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Hello.
There are some goo freesoftwares, some are also free source.
Scilab - replaces matlab
Maxima- replaces Mathematica
Gnuplot- replaces somehow Origin
R
Root - data analysis
Octave -also replaces matlab
Matlab and MathCad are both widely respected and well integrated mathmatics evironment packages. I have personally used Matlab for near 10 years, and have never had trouble finding a function or writing scripts to do a variety of engineering tasks. However, Matlab has a much wider following than MathCad.
One way to show this is to go to an employment site such as https://www.monster.com and run a job search using the word "Matlab" and compare it to the word "Mathcad." Today, it is a 5:1 ratio in favor of Matlab. Just to make sure Matlab is a favorite of the engineering community, I added the word "engineer." It still remained about 5:1 (375 to 75 jobs posted).
If you are a student, you can get a student version for $99(USD) at: https://www.mathworks.com The student versions are matrix size restricted, but most of the standard toolboxes are still included.
Mathworks also developed Simulink which gives the user the ability to create large scale control systems models, dsp system models, etc., in an easy graphical format.
Shareware is generally very good for some individual applications, but the truly robust software is something you usually have to cough up some money for. And shareware is rarely used extensively in industry.
If you are going to invest time learning an application, make it one that can better help you make a living.
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