MATH/SCIENTIFIC

EXCALIBUR
A RPN (Reverse Polish Notation) calculator. Once you get used to RPN you may never go back to a regular calculator. Has scientific, business and statistics modes,
and can also be used in the traditional mode. This is an excellent app for exploring RPN  - if you discover you prefer RPN as much I do and want an RPN calculator,
you can still get them from hp HERE for about $60 (the current model (4/19) is the 35s).

GNU OCTAVE  (Linux, Apple, Windows)
      An excellent clone of Matlab®. It does an excellent conversion from Matlab codes. I can confirm that my Matlab codes have worked perfectly on Octave, with
occasional minor modifications. Computation times are about the same time as Matlab.
(1) Function files for Octave have an .m suffix, exactly like Matlab. Amazingly, this is not stated in the Octave documentation the last time I looked..
(2) Matlab m-files must be written as, copied to, or saved as, a text file before being transferred to the working Octave directory (Matlab files that are directly copied are
not recognized by Octave).
(3) Once Octave is installed additional packages will usually have to be installed to activate many of the commonly used functionalities. These are essentially equivalent to
Matlab's Toolboxes.
(4) I have done successful optimizations using the unconstrained built-in Octave function fminunc rather than Matlab's fminsearch - the input arguments are formatted
identically so that the call to fminsearch in Matlab is replaced by a call to fminunc in Octave, keeping everything else the same. Optimization times are about the
same. Alternatively, fminsearch can be used after installing the Octave optimization package(s).
(5) In function programs Octave can use additonal end formats depending on the loop being finished. For example in a for or if  loop the formats can be endfor or
endif respectively.
(6) Octave does not (yet?) support multiple conditions in conditional loops. For example "if i == 0 & j==1" in Matlab must be split into separate loops.

SCILAB
Another mathematical programming package. I tried this in ca. 2010 and it worked well, but I have had so much success with Octave that I have not tried to use it since. It has
a Matlab-to-Scilab converter, although my attempts at such conversions were not successful in 2010 (perhaps this has improved). 

WOLFRAM INTEGRAL SOLVER
Just type "integrate f(x)" in the displayed box, or select the orange icon on the far right. (CAUTION: I have found some mistakes)

WOLFRAM RESIDUES
Enter any function with a singularity and get the residue at that singularity. (CAUTION: I have found some mistakes)

LYX WORD PROCESSOR
This requires two downloads:
(1) LaTeX application HERE
(2) Lyx application HERE.

TABLE OF INTEGRALS

SciDAVis PLOTTING (Excellent plotting from tabulated data  (rows can be added to the default 30, one at a time) HERE.