An Introduction to Asymptotic Analysis
by Simon J.A. Malham
Publisher: Heriot-Watt University 2010
Number of pages: 56
From the table of contents: Order notation; Perturbation methods; Asymptotic series; Laplace integrals (Laplace's method, Watson's lemma); Method of stationary phase; Method of steepest descents; Bibliography; Notes; Exam formula sheet; etc.
Download or read it online for free here:
by Raghavan Narasimhan - Tata Institute of Fundamental Research
Topics covered: Differentiable functions in Rn; Manifolds; Vector bundles; Linear differential operators; Cauchy Kovalevski Theorem; Fourier transforms, Plancherel's theorem; Sobolev spaces Hm,p; Elliptic differential operators; etc.
by I.M. Sigal, M. Merkli - University of Toronto
In this course, we deal with modern analysis. Properties of functions are studied as much as they are needed for understanding maps. More specifically, our emphasis is on applications of modern analysis and the material is selected accordingly.
by Irena Swanson - Reed College
Students learn to write proofs while at the same time learning about binary operations, orders, fields, ordered fields, complete fields, complex numbers, sequences, and series. We also review limits, continuity, differentiation, and integration.
by Victor Guillemin, Shlomo Sternberg - Harvard University
In semi-classical analysis many of the basic results involve asymptotic expansions in which the terms can by computed by symbolic techniques and the focus of these lecture notes will be the 'symbol calculus' that this creates.