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Books in Mathematics and applied mathematics

  • Boundary Value Problems and Partial Differential Equations

    • 7th Edition
    • David L. Powers + 3 more
    • English
    For over fifty years, Boundary Value Problems and Partial Differential Equations, Seventh Edition has provided advanced students an accessible and practical introduction to deriving, solving, and interpreting explicit solutions involving partial differential equations with boundary and initial conditions. Fully revised and now in its Seventh Edition, this valued text aims to be comprehensive without affecting the accessibility and convenience of the original. The resource’s main tool is Fourier analysis, but the work covers other techniques, including Laplace transform, Fourier transform, numerical methods, characteristics, and separation of variables, as well, to provide well-rounded coverage. Mathematical modeling techniques are illustrated in derivations, which are widely used in engineering and science. In particular, this includes the modeling of heat distribution, a vibrating string or beam under various boundary conditions and constraints. New to this edition, the text also now uniquely discusses the beam equation. Throughout the text, examples and exercises have been included, pulled from the literature based on popular problems from engineering and science. These include some "outside-the-box" exercises at the end of each chapter, which provide challenging and thought-provoking practice that can also be used to promote classroom discussion. Chapters also include Projects, problems that synthesize or dig more deeply into the material that are slightly more involved than standard book exercises, and which are intended to support team solutions. Additional materials, exercises, animations, and more are also accessible to students via links and in-text QR codes to support practice and subject mastery.

  • Measure and Integration

    Concepts, Examples, and Applications
    • 1st Edition
    • Ahmed Ghatasheh + 2 more
    • English
    Measure and Integration: Examples, Concepts, and Applications instructs on core proofs, theorems, and approaches of real analysis as illustrated via compelling exercises and carefully crafted, practical examples. Following early chapters on core concepts and approaches of real analysis, the authors apply real analysis across integration on product spaces, radon functionals, bounded variation and lebesgue-stieltjes measures, convolutions, probability, and differential equations, among other topics. From chapter one onward, students are asked to apply concepts to reinforce understanding and gain applied experience in real analysis. In particular, exercises challenge students to use key proofs of major real analysis theorems to encourage independent thinking, problem-solving, and new areas of research powered by real analysis.

  • An Introduction to Point-Set Topology

    A Hybrid Texas Style Approach
    • 1st Edition
    • Shelby J. Kilmer
    • English
    An Introduction to Point-Set Topology is intended for use in a beginning topology course for undergraduates or as an elective course for graduate students. The book’s style can be thought of as a hybrid between the Texas style (Moore method) of teaching topology and the more traditional styles. In the Texas style the students are given the definitions and the statements of the theorems and then they present their proofs to the class. This type of participation builds students’ confidence and provides them with a deeper understanding of the subject that they will retain longer. This text offers some of the theorems with their proofs and leaves others for the students to prove and present. Those theorems chosen to have their proofs presented in the text keep the course moving forward under the instructors’ guidance and increase student comprehension. An Introduction to Point-Set Topology covers a broad range of topological concepts, including but not limited to, metric spaces, topological spaces, homeomorphisms, connected sets, compact sets, product spaces, Hausdorff spaces, sequences, limits, weak topologies, the axiom of choice, Zorn’s lemma, and Nets. Incorporating both historical references and color graphics, the material keeps readers engaged. The book’s goals include increasing student participation, thus promoting a deeper knowledge through an intuitive understanding of how and why topology was developed in the way that it was. This “instructor-friendly... accessible text is also accompanied by a detailed solutions manual to support both experienced topologists and other mathematicians who would like to teach topology.

  • Machine Learning Solutions for Inverse Problems: Part A

    • 1st Edition
    • Volume 26
    • English
    Machine Learning Solutions for Inverse Problems: Part A, Volume 26 in the Handbook of Numerical Analysis, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Data-Driven Approaches for Generalized Lasso Problems, Implicit Regularization of the Deep Inverse Prior via (Inertial) Gradient Flow, Generalized Hardness of Approximation, Hallucinations, and Trustworthiness in Machine Learning for Inverse Problems, Energy-Based Models for Inverse Imaging Problems, Regularization Theory of Stochastic Iterative Methods for Solving Inverse Problems, and more.Other sections cover Advances in Identifying Differential Equations from Noisy Data Observations, The Complete Electrode Model for Electrical Impedance Tomography: A Comparative Study of Deep Learning and Analytical Methods, Learned Iterative Schemes: Neural Network Architectures for Operator Learning, Jacobian-Free Backpropagation for Unfolded Schemes with Convergence Guarantees, and Operator Learning Meets Inverse Problems: A Probabilistic Perspective

  • Elementary Real Analysis

    A Practical Introduction
    • 1st Edition
    • Thomas Bieske
    • English
    Elementary Real Analysis: A Practical Introduction provides a robust foundation for success in real analysis, presenting traditional material in an accessible, engaging manner with the support of clearly outlined learning objectives and exercises.Organized into two well-designed sections, the book begins with a comprehensive review of prerequisite knowledge. Section I includes chapters such as “Sets,” “Properties of Real Numbers,” “Properties of Integers,” and “Functions and Relations,” each accompanied by a wealth of exercises that encourage exploration and practice. These chapters lay the foundation for the second section which delves into advanced topics such as sequences, continuity, and differentiation, culminating in a synthesis of concepts that prepares students for further study of mathematical analysis. For easy reference, two appendices entitled “Mathematical Statements” and “Proof Methods” provide the reader with an accessible reference to the essential language and techniques of proof writing.Whether used in a classroom or for self-directed learning, Elementary Real Analysis: A Practical Introduction is a vital companion for students seeking an introduction to real analysis, bridging the gap between basic principles and advanced mathematical concepts with clarity and precision.

  • Recent Developments in Theory and Applications of Fractional Order Systems

    • 1st Edition
    • Mehmet Yavuz + 2 more
    • English
    Recent Developments in Theory and Applications of Fractional Order Systems presents a rigorous and thorough analysis of various aspects of Fractional Calculus. The book provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines. The authors present each computational modeling concept with a definition, methods, theorems, and observations followed by typical application problems and step-by-step solutions. Each topic is covered in detail, followed typically by several meticulously worked out examples and a problem set containing many additional related problems.In addition, the book discusses recent developments and the latest research on Fractional Calculus and its applications, demonstrating important applications in Engineering, Computer Science, Management, Social Science, and the Humanities.

  • Methods of Mathematical Modeling

    Advances and Applications
    • 1st Edition
    • Hemen Dutta
    • English
    Methods of Mathematical Modeling: Advances and Applications delves into recent progress in this field, highlighting innovative methods and their uses in different domains. This book covers convergence analysis involving nonlinear integral equations and boundary value problems, Navier-Stokes equations in Sobolev-Gevrey spaces, magneto-hydrodynamic... of ternary nanofluids with heat transfer effects, vortex nerve complexes in video frame shape approximation, hybrid schemes for computing hyperbolic conservation laws, and solutions to new fractional differential equations. Additionally, the book examines dynamics of Leslie-Gower type predator-prey models and models for the dynamics of generic crop and water availability.Readers will find diverse approaches, techniques, and applications needed for modeling various physical and natural systems. Each chapter is self-contained, encouraging independent study and application of the modeling examples to individual research projects. This book serves as a valuable resource for researchers, students, educators, scientists, and practitioners involved in different aspects of modeling.

  • Quaternion Generalized Inverses

    Foundations, Theory, Problems, and Solutions
    • 1st Edition
    • Ivan I. Kyrchei
    • English
    A cornerstone of linear algebra, the determinant's utility in real and complex fields is undeniable, though traditionally limited to invertibility, rank, and solving linear systems. Quaternion Generalized Inverses: Foundations, Theory, Problems, and Solutions ventures into uncharted territory: extending these concepts to linear algebra over the noncommutative quaternion skew field. The author's groundbreaking theory of "noncommutative" row–column determinants is central to this exploration, a significant advancement beyond the Moore determinant. This seven-chapter work thoroughly introduces the history of noncommutative determinants before delving into the author's theory and its application to inverse matrix computation and Cramer's rule for quaternion systems. The main portion of this work is dedicated to a comprehensive examination of quaternion generalized inverses, spanning the well-established Moore–Penrose and Drazin inverses to more recent developments such as core-EP and composite inverses. The book provides their definitions, properties, and, uniquely, their determinantal representations based on the author's noncommutative determinants. It culminates in demonstrating their powerful applications in solving a wide range of quaternion matrix equations, including Sylvester-type and constrained equations, as well as differential matrix equations.

  • Numerical Linear Algebra with Applications

    Using MATLAB and Octave
    • 2nd Edition
    • William Ford + 1 more
    • English
    Numerical Linear Algebra with Applications: Using MATLAB and Octave, Second Edition provides practical knowledge on modern computational techniques for the numerical solution of linear algebra problems. The book offers a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions. Useful to readers regardless of background, the text begins with six introductory courses to provide background for those who haven’t taken applied or theoretical linear algebra. This approach offers a thorough explanation of the issues and methods for practical computing using MATLAB as the vehicle for computation.Appropri... for advanced undergraduate and early graduate courses on numerical linear algebra, this useful textbook explores numerous applications to engineering and science.

  • An Introduction to Discrete Mathematics

    • 1st Edition
    • Vidyadhar Kulkarni
    • English
    An Introduction to Discrete Mathematics offers an engaging and accessible introduction to discrete mathematics for beginning undergraduate students across a wide range of application areas, from mathematics to statistics, operations research, business, engineering, and the sciences. It provides solid foundation in precise proof writing methods, with early chapters introducing set theory and logic that are followed by deductive and inductive proof techniques, number theory, counting principles, permutations and combinations, probability of events, random variables, graphs, and weighted graphs.The book illustrates fundamental concepts in discrete mathematics with clear and precise definitions that are paired with examples and counter-examples as applied in combinatorics, discrete probability, and graph theory. Chapters include student exercises to enhance learning, and a solutions manual and example questions are available for instructors on a companion website.

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