This book presents the theoretical foundations of the comparison approach and demonstrates how this method can be used for the development of techniques for the analysis and design of control systems in the state-space domain. It provides a framework for using the comparison approach to solve fundamental analysis and design problems of control systems, including invariance and contractivity, stability analysis and constrained control.Within this framework, the book shows the reader...

Unlock the essentials of linear algebra to build a strong foundation for machine learning. Dive into vectors, matrices, and principal component analysis with expert guidance in "Before Machine Learning Volume 1 - Linear Algebra."Key FeaturesComprehensive introduction to linear algebra for machine learningDetailed exploration of vectors and matricesIn-depth study of principal component analysis (PCA)Book DescriptionIn this boo...

Everything you need to know about 100 key mathematical concepts condensed into easy-to-understand sound bites designed to stick in your memory and give you an instant grasp of the concept.On each topic, you'll start with a helicopter overview of the subject, which will give you an introduction to the idea and some context surrounding it. Next, you'll zoom in on the core elements of the theory, with clear explanation of each point to make sure you really understand the concept, alon...

This open access book covers the main topics for a course on the differential geometry of curves and surfaces. Unlike the common approach in existing textbooks, there is a strong focus on variational problems, ranging from elastic curves to surfaces that minimize area, or the Willmore functional. Moreover, emphasis is given on topics that are useful for applications in science and computer graphics. Most often these applications are concerned with finding the shape of a curve or a surface ...

Mathematics for Physical Chemistry is the ideal supplementary text for practicing chemists and students who want to sharpen their mathematics skills while enrolled in general through physical chemistry courses. This book specifically emphasizes the use of mathematics in the context of physical chemistry, as opposed to being simply a mathematics text. This 4e includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage sel...

The book begins by examining in dynamic terms Planck's constant h as the “Least Action” to end in the operational logic of quantum gravity. This topic has so far been addressed by physicists with little clarity and too much mathematics. It is useful to recall a famous suggestion that Feynman gave to his students, namely to "write your equations only when you know the result".The scenario in which this research takes place is a quantized sp...

There is an increasing need for undergraduate students in physics to have a core set of computational tools. Most problems in physics benefit from numerical methods, and many of them resist analytical solution altogether. This textbook presents numerical techniques for solving familiar physical problems where a complete solution is inaccessible using traditional mathematical methods. The numerical techniques for solving the problems are clearly laid out, with a focus on the logic and appli...

This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A.The book contains the relevan...

This open access book is about spontaneous symmetry breaking, which is a classic area of theoretical physics that lies at the core of many fascinating phenomena such as ferromagnetism, superfluidity, superconductivity, or the Higgs mechanism. The book brings an up-to-date overview of spontaneous symmetry breaking and of modern effective field theory description thereof. The topics covered include the classification of Nambu–Goldstone bosons, nonlinear realization of internal and spacetime ...

Many physicists have pointed out that the formulation of Quantum Mechanics is missing an important piece. Its theoretical incompleteness has been evoked, there has been talk of hidden variables, non-locality of the theory, provoking long debates which have left things at a standstill. There is even Einstein's famous phrase in which he says that "God does not play dice". A big mistake! If God did not play dice, as Darwin taught us, there would be neither evolution nor the immense v...

Covers ODEs and PDEs-in One TextbookUntil now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn't exist. Fulfilling this need, Ordinary and Partial Differential Equations provides a complete and accessible course on ODEs and PDEs using many examples and exercises as well as

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26–29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of th...