Check out "Further Mathematics for Economic Analysis" by Knut Sydsaeter, et. al. It has some pretty good sections on Dynamic Programming and Optimal Control.
I'm planning to study Mathematics for Economists on my own. I have a decent Calculus III and Linear Algebra background, but I've mostly forgotten about them. Although I'm taking other math courses right now (see my other thread (Math Advice for 3rd Year)), I want to make sure that I have a very thorough understanding of mathematical economics. I'm hoping to finish the book in 6 months.
Are there any particular weaknesses in this book? If so, are there books that can be used mitigate its weakness?
Hmm, well there's Leonard and van Long, Takayama, and Efe Ok. I stole from a syllabus I remembered, so I cant attest to their quality. Efe Ok is perhaps as advanced as they come.
I'd suggest reading de la Fuente's Mathematical Methods and Models for Economists.
First it more rigorously treats most topics covered in Simon and Blume. Second it covers some important topics that S&B doesn't - e.g. dynamic programming and optimal control theory.
You also should study some real analysis (there are many threads here on book suggestions)
S&B is a great review book, but falls short of rigorous treatment of analysis. DLF covers much more and it is in fact the book used at Berkeley math camp.
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