Linear Mathematics In Infinite Dimensions by Ulrich H. Gerlach
Linear Mathematics In Infinite Dimensions - Table of Contents
PART I: FOUNDATIONS & OPERATOR THEORY
- 0. Introduction to Linear Mathematics
- 1. Sturm–Liouville Theory and Eigenfunctions
- 2. Infinite Dimensional Vector Spaces & Hilbert Spaces
PART II: INTEGRAL TRANSFORMS & DIFFERENTIAL EQUATIONS
- 3. Fourier Theory and Integral Transforms
- 4. Green’s Function Theory for Differential Operators
- 5. Special Function Theory in Mathematical Physics
- 6. Partial Differential Equations Solutions
What You Will Learn in Linear Mathematics In Infinite Dimensions
Linear Mathematics In Infinite Dimensions by Ulrich H. Gerlach is an authoritative, advanced textbook that bridges infinite-dimensional linear algebra, functional analysis, and mathematical physics. This comprehensive volume guides readers through Sturm–Liouville boundary value problems, infinite-dimensional vector spaces, Fourier transforms, Green’s function theory, special functions, and partial differential equations with exceptional physical insight and mathematical rigor.
Designed for graduate students, theoretical physicists, applied mathematicians, and engineering scientists, this foundational text details the infinite-dimensional mathematical structure underlying quantum mechanics and field theory. Gerlach provides step-by-step developments of complete orthonormal sets, linear differential operators, and integral representations for boundary value problems. Whether you are studying Hilbert spaces, eigenfunction expansions, or wave equations, this book offers an indispensable roadmap.
Recognized globally for its deep physical intuition and unified operator approach, it remains one of the best infinite-dimensional linear algebra books for self-study. By balancing abstract functional analysis with concrete differential operator methods, it serves as an essential tool for mastering linear mathematics in infinite dimensions with confidence.
Book Details & Specifications
Title:
Linear Mathematics In Infinite Dimensions by Ulrich H. Gerlach
Publisher:
The Ohio State University
Year:
2020
Pages:
520
Type:
PDF
Language:
English
ISBN-10 #:
0387944753
ISBN-13 #:
978-0387944753
License:
University Resource
Amazon:
Amazon
About the Author: Ulrich H. Gerlach
The author Ulrich H. Gerlach
is an Emeritus Professor in the Department of Mathematics at The Ohio State University, internationally recognized for his research in mathematical physics, general relativity, quantum optics, and black hole thermodynamics. He earned his doctorate from Princeton University under the supervision of John Archibald Wheeler and spent decades teaching advanced linear algebra, differential equations, and mathematical physics.
Developed from years of university instruction, Gerlach authored Linear Mathematics In Infinite Dimensions to provide students with a cohesive geometric and operator-theoretic approach to infinite-dimensional vector spaces. His commitment to physical relevance, intuitive geometric reasoning, and complete analytical proofs makes this text a classic reference for infinite-dimensional vector spaces that continues to be valued by mathematicians and physicists worldwide.
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