Geometric and Computational Spectral Theory 1st Edition by Alexandre Girouard, Dmitry Jakobson, Michael Levitin ISBN 9781470442583 1470442582

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Product details:

ISBN 10: 1470442582
ISBN 13: 9781470442583
Author: Alexandre Girouard, Dmitry Jakobson, Michael Levitin

Geometric and Computational Spectral Theory 1st Edition Table of contents:

Part I – Foundations

1.Introduction to Spectral Theory

2.Laplace Operators on Manifolds

3.igenvalues and Eigenfunctions

4.Heat Kernel Methods

5.Variational Principles

Part II – Geometric Aspects
6. Spectral Geometry and Isoperimetric Inequalities
7. Nodal Sets and Domains
8. Geodesics, Dynamics, and Spectrum
9. Quantum Ergodicity and Chaos
10. Spectral Invariants and Geometry of Manifolds

Part III – Computational Approaches
11. Numerical Methods for Eigenvalue Problems
12. Finite Element Methods in Spectral Theory
13. Spectral Approximations on Graphs and Networks
14. Computational Techniques for Laplacians on Domains
15. Algorithms for High-Dimensional Spectral Problems

Part IV – Applications
16. Spectral Methods in Mathematical Physics
17. Random Spectra and Probabilistic Approaches
18. Spectral Problems in Geometry and Topology
19. Connections to Number Theory
20. Emerging Directions in Computational Spectral Theory

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Tags: Alexandre Girouard, Dmitry Jakobson, Michael Levitin, Computational Spectral