TY  - BOOK
AU  -  Frank Morgan
TI  - Real analysis and applications: : including fourier series and the calculus of variations
SN  - 978-1-4704-6501-8
AV  - QA300 
PY  - 2005///]
CY  - Rhode Island
PB  - American Mahematical Society
KW  - Mathematics
N1  - Part I: Real Numbers and Limits
Part II: Topology
Part III: Calculus
Part IV: Fourier Series
Part V: The Calculus of Variations
N2  - Real Analysis and Applications starts with a streamlined, but complete, approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]."The text not only provides clear, logical proofs, but also shows the student how to derive them. The excellent exercises come with select solutions in the back. This is a text that makes it possible to do the full theory and significant applications in one semester.---Summary provided by publisher
ER  -