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Generalized Trigonometric and Hyperbolic Functions

Generalized Trigonometric and Hyperbolic Functions

Autorzy
Wydawnictwo Taylor & Francis Ltd
Data wydania 14/01/2019
Liczba stron 194
Forma publikacji książka w twardej oprawie
Poziom zaawansowania Dla szkół wyższych i kształcenia podyplomowego
Język angielski
ISBN 9781138333017
Kategorie Trygonometria
904.05 PLN (z VAT)
$203.36 / €193.83 / £168.26 /
Produkt na zamówienie
Dostawa 5-6 tygodni
Ilość
Do schowka

Opis książki

Generalized Trigonometric and Hyperbolic Functions highlights, to those in the area of generalized trigonometric functions, an alternative path to the creation and analysis of these classes of functions. Previous efforts have started with integral representations for the inverse generalized sine functions, followed by the construction of the associated cosine functions, and from this, various properties of the generalized trigonometric functions are derived. However, the results contained in this book are based on the application of both geometrical phase space and dynamical systems methodologies.


Features








Clear, direct construction of a new set of generalized trigonometric and hyperbolic functions







Presentation of why x2+y2 = 1, and related expressions, may be interpreted in three distinct ways







All the constructions, proofs, and derivations can be readily followed and understood by students, researchers, and professionals in the natural and mathematical sciences "Differing from the standard approach, this book argues the benefits of creating and analyzing generalized trigonometric functions using methodologies involving geometrical phase-space and dynamical systems. This is a mouthful, but Mickens (Clark Atlanta Univ.) takes on his subject with vigor. After a brief overview of the standard approaches and results, Mickens discusses square and parabolic forms of periodic and hyperbolic functions, as well as their generalized forms. From this basic understanding, he uses special functional equations to define a 'new class' of generalized trigonometric and hyperbolic functions, which he uses to model important dynamical systems."





-J. Johnson, Emeritus Professor, Western Washington University

Generalized Trigonometric and Hyperbolic Functions

Spis treści

1 TRIGONOMETRIC AND HYPERBOLIC SINE AND CO-SINE FUNCTIONS





2 ELLIPTIC FUNCTIONS





3 SQUARE FUNCTIONS





4 PARABOLIC TRIGONOMETRIC FUNCTIONS





5 GENERALIZED PERIODIC SOLUTIONS OF f(t)2+g(t)2 = 1





6 RESUME OF (SOME) PREVIOUS RESULTS ON GENERALIZED TRIGONOMETRIC FUNCTIONS 99





7 GENERALIZED TRIGONOMETRIC FUNCTIONS: |y|p +|x|q = 1





8 GENERALIZED TRIGONOMETRIC HYPERBOLIC FUNCTIONS: |y|p |x|q = 1





9 APPLICATIONS AND ADVANCED TOPICS





10 FINALE

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