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Introduction to Mathematical Methods in Population Theory (Springer Undergraduate Mathematics Series)
by Jacek BanasiakThis 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. Designed for upper undergraduate courses and beyond, this textbook is written for students and researchers looking to master the mathematics of the tools commonly used to analyse life science models. It therefore goes somewhat deeper into mathematics than typical books at this level but should be accessible to anyone with a good command of calculus with elements of real and complex analysis and linear algebra; the necessary concepts are collected in the appendices.
Introduction to Mathematical Modeling
by Mayer Humi<p>Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes. <p>Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.</p>
Introduction to Mathematical Modeling and Chaotic Dynamics
by Ranjit Kumar Upadhyay Satteluri R. IyengarIntroduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems. Most of the models presented are solved using MATLAB.The book first covers the necessary mathematical preliminaries, including testing of stability. It then describes the modeling of systems from natural sci
Introduction to Mathematical Modeling and Computer Simulations
by Vladimir Mityushev Wojciech Nawalaniec Natalia RylkoIntroduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students.
Introduction to Mathematical Modeling and Computer Simulations
by Vladimir Mityushev Wojciech Nawalaniec Natalia Rylko Radoslaw Antoni KyciaIntroduction to Mathematical Modeling and Computer Simulations, Second Edition continues to serve as an engaging and accessible textbook for undergraduates studying mathematical modeling and computer simulations. The book is heavily focussed on applications, and so may have a particular appeal to applied mathematicians, engineers, and others working in applied quantitative disciplines. The book may also be useful as a reference text for reference text for early-career stage practitioners. New to this Edition: A new chapter on Machine Learning and Data Analysis in order to account for recent developments in the field. Chapter 9, ‘Asymptotic Methods in Composites’, has been entirely re-written to make it more consistent with industry and scientific standards. Includes an elementary introduction to programming in Python language. The Jupyter notebooks with examples for Chapter 10 and Appendix A are available for a download from www.Routledge.com/9781032661513.
Introduction to Mathematical Models in Operations Planning
by Halit Alper TayalıDiscover the intricate nature of a company's production function and the comprehensive principles of planning operations in this book. Through practical applications and enriched by numerical examples, readers gain essential knowledge of elementary mathematical methods in operations planning. The inclusion of the powerful R programming language, accompanied by code scripts and real-world examples, enhances the learning experience. Blending theory with practice, this resource equips readers with the tools necessary to optimize production systems, make informed decisions, and gain a competitive edge in today's dynamic business landscape.
Introduction to Mathematical Oncology (Chapman & Hall/CRC Mathematical Biology Series)
by Yang Kuang John D. Nagy Steffen E. EikenberryIntroduction to Mathematical Oncology presents biologically well-motivated and mathematically tractable models that facilitate both a deep understanding of cancer biology and better cancer treatment designs. It covers the medical and biological background of the diseases, modeling issues, and existing methods and their limitations. The authors introduce mathematical and programming tools, along with analytical and numerical studies of the models. They also develop new mathematical tools and look to future improvements on dynamical models. After introducing the general theory of medicine and exploring how mathematics can be essential in its understanding, the text describes well-known, practical, and insightful mathematical models of avascular tumor growth and mathematically tractable treatment models based on ordinary differential equations. It continues the topic of avascular tumor growth in the context of partial differential equation models by incorporating the spatial structure and physiological structure, such as cell size. The book then focuses on the recent active multi-scale modeling efforts on prostate cancer growth and treatment dynamics. It also examines more mechanistically formulated models, including cell quota-based population growth models, with applications to real tumors and validation using clinical data. The remainder of the text presents abundant additional historical, biological, and medical background materials for advanced and specific treatment modeling efforts. Extensively classroom-tested in undergraduate and graduate courses, this self-contained book allows instructors to emphasize specific topics relevant to clinical cancer biology and treatment. It can be used in a variety of ways, including a single-semester undergraduate course, a more ambitious graduate course, or a full-year sequence on mathematical oncology.
Introduction to Mathematical Proofs (Textbooks in Mathematics)
by Charles RobertsIntroduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs.Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural num
Introduction to Mathematical Sociology
by Phillip Bonacich Philip LuA comprehensive textbook on the tools of mathematical sociology and their applicationsMathematical models and computer simulations of complex social systems have become everyday tools in sociology. Yet until now, students had no up-to-date textbook from which to learn these techniques. Introduction to Mathematical Sociology fills this gap, providing undergraduates with a comprehensive, self-contained primer on the mathematical tools and applications that sociologists use to understand social behavior.Phillip Bonacich and Philip Lu cover all the essential mathematics, including linear algebra, graph theory, set theory, game theory, and probability. They show how to apply these mathematical tools to demography; patterns of power, influence, and friendship in social networks; Markov chains; the evolution and stability of cooperation in human groups; chaotic and complex systems; and more.Introduction to Mathematical Sociology also features numerous exercises throughout, and is accompanied by easy-to-use Mathematica-based computer simulations that students can use to examine the effects of changing parameters on model behavior.Provides an up-to-date and self-contained introduction to mathematical sociologyExplains essential mathematical tools and their applicationsIncludes numerous exercises throughoutFeatures easy-to-use computer simulations to help students master concepts
Introduction to Mathematical Systems Theory: Discrete Time Linear Systems, Control and Identification
by Christiaan Heij André C.M. Ran Frederik van SchagenThis book provides an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering. The focus is on discrete time systems, which are the most relevant in business applications, as opposed to continuous time systems, requiring less mathematical preliminaries. The subjects treated are among the central topics of deterministic linear system theory: controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed, as are modeling, time series analysis and model specification, along with model validation.This second edition has been updated and slightly expanded. In addition, supplementary material containing the exercises is now available on the Springer Link's book website.
Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics (Dover Books on Mathematics)
by Friedrich WaismannThis enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition of mathematic fundamentals. Rather than a system of theorems with completely developed proofs or examples of applications, readers will encounter a coherent presentation of mathematical ideas that begins with the natural numbers and basic laws of arithmetic and progresses to the problems of the real-number continuum and concepts of the calculus.Contents include examinations of the various types of numbers and a criticism of the extension of numbers; arithmetic, geometry, and the rigorous construction of the theory of integers; the rational numbers, the foundation of the arithmetic of natural numbers, and the rigorous construction of elementary arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers.In issues of mathematical philosophy, the author explores basic theoretical differences that have been a source of debate among the most prominent scholars and on which contemporary mathematicians remain divided. "With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics." — Carl B. Boyer, Brooklyn College. 27 figures. Index.
Introduction to Mathematica® for Physicists
by Andrey GrozinThe basics of computer algebra and the language of Mathematica are described. This title will lead toward an understanding of Mathematica that allows the reader to solve problems in physics, mathematics, and chemistry. Mathematica is the most widely used system for doing mathematical calculations by computer, including symbolic and numeric calculations and graphics. It is used in physics and other branches of science, in mathematics, education and many other areas. Many important results in physics would never be obtained without a wide use of computer algebra.
Introduction to Mathematica® with Applications
by Marian MureşanStarting with an introduction to the numerous features of Mathematica®, this book continues with more complex material. It provides the reader with lots of examples and illustrations of how the benefits of Mathematica® can be used. Composed of eleven chapters, it includes the following: A chapter on several sorting algorithmsFunctions (planar and solid) with many interesting examplesOrdinary differential equationsAdvantages of Mathematica® dealing with the Pi numberThe power of Mathematica® working with optimal control problems Introduction to Mathematica® with Applications will appeal to researchers, professors and students requiring a computational tool.
Introduction to Mathematics for Computational Biology (Techniques in Life Science and Biomedicine for the Non-Expert)
by Paola Lecca Bruno CarpentieriThis introductory guide provides a thorough explanation of the mathematics and algorithms used in standard data analysis techniques within systems biology, biochemistry, and biophysics. Each part of the book covers the mathematical background and practical applications of a given technique. Readers will gain an understanding of the mathematical and algorithmic steps needed to use these software tools appropriately and effectively, as well how to assess their specific circumstance and choose the optimal method and technology. Ideal for students planning for a career in research, early-career researchers, and established scientists undertaking interdisciplinary research.
Introduction to Mathematics for Economics with R
by Massimiliano PortoThis book provides a practical introduction to mathematics for economics using R software. Using R as a basis, this book guides the reader through foundational topics in linear algebra, calculus, and optimization. The book is organized in order of increasing difficulty, beginning with a rudimentary introduction to R and progressing through exercises that require the reader to code their own functions in R. All chapters include applications for topics in economics and econometrics. As fully reproducible book, this volume gives readers the opportunity to learn by doing and develop research skills as they go. As such, it is appropriate for students in economics and econometrics.
Introduction to Matrices and Linear Transformations: Third Edition
by Daniel T. Finkbeiner IIThis versatile undergraduate text can be used in a variety of courses in linear algebra. It contains enough material for a one-year course, and it also serves as a support text and reference. A combination of formal theory and related computational techniques, it includes solutions to selected exercises. 1978 edition.
Introduction to Matrices and Vectors (Dover Books on Mathematics)
by Jacob T. SchwartzRealizing that matrices can be a confusing topic for the beginner, the author of this undergraduate text has made things as clear as possible by focusing on problem solving, rather than elaborate proofs. He begins with the basics, offering students a solid foundation for the later chapters on using special matrices to solve problems.The first three chapters present the basics of matrices, including addition, multiplication, and division, and give solid practice in the areas of matrix manipulation where the laws of algebra do not apply. In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations. He also covers special matrices -- including complex numbers, quaternion matrices, and matrices with complex entries -- and transpose matrices; the trace of a matrix; the cross product of matrices; eigenvalues and eigenvectors; and infinite series of matrices. Exercises at the end of each section give students further practice in problem solving. Prerequisites include a background in algebra, and in the later chapters, a knowledge of solid geometry. The book was designed as an introductory text for college freshmen and sophomores, but selected chapters can also be used to supplement advanced high school classes. Professionals who need a better understanding or review of the subject will also benefit from this concise guide.
Introduction to Matrix Analysis and Applications
by Fumio Hiai Dénes PetzMatrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.
Introduction to Matrix Analytic Methods in Queues 1: Analytical and Simulation Approach - Basics
by Srinivas R. ChakravarthyMatrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples.This book&’s approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix Analytic Methods in Queues 1 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially.The book&’s detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.
Introduction to Matrix Theory
by Arindama SinghThis book is designed to serve as a textbook for courses offered to undergraduate and postgraduate students enrolled in Mathematics. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, OR-factorization, Schurtriangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition, and polar decomposition. Along with Gauss-Jordan elimination for linear systems, it also discusses best approximations and least-squares solutions. The book includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics in the book are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts, and problems have been added at the end of each chapter. Most of these problems are theoretical, and they do not fit into the running text linearly. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in senior undergraduate and beginning postgraduate mathematics courses.
Introduction to Matrix-Analytic Methods in Queues 2: Analytical and Simulation Approach - Queues and Simulation
by Srinivas R. ChakravarthyMatrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples. This book's approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix-Analytic Methods in Queues 2 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially. This book's detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.
Introduction to Measure Theory and Functional Analysis
by Piermarco Cannarsa Teresa D'AprileThis book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two courses, it can be supplemented by additional topics from the third part of the book, such as functions of bounded variation, absolutely continuous functions, and signed measures. This textbook addresses the needs of graduate students in mathematics, who will find the basic material they will need in their future careers, as well as those of researchers, who will appreciate the self-contained exposition which requires no other preliminaries than basic calculus and linear algebra.
Introduction to Mechatronics: An Integrated Approach
by Biswanath SamantaThis textbook presents mechatronics through an integrated approach covering instrumentation, circuits and electronics, computer-based data acquisition and analysis, analog and digital signal processing, sensors, actuators, digital logic circuits, microcontroller programming and interfacing. The use of computer programming is emphasized throughout the text, and includes Matlab for system modeling, simulation, and analysis; LabVIEW for data acquisition and signal processing; and C++ for Arduino-based microcontroller programming and interfacing. Prof. Samanta provides numerous examples along with appropriate program codes, for simulation and analysis, that are discussed in detail to illustrate the concepts covered in each section. The book also includes the illustration of theoretical concepts through the virtual simulation platform Tinkercad to provide students virtual lab experience.
Introduction to Mediation, Moderation, and Conditional Process Analysis: A Regression-Based Approach
by Andrew F. HayesAcclaimed for its thorough presentation of mediation, moderation, and conditional process analysis, this book has been updated to reflect the latest developments in PROCESS for SPSS, SAS, and, new to this edition, R. Using the principles of ordinary least squares regression, Andrew F. Hayes illustrates each step in an analysis using diverse examples from published studies, and displays SPSS, SAS, and R code for each example. Procedures are outlined for estimating and interpreting direct, indirect, and conditional effects; probing and visualizing interactions; testing hypotheses about the moderation of mechanisms; and reporting different types of analyses. Readers gain an understanding of the link between statistics and causality, as well as what the data are telling them.
Introduction to Mediation, Moderation, and Conditional Process Analysis: A Regression-Based Approach (Methodology in the social sciences)
by Andrew F. HayesThis book explains the fundamentals of mediation and moderation analysis and their integration as "conditional process analysis." Procedures are described for testing hypotheses about the mechanisms by which causal effects operate, the conditions under which they occur, and the moderation of mechanisms.