<p>I need the names of one or more software that can do the following. I am willing to pay any price to get these so don't mind giving the names of expensive software.</p>
<ul>
<li>Sketch 2D graphs with easy to use interface</li>
<li>Sketch 3D graphs with easy to use rotable interface.</li>
<li>Sketch slope fields in 2D and 3D.</li>
<li>Sketch scalar fields in 2D and 3D.</li>
<li>Sketch vector fields in 2D and 3D.</li>
<li>Solve first-order and second-order differential equations.</li>
<li>Evaluate definite integrals in both the real and complex plane.</li>
<li>Evaluate partial derivatives, curl, divergence and del operators of a function.</li>
</ul>
<p>I would also prefer the following tools:
- Graph in Polar co-ordinates for 2D graphs
- Graph in Cylindrical and Spherical co-ordinates with rotable interface in 3D
- Sketch parametric curves.
- Solve n-degree polynomial equations (I already have this but my current software provides only one root for each polynomial)
- Generate Taylor expansions for any function</p>
<p>Most importantly, I need the software to be able to solve the differential equations.</p>
<p>Thank you.</p>
<p>~Equuleus</p>