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As a person who just graduated from college with a degree in civil engineering and is currently teaching himself how to program in C++ I feel that I can offer some insight. First have you considered staying in civil and maybe double majoring in comp sci? I think it would be awesome work to write the structural analysis software that's used in industry. Then you're getting the best of both worlds. In my first year engineering fundamentals class we learned Matlab. Is this true for you? Maybe you could get a taste for programming there.
Learning to program for me has been a cool experience. You immediately see results in what you're learning and there's no lag time in finding out if you did something wrong. You get an error message or your output isn't what you expected and you go off and fix it and see results immediately.
As far as how difficult it has been, I find myself every day saying, "Screw this, I can't do it!" I ask myself, "I wonder if I can code something like X." I find I can't do it. I quit trying. I read online how other people do it. Still can't do it. Keep reading until finally it clicks. I get in over my head and repeat the process.
As far as books, I usually start out with C++ Tutorial which is free online. The pdf is short and offers a brief introduction to various C++ topics. I then read the more lengthy chapters in C++ Without Fear and C++ Primer Plus. People have highly recommended these books in various threads. I think it's important to learn from many books. Get the seed planted with one book and fertilize with others. Then harvest the results.
I have also bookmarked various sites that have reference info and problems to solve and places to submit your code when you get really stuck or have questions.
You miss 100% of the shots you don't take. -Wayne Gretzky- So fuck it, you might as well try! -Me-