Mathematics for the Physical Sciences
by Leslie Copley
Publisher: De Gruyter Open 2014
Number of pages: 446
A text on advanced mathematical methods with numerous applications, detailed derivations and solutions, and a unique range of practical topics. The book begins with a thorough introduction to complex analysis, which is then used to understand the properties of ordinary differential equations and their solutions. The latter are obtained in both series and integral representations. Integral transforms are introduced, providing an opportunity to complement complex analysis with techniques that flow from an algebraic approach. This moves naturally into a discussion of eigenvalue and boundary vale problems.
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by Florentin Smarandache, at al. - arXiv
Throughout this book, the authors discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics, etc. Some parts of these problems may be found useful for scholarly stimulation.
by J. Douglas, P. Franklin, C.J. Keyser, L. Infeld - Morrill Press
Addresses delivered by Jesse Douglas, Philip Franklin, Cassius Jackson Keyser, and Leopold Infeld. Contents: Survey of the theory of integration; The four color problem; Charles Sanders Peirce as a pioneer; The fourth dimension and relativity.
by John Hutchinson - Australian National University
The goal is to introduce you to contemporary mainstream 20th and 21st century mathematics. If you are doing this course you will have a strong interest in mathematics, and probably be in the top 5% or so of students academically.
by Evan Chen - MIT
The book is aimed at making higher math accessible to high school students. Topics: Basic Algebra and Topology; Linear Algebra; Multivariable Calculus; Groups and Rings; Complex Analysis; Quantum Algorithms; Algebraic Topology; Category Theory; etc.