Advanced Calculus by Lynn H. Loomis, Shlomo Sternberg
Advanced Calculus - Table of Contents
1. Introduction
2. Vector Spaces
3. Finite-Dimensional Vector Spaces
4. Differential Calculus
5. Compactness and Completeness
6. Scalar Product Spaces
7. Differential Equations
8. Multilinear Functionals
9. Integration
10. Differentiable Manifolds
11. Integral Calculus on Manifolds
12. Exterior Calculus
13. Potential Theory in Rn
14. Classical Mechanics
What You Will Learn in Advanced Calculus
"Advanced Calculus" by Lynn H. Loomis and Shlomo Sternberg is a "rigorous" and comprehensive textbook designed for students seeking a deep understanding of "multivariable calculus" and its foundations. Unlike standard calculus texts, this book emphasizes "proofs", logical reasoning, and the conceptual structure behind mathematical ideas, making it ideal for advanced undergraduates and beginning graduate students.
The book covers a wide range of topics including "differentiable manifolds", vector calculus, integration in higher dimensions, and the underlying principles of "analysis". Each chapter blends formal definitions, theorems, and examples to guide students from intuitive understanding to precise mathematical thinking. The exercises are carefully crafted to reinforce concepts, develop problem-solving skills, and challenge students to think critically about abstract ideas.
Loomis and Sternberg’s text is perfect for anyone aiming to transition from computational calculus to a more abstract, theoretical perspective. Its clarity, depth, and focus on rigorous "mathematics" make it a cornerstone reference for advanced studies. Whether used for self-study, coursework, or as a foundation for research in mathematics, "Advanced Calculus" equips readers with the tools to master higher-level calculus and prepares them for further exploration in pure and applied analysis.
Book Details & Specifications
Title:
Advanced Calculus by Lynn H. Loomis, Shlomo Sternberg
Publisher:
Jones & Bartlett Publishers
Year:
1989
Pages:
592
Type:
PDF
Language:
English
ISBN-10 #:
0867201223
ISBN-13 #:
978-0867201222
License:
CC BY-NC-SA 2.0
Amazon:
Amazon
About the Author: Lynn H. Loomis and Shlomo Z. Sternberg
The author
Lynn H. Loomis and Shlomo Z. Sternberg
are renowned mathematicians and Harvard professors known for their expertise in "Advanced Calculus" and higher-level mathematics. Loomis contributed to analysis and the "Loomis–Whitney inequality", while Sternberg specialized in geometry and rigorous mathematical instruction. Their textbook "Advanced Calculus" provides a comprehensive, proof-based approach to topics like "Normed Vector Spaces", manifolds, and rigorous calculus. Designed for advanced undergraduates and early graduate students, it reflects their deep "Mathematical Scholarship" and emphasizes logical reasoning, precise definitions, and conceptual understanding, making it a foundational resource in modern analysis and higher mathematics education.
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