A first course in ordinary differential equations. Analytical and numerical methods.

*(English)*Zbl 1296.34001
New Delhi: Springer (ISBN 978-81-322-1834-0/hbk; 978-81-322-1835-7/ebook). xiv, 288 p. (2014).

Ordinary differential equations are used to describe a multitude of phenomena in natural and engineering sciences. Consequently, the applied scientist needs a fundamental understanding and knowledge about the characteristics of ordinary differential equations, their mathematical behavior, ways to determine a solution as well as numerical methods to calculate solutions using computing devices. This book presents mathematical techniques for solving initial and boundary value problems in linear ordinary differential equations (ODEs). The topics covered are an introduction to ODEs, scalar first order ODEs, second order ODEs, Laplace transforms for scalar ODEs and system of first order ODEs, solution methods based on eigenvalues as well as power-series techniques. The presentation uses a lot of examples of different ODEs and presents detailed solutions for them. This makes the book unique in the sense that it tries to give an insight to the ODEs and their behavior through these examples, which might be very valuable for the intended reader in advanced undergraduate or graduate courses. Also, the later chapter an numerical methods gives many examples and detailed calculations.

Reviewer: Gudula Rünger (Chemnitz)

##### MSC:

34-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations |

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |

34A30 | Linear ordinary differential equations and systems, general |