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1. Arithmetical Operations 2. Real Term Series 3. Series with Complex Terms 4. The Elementary Functions 5. Real Variables 6. Differentiation and Integration 7. Analytic Functions 8. Infinite Products 9. B and G Functions; Asymptotic Expansions 10. Functions of Weierstrass 11. Functions of Legendre and Jacobi 12. Theta Functions 13. Linear Differential Equations 14. Functions of Legendre and Laplace
"Theory of Functions" by James Pierpont is a foundational text in mathematical analysis that explores the structure of functions, limits, and continuity. The book introduces rigorous concepts of "function theory" and builds the logical framework needed for advanced study in real and complex analysis. Pierpont’s exposition reflects early twentieth-century mathematical precision and remains historically important. The work explains fundamental ideas such as series expansions, analytic functions, and properties of continuous mappings. It connects elementary analysis with deeper theoretical insights, helping readers understand how functions behave under different mathematical conditions. The treatment is systematic and suitable for students transitioning to higher mathematics. For learners and researchers of "complex analysis" and "function theory", this book serves as a valuable reference. It contributes to the historical development of modern analysis and continues to influence mathematical education. Its emphasis on rigor and conceptual clarity makes it significant for understanding the foundations of mathematical science.
Title: Theory of Functions by James Pierpont Publisher: Ginn and Co. Year: 1914 Pages: 595 Type: PDF Language: English ISBN-10 #: 1295893630 ISBN-13 #: 978-1295893638 License: Public Domain Work Amazon: Amazon
The author James Pierpont was a prominent American mathematician known for his contributions to "real analysis" and mathematical education. His book "Theory of Functions" provides a systematic study of function theory with rigorous proofs and logical structure. It became an important text for students learning advanced mathematics and analytical reasoning. The book focuses on topics of "analytic functions" and foundational ideas in mathematics. It emphasizes "mathematical rigor" and clear explanations of "calculus" concepts.
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