MATLAB and Mathematica both are good for symbolic calculations. I suggest you use them both. Because some commands are in Mathematica but not in MATLAB and vice versa.
If you are dealing with analytical solution use Maple, Instead if you are interested in numerical go with Mathematica. In my experience, Plot options of Mathematica are better than Maple.
MATLAB and Mathematica both are good for symbolic calculations. I suggest you use them both. Specifically, if you compare between the two or more waves or others things, then MATHLAB is better than mathematica. Saurabh Tomar
I definitely prefer Maple. In particilar for calculations on differential geometry, Lie groups and differential equations. It is almost like pen and paper. On the down side, there is very little help outside the very well documented help page. Specially for high quality print output, which is amazing when you get the command combo right.
I think it is a somewhat subjective question. It depends on which platform each one is more used to or is more skilled. On the other hand, Maple and Mathematica originally emerged as CAS (Computer Algebra System) while Matlab began as a fundamentally numerical system (IMHO).
I have been working in all three software for years. As all three software are Computer algebra systems so have same functionality upto some points. The difference occurs when we seek some built-in functions to do our job easily. So, for a mathematician or physicist researcher, Maple provides more built-in function what we use in our research. Although, you can create your own function in any of one. Other things is being easy to write code and in it Mathematica is better than Maple and Matlab lies between them. So look what you want more handy to do codes or using the more built-in functions.
I used Maple and Matlab . But I found Mathematica is the best with me. It is easy to do calculations and plot with quality and quickly. In the end, this software different from person to person. For any helpful, I will be ready.
Maple is undisputed king of computation especially related to mathematics. Its Differential Geometry and Jet Calculus packages are way ahead of Mathematica.
MATLAB is mostly used in engineering, not much useful in advance mathematics.
In my case, I prefer Matlab and Mathematica. I think that all depend on the Libraries and the skill in the actions you want to employ, program and execute.