Great Math Software for Curves and Surfaces
3DXM Virtual Math Museum
by differential geometer Richard Palais and Hermann Karcher.
Lots beautiful surfaces and animations.
The 3DXM software is Mac only, and is quite outdated. But the web site is nice for learning math.
It can plot equations of 3 variables and parametric formulas for higher-dimension surfaces, and can do morph based on a variable.
Spivak is a surface plotter by Jacob Siehler. One interesting feature is that users can drag a point inside a box, and the corresponding point on the surface moves dynamically. User can also turn on the drawing of tangent plane, tangent line, geodesic, and principal curvature lines at that point. There is also SpaceCurve program by the author.
Mathematica is the most powerful math software.
Mathematica comes free bundled with Raspberry Pi Raspberry Pi
for more about Mathematica, see Wolfram Language, Mathematica
Graphing Calculator by Ron Avitzur. Imagine your hand-held graphing calculator with the power of a desktop computer, then you get the idea of what this program is about.
Out of 10 or 20 programs that plots curves and surfaces i've tried, I think this is the best. Most versatile and most easy to use. Go download a demo and see for yourself. If you want a plotting program for your highschool or college installation, I suggest this one.
Microsoft Windows, Math Plotters
Here is a list of Curves and Surface plotters for Windows
For books, you want to study calculus, then, differential geometry or algebraic geometry.
If you have a question, put $5 at patreon and message me.