Singular Differential Equations and Special Functions: 1st Edition (Hardback) book cover

Singular Differential Equations and Special Functions

1st Edition

By Luis Manuel Braga da Costa Campos

CRC Press

392 pages | 21 B/W Illus.

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Hardback: 9780367137236
pub: 2019-11-20
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Singular Differential Equations and Special Functions is the fifth book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology.

This fifth book consists of one chapter (chapter 9 of the set). The chapter starts with general classes of differential equations and simultaneous systems for which the properties of the solutions can be established 'a priori', such as existence and unicity of solution, robustness and uniformity with regard to changes in boundary conditions and parameters, and stability and asymptotic behavior. The book proceeds to consider the most important class of linear differential equations with variable coefficients, that can be analytic functions or have regular or irregular singularities. The solution of singular differential equations by means of (i) power series; (ii) parametric integral transforms; and (iii) continued fractions lead to more than 20 special functions; among these is given greater attention to generalized circular, hyperbolic, Airy, Bessel and hypergeometric differential equations, and the special functions that specify their solutions.

  • Includes existence, unicity, robustness, uniformity, and other theorems for non-linear differential equations
  • Discusses properties of dynamical systems derived from the differential equations describing them, using methods such as Liapunov functions
  • Includes linear differential equations with periodic coefficients, including Floquet theory, Hill infinite determinants and multiple parametric resonance
  • Details theory of the generalized Bessel differential equation, and of the generalized, Gaussian, confluent and extended hypergeometric functions and relations with other 20 special functions
  • Examines Linear Differential Equations with analytic coefficients or regular or irregular singularities, and solutions via power series, parametric integral transforms, and continued fractions


Table of Contents

1. Existence Theorems and Special Functions.

About the Author

Luis Manuel Braga da Costa Campos graduated in 1972 as a Mechanical Engineer from the Instituto

Superior Tecnico (IST) of Lisbon Technical University. His tutorials as a student (1970) were

followed by a career at the same institution (IST) through all levels: Assistant (1972), Assistant

with tenure (1974), Assistant Professor (1978), Associate Professor (1982), Chair de Applied

Mathematics and Mechanics (1985). He has been coordinator of undergraduate and post-graduate

degrees in Aerospace Engineering since their creation in 1991. He is also coordinator of the

Scientific Area of Applied and Aerospace Mechanics in the Department of Mechanical Engineering and

director and founder of the Center for Aeronautical and Space Science and Technology.

About the Series

Mathematics and Physics for Science and Technology

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations
MEDICAL / General