This two-part treatment explains basic theory and details, including oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention to stability problems and coexistence of periodic solutions. 1966 edition.
This two-part treatment of Hill's equation encompasses the subject's most pertinent information, explaining both basic theory and numerous details, including elementary formulas, oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention is given to stability problems and the question of coexistence of periodic solutions. 1966 edition.
Maximum Principles for the Hill's Equation focuses on the application of these methods to nonlinear equations with singularities (e.g. Brillouin-bem focusing equation, Ermakov-Pinney,...) and for problems with parametric dependence. The authors discuss the properties of the related Green's functions coupled with different boundary value conditions. In addition, they establish the equations' relationship with the spectral theory developed for the homogeneous case, and discuss stability and constant sign solutions. Finally, reviews of present classical and recent results made by the authors and by other key authors are included. - Evaluates classical topics in the Hill's equation that are crucial for understanding modern physical models and non-linear applications - Describes explicit and effective conditions on maximum and anti-maximum principles - Collates information from disparate sources in one self-contained volume, with extensive referencing throughout
This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.
Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relatively focused need of an extraordinarily broad range of scientists.
FBI agent Max Carter lives his life by a strict set of rules—rules that don't allow for distraction, deviation...or a relationship. But tell that to his matchmaking mama. To avoid yet another set-up, he announces he has a girlfriend. And now has to produce said girlfriend at Christmas dinner. Maybe Santa has a suitable actress in that red bag of his... Gina Castillo is about to break her building’s iron-clad “no pets” policy to give her little brother the perfect Christmas gift—a dog. Too bad Max, the most inconveniently sexy tenant in the building, catches her red-handed. Gina expects to be evicted, but instead finds herself blackmailed into playing the role of his girlfriend. Two lies plus one dog should equal a hot mess of a holiday, but attraction and Christmas magic might just defy the rules...
We have designed and written this book. not as a text nor for the professional mathematician. but for the general reader who is naturally attracted to mathematics as a great intellec tual challenge. and for the special reader whose work requires him to have a deeper understanding of mathematics than he acquired in school. Readers in the first group are drawn to mental recreational activities such as chess. bridge. and various types of puzzles. but they generally do not respond enthusiastically to mathematics because of their unhappy learning experiences with it during their school days. The readers in the secondgrouptum to mathematics as a necessity. but with painful resignation and considerable apprehension regarding their abilities to master the branch ofmathematics they need in their work. In either case. the fear of and revulsion to mathematics felt by these readers usually stem from their earlier frustrating encounters with it. vii viii PREFACE This book will show these readers that these fears, frustrations, and general antipathy are unwarranted, for, as stated, it is not a textbook full of long, boring proofs and hundreds of problems, rather it is an intellectual adventure, to be read with pleasure. It was written to be easily accessible and with concern for the mental tranquilityofthe reader who willexperience considerable fulfillment when he/she sees the simplicity of basic mathematics. The emphasis throughout this book is on the clear explanation of mathematical con cepts.