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My Applied Mathematics course covers these subjects:
-Calculus of Variations
-Laplace Transform
-Fourier Analysis
-Special Functions
-Integral Equations

And as an introduction to the subject it has several things from calculus like maxima/minima of functions of several variables, some differential(also partial differential equations) equations, Jacobians, Lagrange multipliers, Leibniz rule and partial differential equations(primarily the variable separable method).

While some of you might find these subjects easy, bear in mind that i study physics and because i want to become a theoretical physicist i am attending this course which is from the mathematics department of my university. As i am only a second year undergraduate student, i feel like i am in some deep mathematics, so i will be needing some help(from a book). Any suggestion(s) for a book on the prerequisites(introductory topics that i mentioned) are appreciated.

P.S. Any suggestion for the actual topics of the course are also appreciated!

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  • $\begingroup$ Did you look into books like "Mathematical Methods in the Physical Sciences" 3rd Edition by Mary L. Boas? There are more like this one too. $\endgroup$ – Moo Jan 19 '16 at 14:27
  • $\begingroup$ @Moo I will check it out, thank you. But, as the course is for mathematicians, shouldn't i learn those subject from an applied mathematics book that is fit for mathematicians rather than physicists? $\endgroup$ – TheQuantumMan Jan 19 '16 at 17:54
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    $\begingroup$ It is just one recommendation and I think it is helpful for your degree pursuits to look at a book from the perspective of a physicist. That is not to say that you shouldn't peruse math based views also as I think both are the optimal approach. $\endgroup$ – Moo Jan 19 '16 at 17:58
  • $\begingroup$ Do you read Russian by any chance? :) There are two books by Anatoly Myshkis, which cover all the topics that you mentioned and also a lot more and written specifically for applied mathematicians and engineers. (there are English translations but I am pretty sure they are very difficult to get hold of). $\endgroup$ – Artem Jan 27 '16 at 22:03
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    $\begingroup$ In the English translation the first one is "Lectures on higher mathematics" and the second is "Mathematics for students of higher technical institutions: special courses." $\endgroup$ – Artem Jan 27 '16 at 23:02
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I recommend checking out Gilbert Strang's book Introduction to Applied Math.

Strang has great intuition and I think he explains things in a very clear, simple, and yet deep way.

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    $\begingroup$ Hello and thanks for the answer, although my course is for mathematicians while this book is for students of engineering and physics $\endgroup$ – TheQuantumMan Jan 23 '16 at 10:18
  • $\begingroup$ I think this book is written for applied math students just as much as it's written for engineering and physics students. $\endgroup$ – littleO Jan 23 '16 at 10:48
  • $\begingroup$ I will check it out then. Thanks for the recommendation. $\endgroup$ – TheQuantumMan Jan 23 '16 at 10:55
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I have dug up some book titles that i found useful, so i am writing my own answer. Namely:

-Mathematical methods for physics and engineering by Riley, Hobson, Bence. -Many books or chapters from books of the author Vladimir Arnold.
-Strang's Calculus
-Hildebrand's Methods of Applied Mathematics
-Churchill's Fourier Series and Boundary Value Problems

The first covers a lot of subjects and is a pretty big book although it relies on the computational part.

The books of the second point all rely on computation and on intuition with graphs to illustrate what something means in mathematical language but also in physics. It is a bit difficult for a beginner but very useful. Its a unique and the best approach in my opinion.

The third book might cover a lot of single algebra, but it multivariable calculus part(roughly half of the book) is a gem of intuition(like the explanation of the Jacobian--not simply stating that it is used for change of variables)

Hildebrand's books covers integral equations and calculus of variations among others. It seems to be a pretty good book.

Churchill's book covers Partial differential equations, Fourier analysis, Laplace transforms, Bessel functions, Legendre polynomials etc. It is a popular book so i guess it might be good.

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