An Elementary Treatise on Elliptic Functions by Arthur Cayley - PDF

About this book :-
"Arthur Cayley’s An Elementary Treatise on Elliptic Functions" is a classic introduction to "elliptic functions", providing a clear and structured guide for students and mathematicians alike. This treatise builds a solid foundation in "complex analysis", helping readers understand the theory behind these important mathematical functions. Cayley’s approach emphasizes clarity, rigor, and systematic development of concepts, making challenging ideas accessible without oversimplifying. The book covers essential topics such as "elliptic integrals", theta functions, and algebraic properties of "elliptic functions". Cayley carefully explains addition theorems, transformations, and practical methods for working with these functions, offering numerous examples and step-by-step derivations. The treatise bridges theory and application, showing how "complex analysis" can be applied to solve real mathematical problems. Designed for both learners and researchers, this work also highlights connections to "mathematical physics", demonstrating the role of elliptic functions in geometry, mechanics, and other applied fields. Whether used as a study resource or a historical reference, Cayley’s treatise remains a foundational work, combining elegant mathematical reasoning with practical insights. It continues to be an essential reference for anyone exploring the world of "elliptic functions" and "complex analysis".

Book Detail :-
Title: An Elementary Treatise on Elliptic Functions by Arthur Cayley - PDF
Publisher: G. Bell and sons
Year: 1895
Pages: 411
Type: PDF
Language: English
ISBN-10 #: 1429700491
ISBN-13 #: 978-1429700498
License: Public Domain Work
Amazon: Amazon

About Author :-
The author Arthur Cayley (1821–1895) was a pioneering British mathematician known for his groundbreaking contributions to "mathematics", including "elliptic functions", algebra, and geometry. He played a key role in developing "complex analysis" and modern algebraic theory, influencing generations of mathematicians. Cayley’s writings, especially "An Elementary Treatise on Elliptic Functions", are celebrated for their clarity, structure, and rigor. His work bridges theoretical and practical aspects of mathematics, making advanced concepts accessible. Today, Cayley remains a foundational figure in the study of "elliptic functions" and "complex analysis", with enduring impact in both pure and applied mathematics.

Book Contents :-
1. General Outline 2. The Addition-Equation. Landen’s Theorem 3. Miscellaneous Investigations 4. On the Elliptic Functions sn, cn, dn 5. The Three Kinds of Elliptic Integrals 6. The Functions T(u), H(u), Z(u), ?2(u), ?3(u), ?4(u) 7. Transformation. General Outline 8. The Quadratic Transformation (n = 2); and the Odd-Prime Transformations (n = 3, 5, 7). Properties of the Modular Equation and the Multiplier 9. Jacobi’s Partial Differential Equations for H, T, and for the Numerators and Denominators in the Multiplication and Transformation of the Elliptic Functions sn, cn, dn 10. Transformation for an Odd n, and in Particular an Odd-Prime Order: Development of the Theory by Means of the Expansion of the Complete Functions 11. The q-Functions: Further Theory of the Functions H, T 12. Reduction of a Differential Expression 13. Quadratic Transformation of the Elliptic Integrals of the First and Second Kinds: The Arithmetic–Geometric Mean 14. The General Differential Equation 15. On the Determination of Certain Curves whose Arc is Represented by an Elliptic Integral of the First Kind 16. On Two Integrals Reducible to Elliptic Integrals

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