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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.

> I really appreciate you taking the time to help me

Glad to help. Ive ended up learning a good amount about how computers work in an attempt to deal with problems that are laughably too big for my system, and its always nice to put some of that info to practical use.

> It looks like its 2GB per slot

This is a bit less ideal, just cause youd have to buy 2x 4gb sticks instead of 1. Id see if you can actually get to the ram and then make sure it isnt soldered (id guess it isnt, i think it is mainly apple that soldered the memory in, but idk for sure). A lot of times there is a emovable panel on the bottom of the laptop that lets you easily get to the ram. If not, it might be a bit more effort and require some disassembly and reassembly of the laptop.

> I dont know, what would you recommend?

So, from a quick seach on the internet, it seems you can get a compatable 2x4gb kit for $60, thought it might be worth checking out the used market since you might be able to get a matching pair of used 4gb sticks for almost nothing.

If you are planning on getting a new computer soon regardless and will never use the old one again, it probably isnt worth $60 (but $10-20 if you can find them used would probably be worthwhile).

> is 8gb enough

Id ask your friend what memory usage he saw when running the code. 8gb seems like enough IF what you posted is the code's peak memory usage. It is entirely possible though that running for 30 minutes didnt even get you past the initial setup stage (running on swap is really slow even on much newer systems), and that you didnt get to the part with more significant memory requirements.

Personally id have gotten a new system long ago, but i also work on problems that dealing with them in their full form (not a cut down version) basically requires a small supercomputer, so im not necessairly the best person to ask.

> I feel like I'd lean towards an i5 with 8GB,

Id tend to suggest 16gb otherwise youll just run into this same issue again.

its worth going on /r/buildapc if you have any desire to build a system (you tend to get much more for your money this way than buying prebuilt). IDK what kind of budget you have, but if it were me, id probably go with something like this. Theres a couple places you could scale back the cost, but those all come at a cost.

PCPartPicker part list / Price breakdown by merchant

Type|Item|Price
:----|:----|:----
CPU | Intel - Core i5-8600K 3.6GHz 6-Core Processor | $237.59 @ SuperBiiz
CPU Cooler | Cooler Master - Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler | $19.99 @ Newegg
Motherboard | MSI - Z370-A PRO ATX LGA1151 Motherboard | $89.99 @ Newegg
Memory | G.Skill - Ripjaws V Series 16GB (2 x 8GB) DDR4-3200 Memory | $165.99 @ Newegg
Storage | SanDisk - SSD PLUS 240GB 2.5" Solid State Drive | $60.99 @ Amazon
Case | Cooler Master - HAF 912 ATX Mid Tower Case | $34.99 @ Newegg
Power Supply | EVGA - SuperNOVA G3 650W 80+ Gold Certified Fully-Modular ATX Power Supply | $73.98 @ Newegg
| Prices include shipping, taxes, rebates, and discounts |
| Total (before mail-in rebates) | $738.52
| Mail-in rebates | -$55.00
| Total | $683.52
| Generated by PCPartPicker 2018-04-11 12:36 EDT-0400 |

Note: this doesnt include the OS or peripherals like a monitor. If you need these then itll be a bit more than this, but you can often find good deals on windows 10 and get a decent 1080p monitor for not much more than $100 (maybe much less if you can snag something used).

This build looks good. I built myself a similar rig last year, and it performs well. I basically agree with everything /u/MrTesla said, mutatis mutandis.

• If you want to perform GPU computing just make sure this GPU is CUDA-enabled.
  
  
• I'd get a 1 TB solid state; they are only ~$250 if you went with Crucial instead of Samsung.
  
  
• I have that same CPU cooler. It looks awesome in pictures, when it's by itself, but in retrospect I wish I would have went with something much smaller and simpler. The problem is that it's a brick, and will stick out directly normal from your CPU, and takes up a ton of space. Let me take a picture of mine... here ya go. It makes cable management and everything else happening around your mobo more difficult. If you go with something like this Corsair Hydro, you get the same copper plate with liquid cooling, but move the fan element out of center of the tower, to a location where it should be. I'd highly consider this since you are only going with a mid, and not full tower.
  
  
• I like the modular PSU, but I'd almost want to beef that up a little, to like 800W.
  
  
• CPU looks good. For $50 more you get a decent benchmark bump for the 3.6 i7-6850K. Then again, you might have already said that, a few times.
  
  Overall though, pretty solid build. MATLAB is just an excuse to build this right? No shame in that. When it comes time to actually use MATLAB for analyses I would highly recommend converting whatever you can to MEX files. Like MrTesla mentioned, MATLAB is not the fastest tool available, and may not be the right tool if you're concerned about how long it will take to process your data. Optimizing the lang/software/code used to process your data will result in speed-ups orders of magnitude greater than simply running the same code on a more powerful machine. I experienced this first-hand; I was simulating particle diffusion on ruffled membranes in matlab using standard functions. To run one simulation (~20k steps for 1k particles) it would take about 10 minutes. I went out and build a new rig, and it went down to ~6 min. I converted some of my functions to MEX/C and it dropped to about 45 seconds.

Use your student license to complete the MATLAB Cody Challenge; it's one of the best ways to learn MATLAB's ins and outs. Keep the documentation handy throughout. Maybe check out this style guide (which you can also purchase on Amazon).

Search for (computational) things that interest you in the documentation; you'll find there are a lot of built-ins and excellent examples.

Best of luck!

You should be able to find lots of examples and explanation using Google. Search terms that may help are: Inertial navigation, INS, GPS aided. I found this INS toolkit very easily, and it looks like it has some examples. Might be diving in head-first though. Brown & Hwang's book covers pretty much exactly what you are looking for, specifically using Matlab.

I am not the one who downvoted you, but I think I can guess why someone did. You say you want to compare to audio signals and are asking for advice on how to proceed. But obviously there's a bajillion ways that two different sound signals could differ from each other. You're going to need a much clearer idea of what kind of comparison you want to do, i.e., what kind of question you're trying to answer about the signals.

I can recommend this book: https://www.amazon.com/Music-Data-Analysis-Foundations-Applications/dp/1498719562. There, or perhaps elsewhere, you should be able to find helpful perspectives and ideas.

I agree with the comments already here. Two more options:

• Pull out some old textbooks and see if you can write code to solve the problems. Generalize your code as much as you can.
  
• Get a numerical methods textbook and work your way through it. It's also a great way to learn new analysis methods. The linked book is the one I learned from.

If you are an absolute beginner, consider this textbook: http://amzn.com/0123943981

I started out with it when I first encountered MATLAB at university, and I felt it was a great introductory textbook, with the focus on being an introduction to the language.

Are T_gas and P functions of time or just z?

If they're only functions of z and don't change with time--assuming you're trying to solve for C_i--this is a relatively straightforward PDE to solve, of the form dC_dt = a*dC_dz + b*C + d. You can use a finite difference method, like Euler's Forward / Explicit, to discretize both space and time. You then stick it in a loop to march through each time step until you reach steady-state or you get bored.

If you're using Euler's forward method, each time step would look something like:

C_next = C_now + dt * (a * gradient(C_now, dz) + b * C_now + d)

This is my favourite book on PDEs: https://www.amazon.ca/Numerical-Methods-Partial-Differential-Equations/dp/0128498943 but it's probably at the library!

I found Steven Leon's Linear Algebra with Applications to be one of the better Math books I've ever read. Older editions can be had without much cost.

Mathwork's Aerospace toolbox has an entire Quadcopter project that could give you an idea of how to model a Quadcopter in Simulink.

Idris Putro also has a good book on modelling and control.

https://www.amazon.com/Modeling-Control-Simulation-Autonomous-Quadrotor/dp/3844318062

you can always get yourself some cheap numeric keypad like this which is basically just a small keyboard, and a couple of buttons, take the board of the keypad out, solder wires from the buttons to the 1, 2, 3 and 4 keys and put everything in a project box and voila, you've got a button box that looks like the thing in your link and sends the keystrokes you want yo the computer, dirt cheap and no programming or custom electronics.

I didn't have a relay picked out yet, I'm kind of in the brain storming stage right now. I came across this board on amazon and thought it might do the trick:
https://www.amazon.ca/SainSmart-101-70-101-4-Channel-Relay-Module/dp/B0057OC5O8/ref=sr_1_21?ie=UTF8&qid=1486504628&sr=8-21&keywords=usb+relay

It says it has a Standard interface that can be controlled directly by microcontroller (Arduino , 8051, AVR, PIC, DSP, ARM, ARM, MSP431, TTL logic)

Maybe i'll give it a go.

I had to do a lot of de-bugging. I had some dumb errors like calculating variables before the variables that they were dependent on. I also had to re-apply the BC after the predictor. After your first comment I went back and placed the dlnA1(j) in its own loop because I was not applying it to the boundaries only the interior of the matrices.

I also got this text

It has my exact problem as an example on the last ~50 pages with table values for the first time step which helped verify my code.

I'm not sure if this is what you need but I do have this book lying around if it interests you.

https://www.amazon.com/First-Course-Finite-Elements/dp/0470035803

This is the reading required to get you started. Matlab is suitable for your purposes, but asking on this sub isn't useful.

Given the simplicity of your problem, you could probably derive an analytical or semi-analytical solution... But this depends on how linear your problem is.