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Introduction to Mathematical Analysis
by Naokant Deo and Ryozi Sakai
English | 2024 | ISBN: 9819765676 | 353 Pages | True ePUB | 28 MB

This book is a straightforward and comprehensive presentation of the concepts and methodology of elementary real analysis. Targeted to undergraduate students of mathematics and engineering, it serves as the foundation for mathematical reasoning and proofs. The topics discussed are logic, methods of proof, functions, real number properties, sequences and series, limits and continuity and differentiation and integration (Riemann integral and Lebesgue integral). The book explains the concepts and theorems through geometrical and pictorial representation. Limits of sequences and functions, topology of metric spaces, continuity of functions and the Cauchy sequence have been thoroughly discussed in the book.





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Introduction to Mathematical Analysis
by Naokant Deo and Ryozi Sakai
English | 2024 | ISBN: 9819765676 | 353 Pages | True PDF | 8.65 MB

This book is a straightforward and comprehensive presentation of the concepts and methodology of elementary real analysis. Targeted to undergraduate students of mathematics and engineering, it serves as the foundation for mathematical reasoning and proofs. The topics discussed are logic, methods of proof, functions, real number properties, sequences and series, limits and continuity and differentiation and integration (Riemann integral and Lebesgue integral). The book explains the concepts and theorems through geometrical and pictorial representation. Limits of sequences and functions, topology of metric spaces, continuity of functions and the Cauchy sequence have been thoroughly discussed in the book.





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Jacek Banasiak, "Introduction to Mathematical Methods in Population Theory "
English | ISBN: 3031654900 | 2024 | 628 pages | PDF | 7 MB
This textbook provides an introduction to the mathematical methods used to analyse deterministic models in life sciences, including population dynamics, epidemiology and ecology. The book covers both discrete and continuous models.

The presentation emphasises the solvability of the equations appearing in the mathematical modelling of natural phenomena and, in the absence of solutions, the analysis of their relevant properties. Of particular interest are methods that allow for determining the long-term behaviour of solutions. Thus, the book covers a range of techniques, from the classical Lyapunov theorems and positivity methods based on the Perron-Frobenius theorem, to the more modern monotone dynamical system approach. The book offers a comprehensive presentation of the Lyapunov theory, including the inverse Lyapunov theorems with applications to perturbed equations and Vidyasagar theorem. Furthermore, it provides a coherent presentation of the foundations of the theory of monotone dynamical systems with its applications to epidemiological models. Another feature of the book is the derivation of the McKendrick-von Foerster equation from the discrete Leslie model and the analysis of the long-term behaviour of its solutions.
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Introduction to Nanoscience and Nanotechnology
by Charles P. Poole, Frank J. Owens
English | 2021 | ISBN: 9354240208 | 508 Pages | True ePUB | 17 MB

This book is a comprehensive text and a ready reckoner on the theory and applications of nanotechnology. It provides an insight into the history of nanoscience and nanotechnology. It discusses in-depth the optical, mechanical, electrical, magnetic, and catalytic properties of materials at nanoscale. It is a comprehensive discourse on nanostructured ferromagnetism, optical and vibrational spectroscopy, quantum wells, self-assembly, and biological materials at nanoscale.





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Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with Python and MATLAB, 2nd Edition
by Amir Beck
English | 2023 | ISBN: 1611977614 | 365 Pages | PDF | 24 MB

Built on the framework of the successful first edition, this book serves as a modern introduction to the field of optimization. The author's objective is to provide the foundations of theory and algorithms of nonlinear optimization as well as to present a variety of applications from diverse areas of applied sciences. Introduction to Nonlinear Optimization gradually yet rigorously builds connections between theory, algorithms, applications, and actual implementation. The book contains several topics not typically included in optimization books, such as optimality conditions in sparsity constrained optimization, hidden convexity, and total least squares. Readers will discover a wide array of applications such as circle fitting, Chebyshev center, the Fermat-Weber problem, denoising, clustering, total least squares, and orthogonal regression. These applications are studied both theoretically and algorithmically, illustrating concepts such as duality. Python and MATLAB programs are used to show how the theory can be implemented. The extremely popular CVX toolbox (MATLAB) and CVXPY module (Python) are described and used. More than 250 theoretical, algorithmic, and numerical exercises enhance the reader's understanding of the topics. (More than 70 of the exercises provide detailed solutions, and many others are provided with final answers.) The theoretical and algorithmic topics are illustrated by Python and MATLAB examples.





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Introduction to Numerical Methods: Mathematical Techniques for Students in Engineering, 2nd Edition
by Aniruddha Mitra, Aditi Mitra
English | 2023 | ISBN: 1793559937 | 107 Pages | Image PDF | 21.4 MB

Written primarily for students in mechanical engineering programs and designed to give them the math preparation they need to succeed in higher level courses, Introduction to Numerical Methods introduces key theories, practical engineering-related examples, and relevant laboratory exercises to help students develop and test their knowledge.
The book covers errors in computation, solving nonlinear equations with numerical techniques, matrixes and vectors, and complex numbers. The material also includes an introduction to linear programming problems and instruction in probability and statistics. Many of the exercises in the book suggest the use of a Ti-83/Ti-84 calculator, and tips for using the calculator successfully are integrated into the text.
The second edition features significant updates throughout the text, including the addition of learning objectives at the start of each chapter, clarified and reorganized chapter exercises, and additional introductory and contextual information for key concepts to better frame students' understanding. This edition also has an appendix that includes a brief introduction of popular statistical software, Minitab.
Introduction to Numerical Methods is a well-organized, useful addition to undergraduate course work in engineering programs.





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Introduction to Parallel Computing
by Niranjan N. Chiplunkar, Raju K.
English | 2021 | ISBN: 8126556811 | 528 Pages | True ePUB | 8.5 MB

With every computational gadget boasting of multiple processors, parallel programming becomes very important to fully exploit the power of such processor architectures. Parallel programming simultaneously uses multiple computing resources to solve a computational problem. Pthreads and OpenMP are the programming paradigms in shared address space parallel computers. Message Passing Interface (MPI) is the distributed memory parallel programming model. Graphics Processing Units (GPUs) consist of large number of homogeneous computing cores, and CUDA is a programming framework for GPUs.





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Introduction to Smooth Manifolds by John M. Lee
English | PDF (True) | 2012 | 723 Pages | ISBN : 1441999817 | 7.4 MB
This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research-- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.

This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A fewnew topics have been added, notably Sard's theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures.
Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
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Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Pavel Grinfeld
English | PDF (True) | 2013 | 303 Pages | ISBN : 1461478669 | 2.7 MB
This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds.

Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations.
The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author's skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 - when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject.
The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problemsand dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.
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Introduction to the Interstellar Medium
by Jonathan P. Williams
English | 2021 | ISBN: 1108480802 | 221 Pages | PDF | 14.8 MB

The gas and dust between the stars emit across the electromagnetic spectrum and are found in a range of physical conditions from diffuse plasmas to cold, dense molecules. Through their study we see how quantum processes shape the structure of our Galaxy and fluid mechanics sets the stellar mass scale. The Interstellar Medium is a very broad subject with layers of complexity, a long history and a steady flow of new results. This comprehensive yet accessible textbook provides a self-contained one-semester course for advanced undergraduate or beginning graduate students. It is written in a style that students can follow by themselves and allows instructors to use class time to go deeper into the details or show applications to current research. It makes extensive use of publicly accessible data to illustrate specific points and to encourage students to learn by performing their own analyses.





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Introduction à la résolution des systèmes polynomiaux by Mohamed Elkadi , Bernard Mourrain
Français | PDF | 2007 | 308 Pages | ISBN : 3540716467 | 2.1 MB
Les équations polynomiales apparaissent dans de nombreux domaines, pour modéliser des contraintes géométriques, des relations entre des grandeurs physiques, ou encore des propriétés satisfaites par certaines inconnues. Cet ouvrage est une introduction aux méthodes algébriques permettant de résoudre ce type d'équations. Nous montrons comment la géométrie des variétés algébriques définies par ces équations, leur dimension, leur degré, ou leurs composantes peuvent se déduire des propriétés des algèbres quotients correspondantes. Nous abordons pour cela des méthodes de la géométrie algébrique effective, telles que les bases de Grobner, la résolution par valeurs et vecteurs propres, les résultants, les bezoutiens, la dualité, les algèbres de Gorenstein et les résidus algébriques. Ces méthodes sont accompagnées d'algorithmes, d'exemples et d'exercices, illustrant leurs applications.

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Intuitionistic and Type-2 Fuzzy Logic Enhancements in Neural and Optimization Algorithms: Theory and Applications by Oscar Castillo
English | EPUB | 2020 | 767 Pages | ISBN : 303035444X | 109.45 MB
This book describes the latest advances in fuzzy logic, neural networks, and optimization algorithms, as well as their hybrid intelligent combinations, and their applications in the areas such as intelligent control, robotics, pattern recognition, medical diagnosis, time series prediction, and optimization.

The topic is highly relevant as most current intelligent systems and devices use some form of intelligent feature to enhance their performance. The book also presents new and advanced models and algorithms of type-2 fuzzy logic and intuitionistic fuzzy systems, which are of great interest to researchers in these areas. Further, it proposes novel, nature-inspired optimization algorithms and innovative neural models. Featuring contributions on theoretical aspects as well as applications, the book appeals to a wide audience.
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