Advanced Calculus by Edwin Bidwell Wilson - PDF
Book Contents :-
INTRODUCTORY REVIEW
1. Review of Fundamental Rules
2. Review of Fundamental Theory
Part-I DIFFERENTIAL CALCULUS
3. Taylor's Formulas and Allied Topics
4. Partial Differentiation; Explicit Functions Section
5. Partial Differentiation; Implicit Functions
6. Complex Numbers and Vectors
7. General Introduction to Differential Equations
8. The Commoner Ordinary Differential Equations
9. Additional Types of Ordinary Equations
10. Differential Equations in more than Two Variables
Part-III INTEGRAL CALCULUS
11. On Simple Integrals
12. On Multiple Integrals
13. On Infinite Integrals
14. Special Functions Defined by Integrals
15. The Calculus of Variations
16. Infinite Series
17. Special Infinite Developments
18. Functions of a Complex Variable
19. Elliptic Functions and Integrals
20. Functions of Real Variables
About this book :-
"Advanced Calculus by Edwin Bidwell Wilson" is a landmark, designed to bridge the gap between elementary calculus and modern mathematical analysis. The book emphasizes "rigor", logical reasoning, and generalization, moving beyond computation to the theoretical foundations of calculus. Wilson’s clear structure and precision make it a valuable reference for students of mathematics, physics, and engineering.
The text explores essential topics such as limits, continuity, differentiation, and integration, extending these ideas to functions of several variables. It introduces "vector analysis", including operations like gradient, divergence, and curl, which are crucial for understanding physical applications. Wilson also covers multiple integrals, coordinate transformations, and the use of Jacobians, offering readers both conceptual depth and analytical tools.
As one of the earliest American books to integrate the ideas of European mathematical rigor, "Advanced Calculus" played a key role in shaping the teaching of higher mathematics in the 20th century. It remains notable for its balance of theory and application, clarity of presentation, and influence on future textbooks. For learners seeking a strong theoretical foundation in advanced mathematics, Wilson’s work continues to be an enduring and "influential" resource.
Book Detail :-
Title:
Advanced Calculus by Edwin Bidwell Wilson - PDF
Publisher:
Boston Ginn
Year:
1912
Pages:
588
Type:
PDF
Language:
English
ISBN-10 #:
1173358242
ISBN-13 #:
978-1173358242
License:
Public Domain Work
Amazon:
Amazon
About Author :-
The author
Edwin Bidwell Wilson
(1879–1964) was an American "mathematician" and physicist known for his major contributions to mathematical education and applied science. A student of Josiah Willard Gibbs at Harvard, he became one of the first to promote rigorous and logical approaches to higher mathematics in the United States. Wilson’s most famous work, "Advanced Calculus" (1912), introduced students to modern mathematical analysis and "vector analysis", blending theory with practical application. Beyond mathematics, he contributed to "mathematical physics", public health, and economics, leaving a lasting impact on scientific research and education.
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