prevent me from having a deeper understanding of the material? I don't think the professor is in at all over the summer so I'm on my own in trying to make a determination on this.
 

Related to Question on numerical analysis prerequisites

1. What is numerical analysis?

Numerical analysis is a branch of mathematics that deals with the development and implementation of numerical algorithms to solve mathematical problems. It involves using computers to perform calculations and approximations to obtain numerical solutions.

2. What are the prerequisites for studying numerical analysis?

The prerequisites for studying numerical analysis typically include a strong foundation in calculus, linear algebra, and differential equations. It is also helpful to have knowledge of computer programming and mathematical software such as MATLAB or Python.

3. Why is numerical analysis important?

Numerical analysis plays a crucial role in various fields such as engineering, physics, economics, and computer science. It allows for the efficient and accurate solution of complex mathematical problems that cannot be solved analytically. It also enables the analysis and interpretation of data from experiments and simulations.

4. How is numerical analysis different from theoretical mathematics?

Theoretical mathematics focuses on proving theorems and establishing mathematical truths, while numerical analysis is more concerned with finding practical solutions to mathematical problems. Numerical analysis involves using numerical methods and algorithms to approximate solutions, while theoretical mathematics relies on mathematical proofs.

5. What are some common applications of numerical analysis?

Numerical analysis has many practical applications, such as solving differential equations in physics and engineering, optimizing financial portfolios in economics, and simulating fluid dynamics in computer science. It is also used in data analysis, image processing, and cryptography.

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