How much numerical analysis do we need?

In summary, it depends on what you will be doing, but generally speaking, taking as much numerical analysis as possible in undergrad is a good idea.
  • #1
proton
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for each of these careers: engineer, physicist, mathematician, how much numerical analysis is necessary? is just learning mathematica sufficient? or do you need at least a full class in numerical analysis?
 
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  • #2
The answer of course depends on what you will be doing...
 
  • #3
so since I'm unsure whether to go into theory or industry, it'd be best to take as much numerical analysis as possible in undergrad?
 
  • #4
But numerical analysis is so boring.
 
  • #5
will.c said:
But numerical analysis is so boring.

yea that's why id rather put it off until my last semester of undergrad, so my grade won't matter to grad school admissions

oh i forgot to mention that I'm starting my physics research this summer, and my only programming experience is a class in c++. so would taking a numerical analysis seminar that teaches mathematica be really helpful?
 
  • #6
proton said:
for each of these careers: engineer, physicist, mathematician, how much numerical analysis is necessary? is just learning mathematica sufficient? or do you need at least a full class in numerical analysis?

Yes simply because you shouldn't be one of those people that uses canned software without knowing what it's doing. The computer is not supposed to be a magical black box. When you solve a problem numerically, the effectiveness and appropriateness of the algorithm you use is extremely important.

And say you started doing research in an area where you could just use a program developed by someone else... and then later you want to solve a different problem that program can't do? Will you be able to dyi or will you have to hope that you can find another program that you can buy to get the job done?
 
  • #7
proton said:
for each of these careers: engineer, physicist, mathematician, how much numerical analysis is necessary?

Of course it depends on what you will be doing, but generally speaking the answer is: a lot.
The problem with problems in the real world is that they are almost never as "neat" as the questions you are asked in courses at university. People tend to forget that analytical solutions to e.g. PDEs are actually quite rare, this is especially true in engineering.
Physicists tend to do a bit of both: we use analytical tools (pen and paper) to understand a problem, usually by making simplifying assumptions (e.g. weak perturbations etc), but when we need actual numbers we often have to use a computer.

However, note that "numerical analysis" can mean different things. As far as I remember we spent most of the time on things like error estimations in my NA course which in retrospect is perhaps good to know but not something I use very often (at least not directly); we learned most of the "practical" stuff -like how to actually solve PDEs etc- in various math courses (e.g. the PDE course was mostly about FEM).
 
  • #8
alright, i get the message, we need lots of numerical analysis.

anyways , I'm starting my physics research this summer, and my only programming experience is a class in c++. so would taking a numerical analysis seminar (which only has 1-hr lecture each week)that teaches mathematica be really helpful? if not, i might as well drop the class
 
  • #9
proton said:
alright, i get the message, we need lots of numerical analysis.

anyways , I'm starting my physics research this summer, and my only programming experience is a class in c++. so would taking a numerical analysis seminar (which only has 1-hr lecture each week)that teaches mathematica be really helpful? if not, i might as well drop the class

I think that it can be useful. Why don't you ask your adviser?
 
  • #10
numerical analysis is fun. i think it's so fun I'm going to drop the physics major and just get a computational science degree.
 

1. How is numerical analysis used in scientific research?

Numerical analysis is used to solve complex mathematical equations or problems that have no analytical solution. It involves using numerical methods to approximate the solution to these problems.

2. What are the benefits of using numerical analysis in scientific research?

Numerical analysis allows scientists to solve complex problems that would be impossible to solve analytically. It also provides a more accurate and precise solution compared to manual calculations, especially for large datasets.

3. What are some common numerical methods used in scientific research?

Some common numerical methods used in scientific research include interpolation, extrapolation, numerical integration, root finding, and optimization techniques such as gradient descent.

4. How much knowledge of mathematics is required for numerical analysis?

A strong foundation in mathematics, particularly in calculus and linear algebra, is necessary for understanding and using numerical analysis effectively. However, with the availability of software and tools, one does not need to have advanced mathematical skills to apply numerical analysis in their research.

5. Can numerical analysis be applied to all scientific fields?

Yes, numerical analysis can be applied to a wide range of scientific fields, including physics, chemistry, biology, engineering, and economics. It is a versatile tool that can be used to solve complex problems in any field that involves mathematical equations or models.

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