Differential Calculus by Pierre Schapira
Differential Calculus - Table of Contents
- 1. DIFFERENTIABLE MAPS
- 1.1 Differential
- 1.2 Necessary conditions for extremum
- 1.3 The mean value theorem
- 2. HIGHER DIFFERENTIALS
- 2.1 The Schwarz lemma
- 2.2 The Taylor formula
- 2.3 Applications to extremum
- 3. SUBMANIFOLDS
- 3.1 The local inversion theorem
- 3.2 The constant rank theorem
- 3.3 Submanifolds
- 3.4 Tangent space
What You Will Learn in Differential Calculus
Differential Calculus by Pierre Schapira is an advanced, concise university textbook designed for upper-level undergraduate and graduate mathematics students. The text bridges multi-variable calculus with modern differential geometry, covering core analytical concepts across its primary chapters: Differentiable Maps and Mean Value Theorems, Higher Differentials and Extremum Applications, and Submanifolds, Local Inversion, and Tangent Spaces.
This book serves as an invaluable guide for mathematics majors and researchers in analysis and differential geometry who seek a clear, structural foundation in advanced calculus. Schapira combines precise definitions with elegant, coordinate-free proofs, ensuring readers develop strong analytical intuition.
Due to its logical precision and modern geometric exposition, it is widely recognized as an outstanding transition text for advanced differential analysis and manifold theory. Rather than focusing on routine computational exercises, it equips learners with the formal tools necessary for global analysis, differential topology, and theoretical physics.
Book Details & Specifications
Title:
Differential Calculus by Pierre Schapira
Publisher:
Université Paris VI
Year:
2011
Pages:
68
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
External Educational Resource
Amazon:
Amazon
About the Author: Pierre Schapira
The author Pierre Schapira
(born 1943) is a distinguished French mathematician and professor emeritus at Sorbonne University, renowned worldwide for his pioneering work in algebraic analysis, sheaf theory, and micro-local analysis.
Through Differential Calculus, Schapira successfully distilled complex geometric and analytical concepts into a clear, highly structured textbook. His precise mathematical style makes this text a masterpiece resource for higher differential analysis.
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