Skip to content

Files

Latest commit

nicoguaronicoguaro
Add complex numbers notebook
Jul 31, 2018
7e0d616 · Jul 31, 2018

History

History
executable file
·
92 lines (64 loc) · 4.2 KB

references.md

File metadata and controls

executable file
·
92 lines (64 loc) · 4.2 KB

References

This is a list of references related to Advanced Mathematics, Mathematical Physics, and other topics of interest.

  • Alonso Sepulveda Soto. Fı́sica matemática (Spanish). Ciencia y Tecnologı́a. Universidad de Antioquia, 2009.

    This is a nice little book about Mathematical Physics. I think that it covers most of the relevant topics and it is short enough. The only caveat is the jargon, that it might be a little bit too specific for physicists.

  • Erwin Kreyszig. Advanced engineering mathematics. John Wiley & Sons, 2011.

    A good book in Advanced Mathematics (for engineers). The only but is its extension, that would not make it suitable for a one-semester course. But, definitely a good book to have in one's bookshelf.

  • Stanley J Farlow. Partial differential equations for scientists and engineers. Courier Corporation, 2012.

    This is a PDE book intended for students in areas other than mathematics who are studying partial differential equations. It presents the content in 47 independent lessons instead of presenting it by chapters.

  • H. Hochstadt. Differential equations: a modern approach. Courier Dover Publications, 1975.

    My favorite book on ODE, it does not describe all the common methods for second order equations as is common in most ODE books. The emphasis is on concepts and in matrix methods that are more algorithmic, in my opinion.

  • Antonio Velasco and Ruben Sánchez. Curso Básico de Álgebra Lineal (Spanish). Comex, 1980.

    Yet another little book that I like. It does not give any special treatment to the topics of linear algebra, but it is short (208 page), so you can read it pretty fast. If I had to choose a book with a different approach it would be Coding the Matrix by Philip N. Klein, that gives an intertwined presentation between theory, concepts and (Python) programming.

  • Louis Leithold. The calculus. New York, USA: Harper and Row Publishers, 7 edition, 1995.

    I like this calculus book, but it is probably because I studied in my undergrad with it. Regarding vector calculus, I find more useful the book by Stewart.

Freely-available references

  • Grant Sanderson. Essence of linear algebra., 2016.

    A series of videos that clearly explain the concepts behind the most Common topics in linear algebra.

  • Lloyd Trefethen and Kristine Embree (Editors). The (Unfinished) PDE Coffee Table Book., 2011.

    This is a collection of 2-pages spreads talking about relevant information for different partial differential equations.

  • FWJ Olver, DW Lozier, RF Boisvert, and CW Clark. NIST digital library of mathematical functions.. NIST, 2010.

    The updated version of the classical Handbook of Mathematical Functions. It is an online version, so you can access it wherever you are (with an internet connection, of course).

  • Ondřej Čertík. Theoretical Physics Reference, 2011.

    This is an e-book generated using Sphinx with source code stored in GitHub. The book contains notes related to theoretical and mathematical physics and snippets of code in SymPy.

  • Hans Petter Langtangen, Svein Linge "Finite Difference Computing with PDEs.", Springer, 2017.

    This is a book on Finite Difference methods for PDEs. It has a stronger emphasis on computer implementation and verification, key aspects of scientific computing.

  • Hans Petter Langtangen, Geir K. Pedersen "Scaling of Differential Equations.", Springer, 2017.

    This book is centered on scaling of differential equations. Rewriting differential equations in dimensionless form has several advantages. These advantages are also present in numerical solutions.