# CAS and Numerical Computing

1. Mar 24, 2017

### mech-eng

Until now, I have always think of Matlab as CAS but now I know that it is not. So how do you understand this?

Thank you.

2. Mar 24, 2017

### Staff: Mentor

Matlab competes with Mathematica and it needs to have comparable features.

Folks using CAS systems are interested in working from theory to the equations in a particular situation and CAS can help with the symbolic manipulation.

In contrast engineers want to get actual numbers and charts displayed to aid in analyzing a physical system.

They are coming at a problem from different angles and use symbolics or numerical simulations to get what they need.

Last edited: Mar 24, 2017
3. Mar 24, 2017

### mech-eng

Should not it be "does not compete with Mathematica" because they are in different categories?

Do you mean "numerical calculation" is better for engineering than symbolic calculation, and so matlab is better for engineers than CAS?

Thank you.

4. Mar 24, 2017

### Staff: Mentor

Yes, many engineering problems start with taking measurements and making sense of them. As an example, you might measure the sound intensity in some environment and then use an FFT to determine the primary frequencies and then do some beam forming to find the direction of the sound source. Matlab works great for these kinds of numerical calculations.

5. Mar 24, 2017

### Staff: Mentor

They do compete for students, professionals and other engineer's money. it's why they have student editions to get in early and then when the students graduate they'll demand the product for work and then cost is far higher.

MATLAB has a symbolic math toolkit

https://www.mathworks.com/products/symbolic.html

6. Mar 24, 2017

### mech-eng

I am not familiar with concepts here. Would you please explain why taking units is related to numerical computing but not symbolic? As I know them, numerical computing is better for some cases and vice versa. They are just approaches to obtain a calcuation results and numerical methods/calculation are such as newton-raphson, bisection method and symbolic is calculus, taking a limit, taking a simple derivative or integral, again saying as I know them. I think numerical methods are harder from respect of both understand and application.

Thank you.

7. Mar 24, 2017

### Staff: Mentor

I don't know what else to say here.

Perhaps you can explain what you think CAS is vs numerical computing.

8. Mar 26, 2017

### Jamison Lahman

If you're an engineer, you may have a lot of data to process and need not worry about having absolute precision. In that case, you can use numerical analysis and take advantage of your CPU(s) computational power. The truncation errors with numerical methods will hopefully be much smaller than the maximum error tolerance for your task. If you're an engineer, you want to use the most efficient method, i.e. minimizing the computational time while maintaining some control over the error variability.

Numerical analysis, in some instances, is in fact derived from calculus. For example, the trapezoid rule is the fundamental theorem of calculus without the limit of h approaching 0. Moreover, symbolic math can be used alongside numerical analysis. For example, using Newton's method requires a derivative which is problematic to approximate numerically, so a symbolic derivative may be employed.

9. Nov 14, 2017

### Ian Mitchell

I think one of the more underrated pieces of software out right now is Maple. It's a solid piece of software and is fantastic at differential equations (which are indispensable everywhere). Not only that, but it can solve them numerically and symbolically. Also it has a package for nearly everything you could want. It comes preloaded with loads of different packages that can do anything from find solutions for the Einstein field equations and help you calculate amplitudes of Feynman diagrams to doing just some basic graphs.

But, it is either (A) ultra expensive or (B) hard to get your hands on. To get the personal edition, you need to shell out over 200 dollars, and to get the student discount, you need to basically give them your liver before they'll believe you to be a student.

But, if you can take the pain, it's worth it.