IISc Lecture Notes Series – serie

Computational spectroscopy and computational quantum chemical dynamics is a vast field in physical chemistry. Significant part of this field is developed based on the concepts of time-dependent quantum mechanics and its numerical implementations.This book gives an introduction to the Time-Dependent Quantum Chemistry for use with any introductory college/university course in optics, spectroscopy, kinetics, dynamics, or experimental physical chemistry or chemical physics of the kind usually taken by undergraduate and graduate students in physical chemistry. In this book, different concepts of time-dependent quantum mechanics are systematically presented by first giving emphasis on the contrasting viewpoint of classical and quantum mechanical motion of a particle, then by demonstrating the ways to find classical flavour in quantum dynamics, thereafter by formally defining the wavepacket which represents a quantum particle and finally by demonstrating numerical methods to explore the wavepacket dynamics in one dimension. Along with the analytical theory, accompanying Python chapters in this book take readers to a hands-on tour with Python programming by first giving them a quick introduction to the Python programming, then by introducing the position-space grid representation of the wavefunction, thereafter, by making them familiarized with the Fourier transform to represent the discretized wavefunction in momentum space, subsequently by showing the Python-based methodologies to express Hamiltonian operator in matrix form and finally by demonstrating the entire Python program which solves the wavepacket dynamics in one dimension under influence of time-independent Hamiltonian following split-operator approach.Rigorous class-testing of the presented lecture notes at the Indian Institute of Science, GITAM University and at NPTEL platform reveals that physical chemistry students, after thoroughly going through all chapters, not only develop an in-depth understanding of the wavepacket dynamics and its numerical implementations, but also start successfully writing their own Python code for solving any one dimensional wavepacket dynamics problem.

This unique compendium stresses on physical concepts and the applications to practical problems. The authors' decades of experience in teaching, research and industrial consultancy are reflected in the choice of the solved examples and unsolved problems.The second edition has three additional chapters containing topics of vibration and acoustic sensors and instruments, finite element method (FEM), boundary element method (BEM) and statistical energy analysis (SEA), etc, thus enabling students to solve real-life problems in industrial and automotive noise control.The useful reference text targets senior undergraduate mechanical and environmental engineering students as well as designers of industrial machinery and layouts. The book can readily be used for self-study by practicing designers and engineers. Mathematical derivations are avoided and illustrations, tables and empirical formulae are included for ready reference.

The primary goal of this text book is to ensure that any physical science student, even one who has never heard of the subject, should be able to learn what ultrafast spectroscopy is, why optics related to the subject requires special attention, how to use the basic ideas of the subject in laboratory-based ultrafast spectroscopy experiments, how to interpret the experimental observations and so on. This book gives a more than adequate introduction to mathematical representation of an ultrafast pulse, chirp, time-band width product, nonlinear optical effects, dispersion effects, construction of ultrafast laser, ultrafast measurement techniques and different ultrafast processes of chemical interest.

The primary goal of this text book is to ensure that any physical science student, even one who has never heard of the subject, should be able to learn what ultrafast spectroscopy is, why optics related to the subject requires special attention, how to use the basic ideas of the subject in laboratory-based ultrafast spectroscopy experiments, how to interpret the experimental observations and so on. This book gives a more than adequate introduction to mathematical representation of an ultrafast pulse, chirp, time-band width product, nonlinear optical effects, dispersion effects, construction of ultrafast laser, ultrafast measurement techniques and different ultrafast processes of chemical interest.

This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics.Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.

This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics.Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.

The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date. This volume of lecture notes focuses on its differential geometric developments by several excellent authors including, but not limited to, L Ahlfors, S S Chern, Y C Lu, S T Yau and H L Royden.This volume can be approached by a reader who has basic knowledge on complex analysis and Riemannian geometry. It contains major historic differential geometric generalizations on Schwarz's Lemma and provides the necessary information while making the whole volume as concise as ever.

This book adopts a detailed and methodological algorithmic approach to explain the concepts of pattern recognition. While the text provides a systematic account of its major topics such as pattern representation and nearest neighbour based classifiers, current topics — neural networks, support vector machines and decision trees — attributed to the recent vast progress in this field are also dealt with. Introduction to Pattern Recognition and Machine Learning will equip readers, especially senior computer science undergraduates, with a deeper understanding of the subject matter.

Vibration and noise are two interrelated terms in the field of mechanical engineering. Vibration is caused by unbalanced inertial forces and moments whereas noise is the result of such vibrations. Noisy machines have always been a matter of concern. Lesser vibration ensures manufacturing to closer tolerances, lesser wear and tear, and longer fatigue life. Hence, a quieter machine is more cost-effective in the long run. It is now well understood that a quieter machine is in every way a better machine.This book deals with such industrial and automotive noise and vibration, their measurement and control. This textbook stresses on physical concepts and the application thereof to practical problems. The author's four decades of experience in teaching, research and industrial consultancy is reflected in the choice of the solved examples and unsolved problems.The book targets senior undergraduate students in mechanical engineering as well as designers of industrial machinery and layouts. It can readily be used for self-study by practicing designers and engineers.