Monday, May 11, 2009

Great Books for Mathematical Modelling

I realize it has been over a month since I last posted, and for this I apologize. The reason is simple: I had to write my final exams. Aside from a few evenings spent with friends, I pretty much studied every day in April, after which I spent a week with my parents and then a week in Switzerland. Now it's time to return to my pre-exam life, which is hectic in a very different way.

Fortunately, I have my exam results and they went well. I feel like the last two months have been the months of learning and understanding various tools in mathematical modeling, and there are certain books I simply wouldn't be able to live without. If you are interested in some of the technical aspects of mathematical modelling or are thinking of studying for the formal M.Sc. at Oxford, make sure you keep these books in mind.

Numerical Mathematics (1): focusing on all topics related to actually implementing theoretical mathematical ideas in a computer. The numerical linear algebra section (specifically, solving linear systems) is the best and clearest I've read in a while.

Finite Element Methods and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics (1): impressive and complicated name for an impressive and complicated area of research. Yes, there's a whole course on this in the M.Sc., though we only really get through the first chapter of the book!

Applied Partial Differential Equations (1): focuses on getting you to solve PDEs. Really, that's all I can say... Though I'm convinced that there's an inverse relationship between the number of words used to describe a mathematical problem and the number of things you have to do to actually do it!

Boundary Value Problems of Mathematical Physics (1): a great introduction to how one can use distributions to solve various problems. Think of it as generalizing and abstracting how you actually integrate or solve differential equations.

So to those books and authors thereof, thank you!

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