Introduction to Methods of Applied Mathematics
by Sean Mauch
Publisher: Caltech 2004
Number of pages: 2321
This book contains material on calculus, functions of a complex variable, ordinary differential equations, partial differential equations and the calculus of variations. The text is still under development. It is alternately titled 'Advanced Mathematical Methods for Scientists and Engineers'.
Download or read it online for free here:
by E. Goursat, O. Dunkel, E.R. Hedrick - Ginn & company
Goursat's three-volume 'A Course in Mathematical Analysis' remains a classic study and a thorough treatment of the fundamentals of calculus. As an advanced text for students with one year of calculus, it offers an exceptionally lucid exposition.
by Felix Nagel - arXiv
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. The exposition in this first part includes relation and order theory as well as a construction of number systems.
by Vadim Kuznetsov, Vladimir Kisil - University of Leeds
This text presents fundamentals of special functions theory and its applications in partial differential equations of mathematical physics. The course covers topics in harmonic, classical and functional analysis, and combinatorics.
by Vasily Nekrasov - Yetanotherquant.de
This is a very clear and user-friendly introduction to the Lebesgue measure theory. After reading these notes, you will be able to read any book on Real Analysis and will easily understand Lebesgue integral and other advanced topics.