Linear Mathematics In Infinite Dimensions by Ulrich H. Gerlach
Book Contents :-
0. Introduction
1. Sturm–Liouville Theory
2. Infinite Dimensional Vector Spaces
3. Fourier Theory
4. Green’s Function Theory
5. Special Function Theory
6. Partial Differential Equations
About this book :-
"Linear Mathematics in Infinite Dimensions: Signals, Boundary Value Problems and Special Functions" by Ulrich H. Gerlach is an advanced book that extends familiar "linear algebra" into the world of "infinite-dimensional spaces". It is designed for students of applied mathematics, physics, and engineering who work with functions rather than finite vectors. The book builds a clear bridge between abstract theory and real physical problems.
The text focuses on "Hilbert spaces", orthogonal expansions, and linear operators, showing how these ideas are used to analyze signals and continuous systems. Gerlach carefully explains tools such as Fourier series, eigenfunction expansions, and operator methods. These concepts are essential for solving differential equations that appear in wave motion, heat flow, and electromagnetics.
A major strength of the book is its treatment of "boundary value problems" and "special functions". Topics like Sturm–Liouville theory and Green’s functions are presented with strong intuition and mathematical clarity. Rather than treating infinite-dimensional mathematics as purely abstract, the book emphasizes applications, making it a valuable reference for understanding modern mathematical methods used in science and engineering.
Book Detail :-
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 Author :-
The author
Professor Thomas Gerlach
is a mathematician and professor emeritus known for his work in "applied mathematics" and "mathematical physics". He taught for many years at The Ohio State University, where he focused on advanced topics connecting mathematics with real physical systems. Gerlach is especially recognized for his teaching and writing on "infinite-dimensional spaces", "Hilbert spaces", and "boundary value problems". His work emphasizes clarity and application, helping students understand how abstract mathematical ideas are used in physics, engineering, and signal analysis.
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