A Course in Mathematical Analysis Volume 1 by Edouard Goursat
A Course in Mathematical Analysis Volume 1 - Table of Contents
1. Derivatives and Differentials
1.1 Functions of a Single Variable
1.2 Functions of Several Variables
1.3 The Differential Notation
2. Implicit Functions, Functional Determinants, and Change of Variables
3. Taylor’s Series, Elementary Applications, Maxima and Minima
4. Definite Integrals
5. Indefinite Integrals
6. Double Integrals
7. Surface Integrals
8. Multiple Integrals; Integration of Total Differentials
9. Infinite Series
10. Power Series; Trigonometric Series
11. Plane Curves
12. Skew Curves (Space Curves)
13. Surfaces
What You Will Learn in A Course in Mathematical Analysis Volume 1
"A Course in Mathematical Analysis, Volume 1" by Édouard Goursat is a classic textbook that provides a rigorous introduction to "mathematics" for first-year college students. The book focuses on fundamental concepts in "calculus" and "real analysis", including derivatives, differentials, definite and indefinite integrals, and the study of functions of one variable. Goursat’s approach combines clarity with depth, making complex topics accessible to learners while maintaining mathematical rigor.
The book covers essential topics such as Taylor series, maxima and minima, infinite and power series, and the application of analysis to geometry. Step-by-step examples and exercises are included to reinforce understanding and develop problem-solving skills. This structured approach ensures that students not only learn computational techniques but also gain a deep conceptual understanding of "real analysis" principles.
Volume 1 of Goursat’s series is ideal for students seeking a strong foundation in "calculus" and "mathematics", preparing them for advanced studies in analysis and related fields. Its careful explanations, logical organization, and practical exercises make it both a learning resource and a reliable reference for teachers, students, and anyone interested in classical analysis.
Book Details & Specifications
Title:
A Course in Mathematical Analysis Volume 1 by Edouard Goursat
Publisher:
Ginn & Company
Year:
1904
Pages:
577
Type:
PDF
Language:
English
ISBN-10 #:
1016696558
ISBN-13 #:
978-1016696555
License:
Public Domain Work
Amazon:
Amazon
About the Author: Goursat Edouard
The author Goursat Edouard
(1858–1936) was a renowned French mathematician known for his contributions to "mathematics", particularly in "real analysis" and "complex analysis". He studied at the École Normale Supérieure and later became a professor at the University of Paris, where he influenced generations of students with his clear, rigorous teaching. Goursat is most famous for his *Cours d’analyse mathématique*, a comprehensive three-volume work that covers calculus, series, and function theory.
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