I have read some old discussions about this topic and would like to get some up-to-date advice, if possible.
How can I take math notes, write formulas and draw graphs on my pc (win 7), the easiest and quickest way?
Thanks for your consideration.
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I recommend using Mathematica. The student edition was around $130 the last time I checked, and it's well worth it (if you're not a student, the home edition runs around twice that). Formulas are easier to write than in LaTeX, and you have the option of saving as LaTeX, as well as HTML, postscript, plaintext, rich text, and a few other formats. You also have the option of easily being able to play around with the math and see how it works, which you usually can't do outside of math programs very easily.
Mathematica is designed for notes, and there are already many (Mathematica) notebooks out there that allow you to play around with the math, very easily. I also recommend using a paint program running alongside Mathematica, such as Windows Paint Shop or something similar. This allows you to quickly draw a complicated diagram with all kinds of options, such as colors and effects, that are usually hard to do on paper. You can quickly add in pictures into your Mathematica notes, and their are additional options allowing further manipulations of the pictures in Mathematica.
It's easy to quickly make copies of your notebooks and play around with specific things in each copy. It's generally how I take notes, ESPECIALLY IF I'M IN A HURRY.
If you're planning on sharing you notes, you may prefer to use LaTeX if you feel that you're comfortable with enough time to use it. Generally I convert my Mathematica notebooks in LaTeX and then PDF when I'm sharing something with someone that doesn't have Mathematica. This, however, is generally reserved for when I'm going to make an important presentation, and I have enough time to really make the notes look pretty. However, simply converting Mathematica notebooks into another format is usually good enough, or even preferred if the presentation doesn't have to be spectacular.
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I have been going back to review my calculus and differential equations for myself. I was using Lyx and LaTex for a while but it is slow and tedious to learn(for me). I will say that if you are willing use Microsoft OneNote install the math plugin which you can download from MS(free) also install the Microsoft Graphing Calculator software (also free) where you can create graphs and solve various equations. I was able to do a proof with differential equations to solve the Pythagorean Theorem for a test and it works great. The proof also contained a picture of the problem. BUT for really heavy Math or Engineering crunching you may need to look at professional software like MCAD or Mathematica. Good luck.