All programs are slaves to the imagination of our brains. That means we must fully understand what to expect from our programs or the programs WILL eventually lie to us. That being said, MathCAD is the best and easiest software I have ever used. I have done in minutes with MathCAD problems that could take hours or days with other programs. I have done math problems that shouldn't even be allowed to be called math
MathCAD does vectors and matrice calculations with ease. Cross products, yup. Dot products, yup. Laplace transforms (both ways!), Runge-Kutte, Linear and Non-Linear DiffEQ's, and the most impossible block of equations you could image. It also does simple and complex integration, differentiation, and algebra. It does units also so you can convert miles/hour to cm/sec, and many more. It also remembers units when it solves Diff-Eqs. It does comlex algebra too. It's great, but engineers love it, especially for systems and heat transfer. www.mathsoft.com Of course if you want to do analog modeling, you probably want to use MatLab.
If you are a university student, you may find MathCAD installed in the college computer lab. The student version of MathCAD is $129.99 USD at my Alma Matter, well worth it!