Reddit reviews Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-dependent Problems (Classics in Applied Mathematics)

Earlier this year I finished my PhD in aero (researching computational fluid dynamics). I'll go ahead and reiterate a couple of the other recommendations in this thread, I think they've given you pretty good advice so far.

Numerical Recipes is great, and you can even read their older editions for free online. Don't worry about them being older, their content really hasn't changed much over the years beyond switching around the programming language. A word of warning, though. The code itself in these books come with rather restrictive licenses, and what it ends up meaning for you is you can copy their code and use it yourself, but you aren't allowed to share it (although I don't think this is carefully enforced). If you want to share code, you'll either have to pay for their license, or use their code only as inspiration for writing your own. If you pay close attention to their licensing, they don't even let you store on your computer more than one copy of any of their functions (again, I can't imagine they actually have a way of enforcing this, but it makes me disappointed they do things this way nevertheless), so it can get problematic fast.

If you want more reading material, I've only paged through it myself but Chapra and Canale's book seems like a nice intro text (if it wasn't your textbook already), and uses MATLAB. Reddy has a well-liked intro to finite element methods. Some more graduate level texts are Moin, LeVeque (he has a bunch of good ones), and Trefethen.

Project Euler is indeed great.

I would also recommend you learn some other (any other, really) programming language. MATLAB is a fine tool, but learning something else as well will make you a better programmer and help you be versatile. I don't really recommend you go and learn half a dozen other languages, or even learn every feature available one language--just getting reasonably comfortable with one will do. I'd say pick any of: C, C++, Fortran 90 (or higher), or Python, but there are others as well. Python is probably the easiest to get into and there are lots of packages that will give it a similar "feel" to Matlab, if you like. One nice way of learning (I think) is going through Project Euler in your language of choice.

Slightly more long term, take other numerical/computational courses. As you take them, think about what you like to use computation for (if you don't have a good idea already). If you like to analyze data, develop more or less "simple" simulations to direct design decisions, and don't care so much for heavy simulations, you'll get a better idea of what to look for in industry. If you like physics simulations and solving PDEs, you may lean toward the research end of things and possibly dumping Matlab altogether in favor of more portable and high performance tools.