Hardback ISBN: 9781108423335
Hardback publication date: 06 January 2022
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Quantum Mechanics
, University of Edinburgh, , University of Edinburgh
Online ISBN: 9781108525848
Online publication date:
19 November 2021
Designed for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, are covered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerous exercises are interspersed throughout the text, expanding upon key concepts and further developing students' understanding. A fully worked solutions manual and lecture slides are available for instructors.
Designed for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, are covered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerous exercises are interspersed throughout the text, expanding upon key concepts and further developing students' understanding. A fully worked solutions manual and lecture slides are available for instructors.
Essential Mathematics for Engineers and Scientists
, Michigan State University, , Michigan State University
Online ISBN: 9781108671354
Online publication date:
30 April 2020
Hardback ISBN: 9781108425445
Hardback publication date: 25 June 2020
This text is geared toward students who have an undergraduate degree or extensive coursework in engineering or the physical sciences and who wish to develop their understanding of the essential topics of applied mathematics. The methods covered in the chapters form the core of analysis in engineering and the physical sciences. Readers will learn the solutions, techniques, and approaches that they will use as academic researchers or industrial R&D specialists. For example, they will be able to understand the fundamentals behind the various scientific software packages that are used to solve technical problems (such as the equations describing the solid mechanics of complex structures or the fluid mechanics of short-term weather prediction and long-term climate change), which is crucial to working with such codes successfully. Detailed and numerous worked problems help to ensure a clear and well-paced introduction to applied mathematics. Computational challenge problems at the end of each chapter provide students with the opportunity for hands-on learning and help to ensure mastery of the concepts. Adaptable to one- and two-semester courses.
This text is geared toward students who have an undergraduate degree or extensive coursework in engineering or the physical sciences and who wish to develop their understanding of the essential topics of applied mathematics. The methods covered in the chapters form the core of analysis in engineering and the physical sciences. Readers will learn the solutions, techniques, and approaches that they will use as academic researchers or industrial R&D specialists. For example, they will be able to understand the fundamentals behind the various scientific software packages that are used to solve technical problems (such as the equations describing the solid mechanics of complex structures or the fluid mechanics of short-term weather prediction and long-term climate change), which is crucial to working with such codes successfully. Detailed and numerous worked problems help to ensure a clear and well-paced introduction to applied mathematics. Computational challenge problems at the end of each chapter provide students with the opportunity for hands-on learning and help to ensure mastery of the concepts. Adaptable to one- and two-semester courses.
Lebesgue Integration and Measure
Online ISBN: 9781139171458
Online publication date:
13 September 2019
Paperback ISBN: 9780521097512
Paperback publication date: 29 June 1973
- Textbook
Lebesgue integration is a technique of great power and elegance which can be applied in situations where other methods of integration fail. It is now one of the standard tools of modern mathematics, and forms part of many undergraduate courses in pure mathematics. Dr Weir's book is aimed at the student who is meeting the Lebesgue integral for the first time. Defining the integral in terms of step functions provides an immediate link to elementary integration theory as taught in calculus courses. The more abstract concept of Lebesgue measure, which generalises the primitive notions of length, area and volume, is deduced later. The explanations are simple and detailed with particular stress on motivation. Over 250 exercises accompany the text and are grouped at the ends of the sections to which they relate; notes on the solutions are given.
Lebesgue integration is a technique of great power and elegance which can be applied in situations where other methods of integration fail. It is now one of the standard tools of modern mathematics, and forms part of many undergraduate courses in pure mathematics. Dr Weir's book is aimed at the student who is meeting the Lebesgue integral for the first time. Defining the integral in terms of step functions provides an immediate link to elementary integration theory as taught in calculus courses. The more abstract concept of Lebesgue measure, which generalises the primitive notions of length, area and volume, is deduced later. The explanations are simple and detailed with particular stress on motivation. Over 250 exercises accompany the text and are grouped at the ends of the sections to which they relate; notes on the solutions are given.
Set Theory
A First Course
, State University of New York, Buffalo
Online ISBN: 9781316341346
Online publication date:
09 August 2018
Hardback ISBN: 9781107120327
Hardback publication date: 18 July 2016
- Textbook
Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.
Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.
Linear Algebra
, Case Western Reserve University, Ohio, , Case Western Reserve University, Ohio
Online ISBN: 9781316823200
Online publication date:
21 June 2018
Hardback ISBN: 9781107177901
Hardback publication date: 24 May 2018
- Textbook
Linear Algebra offers a unified treatment of both matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants.
Linear Algebra offers a unified treatment of both matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants.
The Mechanics and Thermodynamics of Continua
, Carnegie Mellon University, Pennsylvania, , McGill University, Montréal, , Massachusetts Institute of Technology
Online ISBN: 9780511762956
Online publication date:
05 June 2012
Hardback ISBN: 9780521405980
Hardback publication date: 19 April 2010
Paperback ISBN: 9781107617063
Paperback publication date: 19 December 2013
- Textbook
The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.
The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.
Mathematical Methods and Models for Economists
Online ISBN: 9780511810756
Online publication date:
05 June 2012
Paperback ISBN: 9780521585293
Paperback publication date: 28 January 2000
This book is intended as a textbook for a first-year PhD course in mathematics for economists and as a reference for graduate students in economics. It provides a self-contained, rigorous treatment of most of the concepts and techniques required to follow the standard first-year theory sequence in micro and macroeconomics. The topics covered include an introduction to analysis in metric spaces, differential calculus, comparative statics, convexity, static optimization, dynamical systems and dynamic optimization. The book includes a large number of applications to standard economic models and over two hundred fully worked-out problems.
This book is intended as a textbook for a first-year PhD course in mathematics for economists and as a reference for graduate students in economics. It provides a self-contained, rigorous treatment of most of the concepts and techniques required to follow the standard first-year theory sequence in micro and macroeconomics. The topics covered include an introduction to analysis in metric spaces, differential calculus, comparative statics, convexity, static optimization, dynamical systems and dynamic optimization. The book includes a large number of applications to standard economic models and over two hundred fully worked-out problems.
General Topology for Beginners
, Sardar Patel University
Coming soon
Online ISBN: 9781009505871
Expected online publication date:
December 2025
Paperback ISBN: 9781009505888
Expected Paperback publication date: 31 December 2025
This textbook focuses on general topology. Meant for graduate and senior undergraduate mathematics students, it introduces topology thoroughly from scratch and assumes minimal basic knowledge of real analysis and metric spaces. It begins with thought-provoking questions to encourage students to learn about topology and how it is related to, yet different from, geometry. Using concepts from real analysis and metric spaces, the definition of topology is introduced along with its motivation and importance. The text covers all the topics of topology, including homeomorphism, subspace topology, weak topology, product topology, quotient topology, coproduct topology, order topology, metric topology, and topological properties such as countability axioms, separation axioms, compactness, and connectedness. It also helps to understand the significance of various topological properties in classifying topological spaces.
This textbook focuses on general topology. Meant for graduate and senior undergraduate mathematics students, it introduces topology thoroughly from scratch and assumes minimal basic knowledge of real analysis and metric spaces. It begins with thought-provoking questions to encourage students to learn about topology and how it is related to, yet different from, geometry. Using concepts from real analysis and metric spaces, the definition of topology is introduced along with its motivation and importance. The text covers all the topics of topology, including homeomorphism, subspace topology, weak topology, product topology, quotient topology, coproduct topology, order topology, metric topology, and topological properties such as countability axioms, separation axioms, compactness, and connectedness. It also helps to understand the significance of various topological properties in classifying topological spaces.
Financial Data Science
, Politecnico di Torino, Italy, and VinUniversity, Hanoi, , VinUniversity, Vietnam, , Politecnico di Torino, , University of California, Berkeley
Online ISBN: 9781009432283
Online publication date:
17 December 2025
Hardback ISBN: 9781009432245
Hardback publication date: 17 July 2025
- Textbook
Confidently analyze, interpret and act on financial data with this practical introduction to the fundamentals of financial data science. Master the fundamentals with step-by-step introductions to core topics will equip you with a solid foundation for applying data science techniques to real-world complex financial problems. Extract meaningful insights as you learn how to use data to lead informed, data-driven decisions, with over 50 examples and case studies and hands-on Matlab and Python code. Explore cutting-edge techniques and tools in machine learning for financial data analysis, including deep learning and natural language processing. Accessible to readers without a specialized background in finance or machine learning, and including coverage of data representation and visualization, data models and estimation, principal component analysis, clustering methods, optimization tools, mean/variance portfolio optimization and financial networks, this is the ideal introduction for financial services professionals, and graduate students in finance and data science.
Confidently analyze, interpret and act on financial data with this practical introduction to the fundamentals of financial data science. Master the fundamentals with step-by-step introductions to core topics will equip you with a solid foundation for applying data science techniques to real-world complex financial problems. Extract meaningful insights as you learn how to use data to lead informed, data-driven decisions, with over 50 examples and case studies and hands-on Matlab and Python code. Explore cutting-edge techniques and tools in machine learning for financial data analysis, including deep learning and natural language processing. Accessible to readers without a specialized background in finance or machine learning, and including coverage of data representation and visualization, data models and estimation, principal component analysis, clustering methods, optimization tools, mean/variance portfolio optimization and financial networks, this is the ideal introduction for financial services professionals, and graduate students in finance and data science.
Introductory Ring Theory
, Shaheed Rajguru College of Applied Sciences for Women, University of Delhi, , Bharati College, University of Delhi
Coming soon
Online ISBN: 9781009633529
Expected online publication date:
December 2025
Paperback ISBN: 9781009633536
Expected Paperback publication date: 31 January 2026
- Textbook
This book provides a clear and accessible introduction to ring theory for undergraduate students. Aligned with standard curricula, it simplifies abstract concepts through structured explanations, practical examples, and real-world applications. Ideal for both students and instructors, it serves as a valuable resource for mastering fundamental concepts in ring theory with ease. The text begins with an introduction to rings and goes on to cover subrings, integral domains, ideals, and factor rings. It also discusses ring homomorphisms and polynomial rings. The book concludes with topics such as polynomial factorization and divisibility in integral domains. Each chapter is supplemented with solved examples to foster a deeper understanding of the subject. A set of practice questions is also provided to sharpen problem-solving skills.
This book provides a clear and accessible introduction to ring theory for undergraduate students. Aligned with standard curricula, it simplifies abstract concepts through structured explanations, practical examples, and real-world applications. Ideal for both students and instructors, it serves as a valuable resource for mastering fundamental concepts in ring theory with ease. The text begins with an introduction to rings and goes on to cover subrings, integral domains, ideals, and factor rings. It also discusses ring homomorphisms and polynomial rings. The book concludes with topics such as polynomial factorization and divisibility in integral domains. Each chapter is supplemented with solved examples to foster a deeper understanding of the subject. A set of practice questions is also provided to sharpen problem-solving skills.
Foundations and Applications of Engineering Mechanics
, Kamla Nehru Institute of Technology, , Kamla Nehru Institute of Technology
Online ISBN: 9781316182567
Online publication date:
26 June 2025
Paperback ISBN: 9781107499836
Paperback publication date: 16 March 2015
- Textbook
Engineering mechanics is the branch of engineering that applies the laws of mechanics in design, and is at the core of every machine that is designed. This book offers a comprehensive discussion of the fundamental theories and principles of engineering mechanics. It begins by explaining the laws and idealization of mechanics, and then establishes the equation of equilibrium for a rigid body and free body diagram (FBD), along with their applications. Chapters on method of virtual work and mechanical vibration discuss in detail important topics such as principle of virtual work, potential energy and equilibrium and free vibration. The book also introduces the elastic spring method for finding deflection in beams and uses a simple integration method to calculate centroid and moment of inertia. This volume will serve as a useful textbook for undergraduates and engineering students studying engineering mechanics.
Engineering mechanics is the branch of engineering that applies the laws of mechanics in design, and is at the core of every machine that is designed. This book offers a comprehensive discussion of the fundamental theories and principles of engineering mechanics. It begins by explaining the laws and idealization of mechanics, and then establishes the equation of equilibrium for a rigid body and free body diagram (FBD), along with their applications. Chapters on method of virtual work and mechanical vibration discuss in detail important topics such as principle of virtual work, potential energy and equilibrium and free vibration. The book also introduces the elastic spring method for finding deflection in beams and uses a simple integration method to calculate centroid and moment of inertia. This volume will serve as a useful textbook for undergraduates and engineering students studying engineering mechanics.
Fundamentals of Transport Processes with Applications
, Indian Institute of Science, Bangalore
Online ISBN: 9781009036658
Online publication date:
28 February 2025
Paperback ISBN: 9781009005333
Paperback publication date: 13 April 2023
- Textbook
The study of transport phenomena is an essential part of chemical engineering, as well as other disciplines concerned with material transformations such as biomedical engineering, microfluidics, reactor design and metallurgy. Material transformations require the motion of constituents relative to each other, the transfer of heat across materials and fluid flow. This lucid textbook introduces the student to the fundamentals and applications of transport phenomena in a single volume and explains how the outcomes of transformation processes depend on fluid flow and heat/mass transfer. It demonstrates the progression from physical concepts to the mathematical formulation, followed by the solution techniques for predicting outcomes in industrial applications. The ordering of the topics, gradual build-up of complexity and easy to read language make it a vital resource for anyone looking for an introduction to the domain. It also provides a foundation for advanced courses in fluid mechanics, multiphase flows and turbulence.
The study of transport phenomena is an essential part of chemical engineering, as well as other disciplines concerned with material transformations such as biomedical engineering, microfluidics, reactor design and metallurgy. Material transformations require the motion of constituents relative to each other, the transfer of heat across materials and fluid flow. This lucid textbook introduces the student to the fundamentals and applications of transport phenomena in a single volume and explains how the outcomes of transformation processes depend on fluid flow and heat/mass transfer. It demonstrates the progression from physical concepts to the mathematical formulation, followed by the solution techniques for predicting outcomes in industrial applications. The ordering of the topics, gradual build-up of complexity and easy to read language make it a vital resource for anyone looking for an introduction to the domain. It also provides a foundation for advanced courses in fluid mechanics, multiphase flows and turbulence.
Introduction to Marine Dynamics
, University of Michigan, Ann Arbor
Online ISBN: 9781009418065
Online publication date:
31 October 2024
Hardback ISBN: 9781009418096
Hardback publication date: 08 August 2024
Master the fundamentals of complex marine systems with this introduction to marine dynamics, vibrations, hydrodynamics, and stochastic processes. It connects key theoretical concepts, including as the velocity potential, impulsive force and L'Hôpital's Rule, to real-world marine engineering applications such as such as marine platform dynamics, extreme motions and exceedance probabilities, and includes over 60 multi-part end-of-chapter problems, building from simplified questions to advanced exercises, enabling students to grow in confidence towards solving complex questions. Students will gain a deep understanding effective design and safe operation of offshore systems and ocean resources; and is supported by downloadable Matlab code, and online solutions for instructors. Including over 300 full-colour illustrations and worked examples, drawing on the author's 45 years of teaching experience in marine dynamics, this textbook provides the ideal introduction to marine dynamics for senior undergraduate and graduate students in marine engineering, and is a comprehensive reference for practitioners in industry.
Master the fundamentals of complex marine systems with this introduction to marine dynamics, vibrations, hydrodynamics, and stochastic processes. It connects key theoretical concepts, including as the velocity potential, impulsive force and L'Hôpital's Rule, to real-world marine engineering applications such as such as marine platform dynamics, extreme motions and exceedance probabilities, and includes over 60 multi-part end-of-chapter problems, building from simplified questions to advanced exercises, enabling students to grow in confidence towards solving complex questions. Students will gain a deep understanding effective design and safe operation of offshore systems and ocean resources; and is supported by downloadable Matlab code, and online solutions for instructors. Including over 300 full-colour illustrations and worked examples, drawing on the author's 45 years of teaching experience in marine dynamics, this textbook provides the ideal introduction to marine dynamics for senior undergraduate and graduate students in marine engineering, and is a comprehensive reference for practitioners in industry.
The Atmospheric General Circulation
, University of Washington, , University of Washington, , Colorado State University, , University of Washington
Online ISBN: 9781108563857
Online publication date:
26 May 2023
Hardback ISBN: 9781108474245
Hardback publication date: 20 April 2023
An engaging, comprehensive, richly illustrated textbook about the atmospheric general circulation, written by leading researchers in the field. The book elucidates the pervasive role of atmospheric dynamics in the Earth System, interprets the structure and evolution of atmospheric motions across a range of space and time scales in terms of fundamental theoretical principles, and includes relevant historical background and tutorials on research methodology. The book includes over 300 exercises and is accompanied by extensive online resources, including solutions manuals, an animations library, and an introduction to online visualization and analysis tools. This textbook is suitable as a textbook for advanced undergraduate and graduate level courses in atmospheric sciences and geosciences curricula and as a reference textbook for researchers.
An engaging, comprehensive, richly illustrated textbook about the atmospheric general circulation, written by leading researchers in the field. The book elucidates the pervasive role of atmospheric dynamics in the Earth System, interprets the structure and evolution of atmospheric motions across a range of space and time scales in terms of fundamental theoretical principles, and includes relevant historical background and tutorials on research methodology. The book includes over 300 exercises and is accompanied by extensive online resources, including solutions manuals, an animations library, and an introduction to online visualization and analysis tools. This textbook is suitable as a textbook for advanced undergraduate and graduate level courses in atmospheric sciences and geosciences curricula and as a reference textbook for researchers.
Actions of Groups
A Second Course in Algebra
, Vassar College, New York
Online ISBN: 9781009158107
Online publication date:
03 May 2023
Hardback ISBN: 9781009158121
Hardback publication date: 05 January 2023
Paperback ISBN: 9781009158114
Paperback publication date: 05 January 2023
Using the unifying notion of group actions, this second course in modern algebra introduces the deeper algebraic tools needed to get into topics only hinted at in a first course, like the successful classification of finite simple groups and how groups play a role in the solutions of polynomial equations. Because groups may act as permutations of a set, as linear transformations on a vector space, or as automorphisms of a field, the deeper structure of a group may emerge from these viewpoints, two different groups can be distinguished, or a polynomial equation can be shown to be solvable by radicals. By developing the properties of these group actions, readers encounter essential algebra topics like the Sylow theorems and their applications, Galois theory, and representation theory. Warmup chapters that review and build on the first course and active learning modules help students transition to a deeper understanding of ideas.
Using the unifying notion of group actions, this second course in modern algebra introduces the deeper algebraic tools needed to get into topics only hinted at in a first course, like the successful classification of finite simple groups and how groups play a role in the solutions of polynomial equations. Because groups may act as permutations of a set, as linear transformations on a vector space, or as automorphisms of a field, the deeper structure of a group may emerge from these viewpoints, two different groups can be distinguished, or a polynomial equation can be shown to be solvable by radicals. By developing the properties of these group actions, readers encounter essential algebra topics like the Sylow theorems and their applications, Galois theory, and representation theory. Warmup chapters that review and build on the first course and active learning modules help students transition to a deeper understanding of ideas.
Stochastic Finance
An Introduction with Examples
, University of Leeds, , Lancaster University
Online ISBN: 9781009049672
Online publication date:
16 February 2023
Hardback ISBN: 9781316511251
Hardback publication date: 06 April 2023
Paperback ISBN: 9781009048941
Paperback publication date: 06 April 2023
- Textbook
Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black–Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.
Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black–Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.
Finite Element and Finite Volume Methods for Heat Transfer and Fluid Dynamics
, Texas A & M University, , Texas A & M University, , Lawrence Livermore National Laboratory, California
Online ISBN: 9781009275453
Online publication date:
27 January 2023
Hardback ISBN: 9781009275484
Hardback publication date: 26 January 2023
- Textbook
Introduces the two most common numerical methods for heat transfer and fluid dynamics equations, using clear and accessible language. This unique approach covers all necessary mathematical preliminaries at the beginning of the book for the reader to sail smoothly through the chapters. Students will work step-by-step through the most common benchmark heat transfer and fluid dynamics problems, firmly grounding themselves in how the governing equations are discretized, how boundary conditions are imposed, and how the resulting algebraic equations are solved. Providing a detailed discussion of the discretization steps and time approximations, and clearly presenting concepts of explicit and implicit formulations, this graduate textbook has everything an instructor needs to prepare students for their exams and future careers. Each illustrative example shows students how to draw comparisons between the results obtained using the two numerical methods, and at the end of each chapter they can test and extend their understanding by working through the problems provided. A solutions manual is also available for instructors.
Introduces the two most common numerical methods for heat transfer and fluid dynamics equations, using clear and accessible language. This unique approach covers all necessary mathematical preliminaries at the beginning of the book for the reader to sail smoothly through the chapters. Students will work step-by-step through the most common benchmark heat transfer and fluid dynamics problems, firmly grounding themselves in how the governing equations are discretized, how boundary conditions are imposed, and how the resulting algebraic equations are solved. Providing a detailed discussion of the discretization steps and time approximations, and clearly presenting concepts of explicit and implicit formulations, this graduate textbook has everything an instructor needs to prepare students for their exams and future careers. Each illustrative example shows students how to draw comparisons between the results obtained using the two numerical methods, and at the end of each chapter they can test and extend their understanding by working through the problems provided. A solutions manual is also available for instructors.
An Elementary Course on Partial Differential Equations
, Aligarh Muslim University, India, , Aligarh Muslim University, India
Online ISBN: 9781009201469
Online publication date:
15 September 2022
Paperback ISBN: 9781009201445
Paperback publication date: 23 February 2023
- Textbook
Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
Game Theory Basics
, London School of Economics and Political Science
Online ISBN: 9781108910118
Online publication date:
22 October 2021
Hardback ISBN: 9781108843300
Hardback publication date: 04 November 2021
Paperback ISBN: 9781108824231
Paperback publication date: 04 November 2021
Game theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years, is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know: the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium. The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory courses in mathematics, computer science, or economics departments.
Game theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years, is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know: the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium. The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory courses in mathematics, computer science, or economics departments.
A First Course in Quantitative Finance
, Ernst-Moritz-Arndt-Universität Greifswald, Germany
Online ISBN: 9781108303606
Online publication date:
06 August 2018
Paperback ISBN: 9781108411431
Paperback publication date: 22 March 2018
Hardback ISBN: 9781108419574
Hardback publication date: 25 April 2018
This new and exciting book offers a fresh approach to quantitative finance and utilises novel features, including stereoscopic images which permit 3D visualisation of complex subjects without the need for additional tools. Offering an integrated approach to the subject, A First Course in Quantitative Finance introduces students to the architecture of complete financial markets before exploring the concepts and models of modern portfolio theory, derivative pricing and fixed income products in both complete and incomplete market settings. Subjects are organised throughout in a way that encourages a gradual and parallel learning process of both the economic concepts and their mathematical descriptions, framed by additional perspectives from classical utility theory, financial economics and behavioural finance. Suitable for postgraduate students studying courses in quantitative finance, financial engineering and financial econometrics as part of an economics, finance, econometric or mathematics program, this book contains all necessary theoretical and mathematical concepts and numerical methods, as well as the necessary programming code for porting algorithms onto a computer.
This new and exciting book offers a fresh approach to quantitative finance and utilises novel features, including stereoscopic images which permit 3D visualisation of complex subjects without the need for additional tools. Offering an integrated approach to the subject, A First Course in Quantitative Finance introduces students to the architecture of complete financial markets before exploring the concepts and models of modern portfolio theory, derivative pricing and fixed income products in both complete and incomplete market settings. Subjects are organised throughout in a way that encourages a gradual and parallel learning process of both the economic concepts and their mathematical descriptions, framed by additional perspectives from classical utility theory, financial economics and behavioural finance. Suitable for postgraduate students studying courses in quantitative finance, financial engineering and financial econometrics as part of an economics, finance, econometric or mathematics program, this book contains all necessary theoretical and mathematical concepts and numerical methods, as well as the necessary programming code for porting algorithms onto a computer.