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Pereyra N: Limits and Derivatives of
Real Functions for Physicists

Limits and Derivatives of Real Functions for Physicists

This book covers complex analysis (the study of boundary behaviors of analytic functions) and its applications with engineering problems, especially control theory from the viewpoint of boundary functions. The metascience part is rather unique and illustrates a metascientific way of thinking engineering problems by examples of batteries which are cores of electric vehicles.This book gives a way of looking at the phenomena from a higher and brighter point of view through the windows of boundary behavior and metascience. In Chapter 1 which is meant for mathematics-oriented readers, we state materials in standard complex analysis with emphasis on similarity and Laurent expansions. Non-mathematical readers can also benefit by browsing through many examples and worked-out exercises. Chapter 2 gives some concrete examples of invoking novel ideas in the heap of stereo-typed contributions to a field. Possible replacement of LIB by ECaSS(R) is a typical example through which the reader can learn basics of electromagnetism and electrochemistry. The book also provides hints for a deeper understanding of environmental problems as well as how to manage and create a sustainable society.

From Complex Analysis To Metascience: A Stroll Around Boundary Behavior, Similarity And Duality

Dynamics and Astrophysics of Galaxies

This book presents a comprehensive treatment of pricing and hedging soccer betting contracts using the modern techniques of probability, statistics, finance, and portfolio management. It introduces betting in general and then addresses the probabilistic intuition needed in the more complex world of soccer betting. The author presents an innovative perspective by thinking about betting odds in terms of the expected number of goals of both teams. In addition, when the betting market is in play, the book treats betting before the game and during the game separately.

Science of Soccer Statistics

Soccermetrics

Lectures On Quantum State Estimation

This book covers the basics of nanotechnology and its role in biomedical engineering. It clubs different applications of nanotechnology in medicine, disease diagnostics, artificial implants; nano-enabled implantable devices and nanorobots as future mode of treatment of various diseases. It provides a comprehensive overview to the reader about the basics of above areas as well as advanced implementation strategies. Case studies included in the book will help readers get a proper understanding of the subject and how nanotechnology is a boon for medical and bioengineering.

Nanotechnology in Biomedicine

This book makes an attempt to introduce the physical concept behind the operation of microwave and millimeter wave semiconductor devices in detail. It is written for undergraduates and postgraduates of Physics, Electronics, Electrical and Electronics Engineering.

Physics and Application

Microwave Semiconductor Devices

In this volume various aspects of non-Archimedean quantum systems are discussed, such as spectral properties of their Schrödinger operators, and their ability to be approximated by finite systems. Non-Archimedean stochastic methods are also discussed.

Quantum Systems And Finite Approximations: Archimedean And Non-archimedean

While the field of Deep Learning has been advancing at frightening speeds during the last ten years, we do not have a plausible theoretical explanation of its success yet. One can safely say that Deep Learning works, but nobody really understands why. Nevertheless, starting around five years before now, a decent number of theoretical papers specifically concerning neural nets started to emerge at top machine learning venues. This makes us think that the core of Deep Learning theory has already started to crystallize.The goal of the present book is to present these core concepts of Deep Learning theory to readers so that they could directly dive into recent papers of this area. For this purpose, each chapter elaborates a simple model or a classical result in details first and then discusses possible generalizations and more recent developments of the same idea.We have to warn the reader that the present book is not a mathematical manuscript. Not all results here are stated as formal theorems and not all theorems are provided with complete and rigorous proofs. Many of the theorems of the book are proven up to some technical lemmas, while for some there is only a proof sketch. This conforms with the main idea of the book: present and illustrate concepts rather than reproduce all the results.The book, in its present form, covers the following topics: uniform generalization bounds, PAC-bayesian generalization bounds, double descent phenomena, infinitely-wide networks, implicit bias of gradient descent, loss landscape, gradient descent convergence guarantees, and initialization strategies.

Elements Of Deep Learning Theory

Why Not Nonlinear Algebra: Math, Science, Applications And Funding

Gibbs Measures In Machine Learning

Series in Materials Science and Engineering

This book provides an introduction to the geometrical and topological methods that have become essential tools for soft condensed matter physicists. The emphasis is on providing mathematical tools in clear but precise language, focusing on fundamental concepts using real examples to illustrate for readers in vivid, three-dimensional fashion. The motivation is clearly provided using problems from soft condensed matter, from the packing of colloids to liquid crystals and thermal fluctuations of lipid membranes.

Geometry and Topology of Soft Materials

Limits and Derivatives of Real Functions for Physicists

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