Hyperbolic Functions by James McMahon

Hyperbolic Functions - Table of Contents

1. Correspondence of Points on Conics 2. Areas of Corresponding Triangles 3. Areas of Corresponding Sectors 4. Characteristic Ratios of Sectorial Measures 5. Ratios Expressed as Triangle-Measures 6. Functional Relations for Ellipse 7. Functional Relations for Hyperbola 8. Relations Among Hyperbolic Functions 9. Variations of the Hyperbolic Functions 10. Anti-Hyperbolic Functions 11. Functions of Sums and Differences 12. Conversion Formulas 13. Limiting Ratios 14. Derivatives of Hyperbolic Functions 15. Derivatives of Anti-Hyperbolic Functions 16. Expansion of Hyperbolic Functions 17. Exponential Expressions 18. Expansion of Anti-Functions 19. Logarithmic Expression of Anti-Functions 20. The Gudermannian Function 21. Circular Functions of the Gudermannian 22. Gudermannian Angle 23. Derivatives of the Gudermannian and Its Inverse 24. Series for the Gudermannian and Its Inverse 25. Graphs of Hyperbolic Functions 26. Elementary Integrals 27. Functions of Complex Numbers 28. Addition-Theorems for Complex Arguments 29. Functions of Pure Imaginaries 30. Functions of (x + i y) in the Form (X + i Y) 31. The Catenary 32. The Catenary of Uniform Strength 33. The Elastic Catenary 34. The Tractory 35. The Loxodrome 36. Combined Flexure and Tension 37. Alternating Currents 38. Miscellaneous Applications 39. Explanation of Tables 40. Appendix (Historical and Bibliographical)

What You Will Learn in Hyperbolic Functions

"Lectures on the Hyperbolic Functions" by "James McMahon" is a classic text exploring "hyperbolic functions" and their applications in "mathematical analysis" and "function theory". The book systematically develops the properties, identities, and relationships of functions such as sinh, cosh, and tanh. McMahon presents the material in a clear, lecture-style format, making advanced topics accessible to students, researchers, and mathematicians. The text covers differentiation, integration, series expansions, and the connections between "hyperbolic functions" and "trigonometric functions", highlighting their use in solving complex mathematical problems. Through worked examples and exercises, McMahon provides a rigorous foundation for understanding the behavior and applications of these functions, bridging theoretical concepts with practical computation and problem-solving techniques. Renowned for clarity and thoroughness, McMahon’s lectures remain a valuable reference in "function theory", advanced analysis, and applied mathematics. The book is essential for anyone studying hyperbolic functions in both pure and applied contexts, offering insight into their properties, transformations, and applications. Its systematic approach continues to guide students and researchers, making it a foundational work in the study of "mathematical functions".

Book Details & Specifications

Title: Hyperbolic Functions by James McMahon
Publisher: J. Wiley
Year: 1906
Pages: 110
Type: PDF
Language: English
ISBN-10 #: 0331218070
ISBN-13 #: 978-0331218077
License: Public Domain Work
Amazon: Amazon

About the Author: James McMahon

The author James McMahon (1856–1922) was an American mathematician and educator known for his work on "hyperbolic functions", "trigonometric functions", "function theory", and "mathematical analysis". He taught at the University of Notre Dame, where he advanced the study and teaching of higher mathematics. McMahon authored "Lectures on the Hyperbolic Functions", a classic text on "mathematical functions". His books are celebrated for clarity, rigorous proofs, and systematic presentation, making complex topics accessible to students, researchers, and mathematicians. His work continues to influence the study of hyperbolic and trigonometric functions in both pure and applied mathematics.

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