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Edit:

Ok, user Chinny84 made comment that truly helps narrow the focus of my question. Basically, I'm asking for a self-study course of Mathematical Methods.

Thanks to his recommendation I identified a book that is very close to the answer:

Mathematical Methods in the Physical Sciences by Mary L. Boas

Supposedly, the book covers most of the Math a person needs to learn in order to understand the simulations I presented.

Does this book suit my needs?


Hello,

I have always been interested on the idea to study Math at an Undergraduate level to be able to implement simulations like the followings:

Finite Difference Simulation of the Wave Equation

enter image description here

Heat Equation in Two Dimensions

https://upload.wikimedia.org/wikipedia/commons/a/a9/Heat_eqn.gif

Besides my precollege experience in Math, I have only been able to do very simple simulations due to my lack of knowledge of Advanced Math. Every time I ask about the inner workings of the simulations I get redirected to papers that look like foreign language to me and, unfortunately, I depend on easy-to-read tutorials to understand them, and while I have found very helpful explanations I'm more interested in reaching the solution myself.

I checked some of the questions related to book recommendations for self-study and while they are very helpful I'm interested in learning by example (There is a book called: "Accelerated C++ Practical Programming by Example" that fits very well my study habits)

Thanks in advance.

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    $\begingroup$ Welcome to the site! What specifically is your question? $\endgroup$ – HBeel Mar 11 '15 at 21:52
  • $\begingroup$ @HBeel, how to read computer science papers and book recommendations/courses (self study) that cover the topics I posted, with focus on observational training (learning by example) $\endgroup$ – Jane Smith Mar 11 '15 at 21:56
  • $\begingroup$ Have a look at: Theoretical CS and Math - self-study recommendations. $\endgroup$ – Jose Arnaldo Bebita-Dris Mar 11 '15 at 22:25
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    $\begingroup$ The introduction to mathematical methods is just a general name for textbooks that discusses and shows problems/excerises of mathematical methods such as pdes, linear algebra and series etc etc for physicists/engineers. These books tend to cover most of the topics if not all of the ones you mentioned above. $\endgroup$ – Chinny84 Mar 11 '15 at 23:33
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    $\begingroup$ The simulations you showed should be explained in textbooks about numerically solving PDEs, so there's no need to worry about reading papers at this point. The heat equation example could be implemented in like half a page of Matlab using a simple finite difference method. $\endgroup$ – littleO Mar 12 '15 at 0:02
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The courses and book you mentions above is for basic engineering, physics problems. I think in your case, it's more about the applications than theorem. But, here are some books that you should check out and it combines a lot of pure math:

Single and Multi Variable Calculus: Calculus, 7ed by James Stewared

Fourier Transform and Analysis: A First Course in Wavelets with Fourier Analysis by Albert Boggess and Francis J. Narcowich (You should have basic knowledge about linear algebra and some Differential Equation in order to understand Fourier Transform)

Linear Algebra: Linear Algebra and its Application by Gilber Strang. More Advance we have, Linear Algebra Done Right by Axler

Differential Equation: Ordinary Differential Equation by Morris Tenenbau and Harry Pollard. More advance: Introduction to Ordinary Differential Equation by Agarwal, or even deeper: Ordinary Differential Equations by Edward L. Ince

Partial Differential Equation: Partial Differential Equation for Scientists and Engineer by Stanley. More advance: Partial Differential Equation by Strauss (he talks about Fourier Transform in this book too), or Partial Differential Equation by Lawrence C. Evans (I love this book because it's very detail)

About reading papers,let says a paper in Mathematics about PDE; it requires that your knowledge must be very deep in PDE in order to understand that paper, not just reading some basic books.

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  • $\begingroup$ Thanks for answering!, I got a couple of questions: 1) "The courses and book you mentions above" What books? 2)Do the books you mentioned are at an undergraduate level (for the unfamiliar)? 3) "Partial Differential Equation" I read that the books you mentioned are a little advanced, thats why I selected Haberman's book for PDE, is that OK? $\endgroup$ – Jane Smith Mar 12 '15 at 19:57
  • $\begingroup$ 1) My roommate is Physics major, and he has several books about Mathematics for Physics, but, I forgot. I need to check them again. 2)The first book in each topic that I mentioned is always coming with a lot of simple examples,I think you can self study with those books, except the book about Fourier Analysis, it's little bit more advance. But, in the case you want to know more theory, you can go to next book. 3) unfortunately, I haven't read that book, but "Partial Differential Equation for Scientists and Engineer by Stanley" has step by step example, and you can take a look at that. $\endgroup$ – Alexander Mar 12 '15 at 20:20

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