Tensor Analysis

Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living on an n-dimensional smooth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. In contrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies.

The book presents earthquake source, wave propagation, site amplification, and other seismological studies including earthquake simulation, application of Artificial Neural Network (ANN) in seismology, earthquake early warning system, waveform inversion, moment tensor analysis, receiver function analysis, earthquake prediction, and earthquake early warning system applications. To minimize the losses due to an earthquake, it is better to understand the source properties, medium characteristics, site condition, and amplitude of a probable earthquake at a particular site. The evolutions of earthquake source models make it possible to understand the source dynamics. However, analysis of the source using a single-domain method does not provide a better understanding of the source dynamics. Therefore, this book combines methods from the earthquake spectrum to waveform inversion and joint inversion.

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

This book deals with finite element analysis of structures and will be of value to students of civil, structural and mechanical engineering at final year undergraduate and post-graduate level.