Hyperbolic Functions by James McMahon - PDF
Hyperbolic Functions by James McMahon - PDF - 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 by James McMahon - PDF
"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 - PDF
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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