Asymptotic Analysis and Perturbation Theory

• Main Author: Paulsen, William
• Format: eBook Book
• Language: English
• Published: United Kingdom Chapman & Hall 2013; Chapman and Hall/CRC; CRC Press, Taylor & Francis Group; CRC Press LLC; CRC Press
• Edition: 1
• Subjects: Asymptotic theory; Differential equations; Differential equations > Asymptotic theory > Textbooks; Mathematics; Perturbation (Mathematics); Perturbation (Mathematics) > Textbooks; Textbooks; Continued Fraction; Bernoulli Polynomials; Euler Maclaurin Formula; Maclaurin Series; Richardson Extrapolation; Shanks Transformation; Asymptotic Series; Leading Behavior; Continued Fraction Representation; Regular Singular Point; Dominant Balance; Strained Coordinate; Irregular Singular Point; Generalized Richardson Extrapolation; Exact Solution; Airy Functions; Difference Equation; Arbitrary Constants; Recursion Formula; Full Asymptotic Expansion; Frobenius Series; Homogeneous Equation; Stieltjes Function; Inhomogeneous Equation; Borel Sum
• ISBN: 1466515120; 9781466515123; 9781466515116; 1466515112
• DOI: 10.1201/b15165

This self-contained text makes the difficult subject of asymptotics easy to comprehend. It immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals. Along the way, the book explores the properties of some important functions in applied mathematics. Assuming 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.