Asymptotic Analysis and Perturbation Theory
Auteur : Paulsen William
Beneficial to both beginning students and researchers, Asymptotic Analysis and Perturbation Theory immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals. Suitable for those who have completed the standard calculus sequence, the book assumes no prior knowledge of differential equations. It explains the exact solution of only the simplest differential equations, such as first-order linear and separable equations.
With varying levels of problems in each section, this self-contained text makes the difficult subject of asymptotics easy to comprehend. Along the way, it explores the properties of some important functions in applied mathematics. Although the book emphasizes problem solving, some proofs are scattered throughout to give readers a justification for the methods used.
Introduction to Asymptotics. Asymptotics of Integrals. Speeding Up Convergence. Differential Equations. Asymptotic Series Solutions for Differential Equations. Difference Equations. Perturbation Theory. WKBJ Theory. Multiple-Scale Analysis. Appendix. Answers to Odd-Numbered Problems. Bibliography. Index.
William Paulsen is a professor of mathematics at Arkansas State University, where he teaches asymptotics to undergraduate and graduate students. He is the author of Abstract Algebra: An Interactive Approach (CRC Press, 2009) and has published over 15 papers in applied mathematics, one of which proves that Penrose tiles can be three-colored, thus resolving a 30-year-old open problem posed by John H. Conway. Dr. Paulsen has also programmed several new games and puzzles in Javascript and C++, including Duelling Dimensions, which was syndicated through Knight Features. He received a Ph.D. in mathematics from Washington University in St. Louis.
Date de parution : 07-2013
15.6x23.4 cm
Thèmes d’Asymptotic Analysis and Perturbation Theory :
Mots-clés :
Asymptotic Series; Regular Singular Point; series; Irregular Singular Point; regular; Stieltjes Function; singular; Borel Sum; point; Continued Fraction Representation; irregular; Frobenius Series; borel; Continued Fraction; sum; Recursion Formula; continued; Airy Functions; fraction; Inhomogeneous Equation; representation; Full Asymptotic Expansion; Maclaurin Series; Dominant Balance; Arbitrary Constants; Homogeneous Equation; Shanks Transformation; Exact Solution; Leading Behavior; Richardson Extrapolation; Generalized Richardson Extrapolation; Difference Equation; Strained Coordinate; Euler Maclaurin Formula; Bernoulli Polynomials