Applied Analysis by the Hilbert Space Method: An Introduction with Applications to the Wave, Heat and Schrodinger Equations (Dover Books on Mathematics)

Book Details:

• Publisher: Dover

• Author: Samuel S. Holland

• Language: English

• Binding: Paperback

• Edition: Dover Ed

• ISBN: 9780486458014

• Number of Pages: 576

• Dimensions: 8.5 x 5.6 x 1.3 inches

• Release Date: 05-06-2007

About The Book:

"Hermitian Operators in Hilbert Spaces" by Samuel S. Holland provides a unified and accessible treatment of Hermitian operator theory in the context of Hilbert spaces. Aimed at undergraduate students, this book is ideal for self-study and serves as a comprehensive reference for more advanced readers in applied mathematics, physics, and engineering.

Key features of the book include:

• Worked Examples and Exercises: Numerous examples and exercises are included to help students grasp complex concepts and ensure a solid understanding.

• Introduction to Hilbert Space Theory: The book begins by explaining the fundamentals of Hilbert spaces and Hermitian differential operators, which are crucial for various applications in physics and engineering.

• First and Second-Order Linear Differential Equations: Detailed discussions on these equations lay the groundwork for understanding more advanced topics.

• Eigenvalues and Eigenfunctions: The author develops the theory of eigenvalues and eigenfunctions of classical Hermitian differential operators, a foundational concept in quantum mechanics and other fields.

• Schrödinger's Equation: The book provides a comprehensive account of Schrödinger's equation, which is central to quantum mechanics.

• Fourier Transform: A survey of the Fourier transform as a unitary operator, which is a vital tool in both theoretical and applied mathematics.

Samuel S. Holland simplifies some of the proofs to make the text accessible to undergraduates while maintaining the core ideas of essential results. This book is highly recommended for students in applied mathematics, physics, and engineering, as well as for applied mathematicians and theoretical engineers seeking a solid understanding of Hermitian operator theory.

Ideal for:

• Undergraduate students in mathematics, physics, and engineering.

• Self-study learners interested in Hermitian operators and Hilbert space theory.

• Professionals and researchers seeking a comprehensive yet accessible reference in applied mathematics and quantum mechanics.