Paperback ISBN: 9780521457613
Paperback publication date: 27 January 1995
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Combinatorics
Topics, Techniques, Algorithms
Online ISBN: 9780511803888
Online publication date:
28 May 2018
- Textbook
Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.
Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.
Fluid Dynamics
, University of Maryland, College Park
Online ISBN: 9781107785281
Online publication date:
28 May 2018
Hardback ISBN: 9781107071575
Hardback publication date: 05 May 2015
This book presents a focused, readable account of the principal physical and mathematical ideas at the heart of fluid dynamics. Graduate students in engineering, applied math and physics taking their first graduate course in fluids will find this book invaluable in providing the background in physics and mathematics necessary to pursue advanced study. The exposition follows an arc through the subject building towards a detailed derivation of the Navier–Stokes and energy equations followed by many examples of their use in studying the dynamics of fluid flows. Modern tensor analysis is used to simplify the mathematical derivations thus allowing a clearer view of the physics. The motivation behind many fundamental concepts such as Bernoulli's equation and the stream function are included. Many exercises are designed with a view toward using MATLAB® or equivalent to simplify and extend the analysis of fluid motion including developing flow simulations based on techniques described in the book.
This book presents a focused, readable account of the principal physical and mathematical ideas at the heart of fluid dynamics. Graduate students in engineering, applied math and physics taking their first graduate course in fluids will find this book invaluable in providing the background in physics and mathematics necessary to pursue advanced study. The exposition follows an arc through the subject building towards a detailed derivation of the Navier–Stokes and energy equations followed by many examples of their use in studying the dynamics of fluid flows. Modern tensor analysis is used to simplify the mathematical derivations thus allowing a clearer view of the physics. The motivation behind many fundamental concepts such as Bernoulli's equation and the stream function are included. Many exercises are designed with a view toward using MATLAB® or equivalent to simplify and extend the analysis of fluid motion including developing flow simulations based on techniques described in the book.
A Gentle Introduction to Optimization
1st edition
, University of Waterloo, Ontario, , University of Waterloo, Ontario, , University of Waterloo, Ontario
Online ISBN: 9781107282094
Online publication date:
28 May 2018
Hardback ISBN: 9781107053441
Hardback publication date: 29 September 2014
Paperback ISBN: 9781107658790
Paperback publication date: 15 September 2014
Optimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. Chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material.
Optimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. Chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material.
Turbulent Flows
, Cornell University, New York
Online ISBN: 9780511840531
Online publication date:
05 June 2012
Paperback ISBN: 9780521598866
Paperback publication date: 16 October 2000
This is a graduate text on turbulent flows, an important topic in fluid dynamics. It is up-to-date, comprehensive, designed for teaching, and is based on a course taught by the author at Cornell University for a number of years. The book consists of two parts followed by a number of appendices. Part I provides a general introduction to turbulent flows, how they behave, how they can be described quantitatively, and the fundamental physical processes involved. Part II is concerned with different approaches for modelling or simulating turbulent flows. The necessary mathematical techniques are presented in the appendices. This book is primarily intended as a graduate level text in turbulent flows for engineering students, but it may also be valuable to students in applied mathematics, physics, oceanography and atmospheric sciences, as well as researchers and practising engineers.
This is a graduate text on turbulent flows, an important topic in fluid dynamics. It is up-to-date, comprehensive, designed for teaching, and is based on a course taught by the author at Cornell University for a number of years. The book consists of two parts followed by a number of appendices. Part I provides a general introduction to turbulent flows, how they behave, how they can be described quantitatively, and the fundamental physical processes involved. Part II is concerned with different approaches for modelling or simulating turbulent flows. The necessary mathematical techniques are presented in the appendices. This book is primarily intended as a graduate level text in turbulent flows for engineering students, but it may also be valuable to students in applied mathematics, physics, oceanography and atmospheric sciences, as well as researchers and practising engineers.
Mathematical Methods in Data Science
Bridging Theory and Applications with Python
, University of Wisconsin, Madison
Coming soon
Online ISBN: 9781009509435
Expected online publication date:
September 2025
Hardback ISBN: 9781009509459
Expected Hardback publication date: 30 September 2025
Paperback ISBN: 9781009509404
Expected Paperback publication date: 30 September 2025
- Textbook
Bridge the gap between theoretical concepts and their practical applications with this rigorous introduction to the mathematics underpinning data science. It covers essential topics in linear algebra, calculus and optimization, and probability and statistics, demonstrating their relevance in the context of data analysis. Key application topics include clustering, regression, classification, dimensionality reduction, network analysis, and neural networks. What sets this text apart is its focus on hands-on learning. Each chapter combines mathematical insights with practical examples, using Python to implement algorithms and solve problems. Self-assessment quizzes, warm-up exercises and theoretical problems foster both mathematical understanding and computational skills. Designed for advanced undergraduate students and beginning graduate students, this textbook serves as both an invitation to data science for mathematics majors and as a deeper excursion into mathematics for data science students.
Bridge the gap between theoretical concepts and their practical applications with this rigorous introduction to the mathematics underpinning data science. It covers essential topics in linear algebra, calculus and optimization, and probability and statistics, demonstrating their relevance in the context of data analysis. Key application topics include clustering, regression, classification, dimensionality reduction, network analysis, and neural networks. What sets this text apart is its focus on hands-on learning. Each chapter combines mathematical insights with practical examples, using Python to implement algorithms and solve problems. Self-assessment quizzes, warm-up exercises and theoretical problems foster both mathematical understanding and computational skills. Designed for advanced undergraduate students and beginning graduate students, this textbook serves as both an invitation to data science for mathematics majors and as a deeper excursion into mathematics for data science students.
Fluid Mechanics
Lectures on Theoretical Physics, Volume 4
, University of Cambridge
Online ISBN: 9781009594714
Online publication date:
26 June 2025
Paperback ISBN: 9781009594691
Expected Paperback publication date: 21 August 2025
Hardback ISBN: 9781009594738
Expected Hardback publication date: 21 August 2025
- Textbook
Take anything in the universe, put it in a box, and heat it up. Regardless of what you start with, the motion of the substance will be described by the equations of fluid mechanics. This remarkable universality is the reason why fluid mechanics is important. The key equation of fluid mechanics is the Navier-Stokes equation. This textbook starts with the basics of fluid flows, building to the Navier-Stokes equation while explaining the physics behind the various terms and exploring the astonishingly rich landscape of solutions. The book then progresses to more advanced topics, including waves, fluid instabilities, and turbulence, before concluding by turning inwards and describing the atomic constituents of fluids. It introduces ideas of kinetic theory, including the Boltzmann equation, to explain why the collective motion of 1023 atoms is, under the right circumstances, always governed by the laws of fluid mechanics.
Take anything in the universe, put it in a box, and heat it up. Regardless of what you start with, the motion of the substance will be described by the equations of fluid mechanics. This remarkable universality is the reason why fluid mechanics is important. The key equation of fluid mechanics is the Navier-Stokes equation. This textbook starts with the basics of fluid flows, building to the Navier-Stokes equation while explaining the physics behind the various terms and exploring the astonishingly rich landscape of solutions. The book then progresses to more advanced topics, including waves, fluid instabilities, and turbulence, before concluding by turning inwards and describing the atomic constituents of fluids. It introduces ideas of kinetic theory, including the Boltzmann equation, to explain why the collective motion of 1023 atoms is, under the right circumstances, always governed by the laws of fluid mechanics.
An Introduction to Classical and Modal Logics
The Outlines of Knowledge
, Carnegie Mellon University, Pennsylvania
Online ISBN: 9781009450669
Online publication date:
08 February 2025
Paperback ISBN: 9781009450676
Paperback publication date: 21 November 2024
Hardback ISBN: 9781009450690
Hardback publication date: 21 November 2024
Classical logic – which studies the structural features of purported claims of fact – and modal logic – which studies relations of necessity and possibility – are different but complementary areas of logical thought. In this lively and accessible textbook, Adam Bjorndahl provides a comprehensive and unified introduction to the two subjects, treating them with the same level of rigour and detail and showing how they fit together. The core material appears in the main text, with hundreds of supplemental examples, comments, clarifications, and connections presented throughout in easy-to-read sidenotes, giving the book a distinct conversational feel. A detailed, multi-part appendix covers important background mathematical material that some students may lack, such as induction or the concept of countable infinity. A fully self-contained learning resource, this book will be ideal for a semester-long upper-level university course on either or both of the topics.
Classical logic – which studies the structural features of purported claims of fact – and modal logic – which studies relations of necessity and possibility – are different but complementary areas of logical thought. In this lively and accessible textbook, Adam Bjorndahl provides a comprehensive and unified introduction to the two subjects, treating them with the same level of rigour and detail and showing how they fit together. The core material appears in the main text, with hundreds of supplemental examples, comments, clarifications, and connections presented throughout in easy-to-read sidenotes, giving the book a distinct conversational feel. A detailed, multi-part appendix covers important background mathematical material that some students may lack, such as induction or the concept of countable infinity. A fully self-contained learning resource, this book will be ideal for a semester-long upper-level university course on either or both of the topics.
Computing in Scilab
, University of Delhi
Online ISBN: 9781009214179
Online publication date:
15 October 2023
Paperback ISBN: 9781009214193
Paperback publication date: 23 February 2023
- Textbook
SciLab is a free open-source computing and graphics tool that allows students to learn physical and mathematical concepts with ease. Computing in SciLab has been designed for undergraduate students of physics and electronics following the CBCS-LOCF syllabus, and with extensive coverage of concepts, it focuses primarily on the applications of SciLab in improving the problem-solving skills of readers. All these tools are classroom-tested and focus on data visualization and numerical computing with SCILAB. The book covers important topics like linear algebra, matrices, plotting tools, curve fitting, differential equations, integral calculus, Fourier analysis, and equation solving.
SciLab is a free open-source computing and graphics tool that allows students to learn physical and mathematical concepts with ease. Computing in SciLab has been designed for undergraduate students of physics and electronics following the CBCS-LOCF syllabus, and with extensive coverage of concepts, it focuses primarily on the applications of SciLab in improving the problem-solving skills of readers. All these tools are classroom-tested and focus on data visualization and numerical computing with SCILAB. The book covers important topics like linear algebra, matrices, plotting tools, curve fitting, differential equations, integral calculus, Fourier analysis, and equation solving.
Mechanics of Fluids
, University of Notre Dame, Indiana
Online ISBN: 9781009026307
Online publication date:
14 July 2023
Hardback ISBN: 9781316515693
Hardback publication date: 29 June 2023
Providing a modern approach to classical fluid mechanics, this textbook presents an accessible and rigorous introduction to the field, with a strong emphasis on both mathematical exposition and physical problems. It includes a consistent treatment of a broad range of fluid mechanics topics, including governing equations, vorticity, potential flow, compressible flow, viscous flow, instability, and turbulence. It has enhanced coverage of geometry, coordinate transformations, kinematics, thermodynamics, heat transfer, and nonlinear dynamics. To round out student understanding, a robust emphasis on theoretical fundamentals and underlying mathematical details is provided, enabling students to gain confidence and develop a solid framework for further study. Included also are 180 end-of-chapter problems, with full solutions and sample course syllabi available for instructors. With sufficient coverage for a one- or two-semester sequence, this textbook provides an ideal flexible teaching pathway for graduate students in aerospace, mechanical, chemical, and civil engineering, and applied mathematics.
Providing a modern approach to classical fluid mechanics, this textbook presents an accessible and rigorous introduction to the field, with a strong emphasis on both mathematical exposition and physical problems. It includes a consistent treatment of a broad range of fluid mechanics topics, including governing equations, vorticity, potential flow, compressible flow, viscous flow, instability, and turbulence. It has enhanced coverage of geometry, coordinate transformations, kinematics, thermodynamics, heat transfer, and nonlinear dynamics. To round out student understanding, a robust emphasis on theoretical fundamentals and underlying mathematical details is provided, enabling students to gain confidence and develop a solid framework for further study. Included also are 180 end-of-chapter problems, with full solutions and sample course syllabi available for instructors. With sufficient coverage for a one- or two-semester sequence, this textbook provides an ideal flexible teaching pathway for graduate students in aerospace, mechanical, chemical, and civil engineering, and applied mathematics.
Introduction to Proofs and Proof Strategies
, University of Toronto
Online ISBN: 9781009089005
Online publication date:
08 June 2023
Paperback ISBN: 9781009096287
Paperback publication date: 22 June 2023
- Textbook
Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof. The material revolves around possible strategies to approaching a problem without classifying 'types of proofs' or providing proof templates. Instead, it helps students develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow. Beginning by discussing familiar and fundamental topics from a more theoretical perspective, the book moves on to inequalities, induction, relations, cardinality, and elementary number theory. The final supplementary chapters allow students to apply these strategies to the topics they will learn in future courses. With its focus on 'doing mathematics' through 200 worked examples, over 370 problems, illustrations, discussions, and minimal prerequisites, this course will be indispensable to first- and second-year students in mathematics, statistics, and computer science. Instructor resources include solutions to select problems.
Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof. The material revolves around possible strategies to approaching a problem without classifying 'types of proofs' or providing proof templates. Instead, it helps students develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow. Beginning by discussing familiar and fundamental topics from a more theoretical perspective, the book moves on to inequalities, induction, relations, cardinality, and elementary number theory. The final supplementary chapters allow students to apply these strategies to the topics they will learn in future courses. With its focus on 'doing mathematics' through 200 worked examples, over 370 problems, illustrations, discussions, and minimal prerequisites, this course will be indispensable to first- and second-year students in mathematics, statistics, and computer science. Instructor resources include solutions to select problems.
Computer Architecture for Scientists
Principles and Performance
, University of Chicago
Online ISBN: 9781009000598
Online publication date:
25 March 2022
Hardback ISBN: 9781316518533
Hardback publication date: 12 May 2022
- Textbook
The dramatic increase in computer performance has been extraordinary, but not for all computations: it has key limits and structure. Software architects, developers, and even data scientists need to understand how exploit the fundamental structure of computer performance to harness it for future applications. Ideal for upper level undergraduates, Computer Architecture for Scientists covers four key pillars of computer performance and imparts a high-level basis for reasoning with and understanding these concepts: Small is fast – how size scaling drives performance; Implicit parallelism – how a sequential program can be executed faster with parallelism; Dynamic locality – skirting physical limits, by arranging data in a smaller space; Parallelism – increasing performance with teams of workers. These principles and models provide approachable high-level insights and quantitative modelling without distracting low-level detail. Finally, the text covers the GPU and machine-learning accelerators that have become increasingly important for mainstream applications.
The dramatic increase in computer performance has been extraordinary, but not for all computations: it has key limits and structure. Software architects, developers, and even data scientists need to understand how exploit the fundamental structure of computer performance to harness it for future applications. Ideal for upper level undergraduates, Computer Architecture for Scientists covers four key pillars of computer performance and imparts a high-level basis for reasoning with and understanding these concepts: Small is fast – how size scaling drives performance; Implicit parallelism – how a sequential program can be executed faster with parallelism; Dynamic locality – skirting physical limits, by arranging data in a smaller space; Parallelism – increasing performance with teams of workers. These principles and models provide approachable high-level insights and quantitative modelling without distracting low-level detail. Finally, the text covers the GPU and machine-learning accelerators that have become increasingly important for mainstream applications.
Design Optimization using MATLAB and SOLIDWORKS
, University of Wisconsin, Madison
Online ISBN: 9781108869027
Online publication date:
17 July 2021
Hardback ISBN: 9781108491600
Hardback publication date: 24 June 2021
A unique text integrating numerics, mathematics and applications to provide a hands-on approach to using optimization techniques, this mathematically accessible textbook emphasises conceptual understanding and importance of theorems rather than elaborate proofs. It allows students to develop fundamental optimization methods before delving into MATLAB®'s optimization toolbox, and to link MATLAB's results with the results from their own code. Following a practical approach, the text demonstrates several applications, from error-free analytic examples to truss (size) optimization, and 2D and 3D shape optimization, where numerical errors are inevitable. The principle of minimum potential energy is discussed to highlight the deep relationship between engineering and optimization. MATLAB code in every chapter illustrates key concepts and the text demonstrates the coupling between MATLAB and SOLIDWORKS® for design optimization. A wide variety of optimization problems are covered including constrained non-linear, linear-programming, least-squares, multi-objective, and global optimization problems.
A unique text integrating numerics, mathematics and applications to provide a hands-on approach to using optimization techniques, this mathematically accessible textbook emphasises conceptual understanding and importance of theorems rather than elaborate proofs. It allows students to develop fundamental optimization methods before delving into MATLAB®'s optimization toolbox, and to link MATLAB's results with the results from their own code. Following a practical approach, the text demonstrates several applications, from error-free analytic examples to truss (size) optimization, and 2D and 3D shape optimization, where numerical errors are inevitable. The principle of minimum potential energy is discussed to highlight the deep relationship between engineering and optimization. MATLAB code in every chapter illustrates key concepts and the text demonstrates the coupling between MATLAB and SOLIDWORKS® for design optimization. A wide variety of optimization problems are covered including constrained non-linear, linear-programming, least-squares, multi-objective, and global optimization problems.
Curved Spaces
From Classical Geometries to Elementary Differential Geometry
, University of Cambridge
Online ISBN: 9781139507677
Online publication date:
14 September 2019
Hardback ISBN: 9780521886291
Hardback publication date: 21 January 2008
Paperback ISBN: 9780521713900
Paperback publication date: 14 January 2008
This self-contained 2007 textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra.
This self-contained 2007 textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra.
Numerical Methods
Fundamentals and Applications
, Central University of Punjab, India
Online ISBN: 9781108685306
Online publication date:
26 April 2019
Paperback ISBN: 9781108716000
Paperback publication date: 20 June 2019
Written in an easy-to-understand manner, this comprehensive textbook brings together both basic and advanced concepts of numerical methods in a single volume. Important topics including error analysis, nonlinear equations, systems of linear equations, interpolation and interpolation for Equal intervals and bivariate interpolation are discussed comprehensively. The textbook is written to cater to the needs of undergraduate students of mathematics, computer science, mechanical engineering, civil engineering and information technology for a course on numerical methods/numerical analysis. The text simplifies the understanding of the concepts through exercises and practical examples. Pedagogical features including solved examples and unsolved exercises are interspersed throughout the book for better understanding.
Written in an easy-to-understand manner, this comprehensive textbook brings together both basic and advanced concepts of numerical methods in a single volume. Important topics including error analysis, nonlinear equations, systems of linear equations, interpolation and interpolation for Equal intervals and bivariate interpolation are discussed comprehensively. The textbook is written to cater to the needs of undergraduate students of mathematics, computer science, mechanical engineering, civil engineering and information technology for a course on numerical methods/numerical analysis. The text simplifies the understanding of the concepts through exercises and practical examples. Pedagogical features including solved examples and unsolved exercises are interspersed throughout the book for better understanding.
Complex Analysis
, University of Washington
Online ISBN: 9781316471227
Online publication date:
08 March 2019
Hardback ISBN: 9781107134829
Hardback publication date: 07 March 2019
This user-friendly textbook introduces complex analysis at the beginning graduate or advanced undergraduate level. Unlike other textbooks, it follows Weierstrass' approach, stressing the importance of power series expansions instead of starting with the Cauchy integral formula, an approach that illuminates many important concepts. This view allows readers to quickly obtain and understand many fundamental results of complex analysis, such as the maximum principle, Liouville's theorem, and Schwarz's lemma. The book covers all the essential material on complex analysis, and includes several elegant proofs that were recently discovered. It includes the zipper algorithm for computing conformal maps, as well as a constructive proof of the Riemann mapping theorem, and culminates in a complete proof of the uniformization theorem. Aimed at students with some undergraduate background in real analysis, though not Lebesgue integration, this classroom-tested textbook will teach the skills and intuition necessary to understand this important area of mathematics.
This user-friendly textbook introduces complex analysis at the beginning graduate or advanced undergraduate level. Unlike other textbooks, it follows Weierstrass' approach, stressing the importance of power series expansions instead of starting with the Cauchy integral formula, an approach that illuminates many important concepts. This view allows readers to quickly obtain and understand many fundamental results of complex analysis, such as the maximum principle, Liouville's theorem, and Schwarz's lemma. The book covers all the essential material on complex analysis, and includes several elegant proofs that were recently discovered. It includes the zipper algorithm for computing conformal maps, as well as a constructive proof of the Riemann mapping theorem, and culminates in a complete proof of the uniformization theorem. Aimed at students with some undergraduate background in real analysis, though not Lebesgue integration, this classroom-tested textbook will teach the skills and intuition necessary to understand this important area of mathematics.
Statistical Thermodynamics
An Engineering Approach
, University of Colorado Boulder
Online ISBN: 9781108233194
Online publication date:
17 December 2018
Hardback ISBN: 9781108415316
Hardback publication date: 28 February 2019
- Textbook
Statistical Thermodynamics: An Engineering Approach covers in a practical, readily understandable manner the underlying meaning of entropy, temperature and other thermodynamic concepts, the foundations of quantum mechanics, and the physical basis of gas, liquid and solid phase properties. It presents simply the relationship between macroscopic and microscopic thermodynamics. In addition, the molecular basis of transport phenomena and chemical kinetics are explored, as are basic concepts in spectroscopy. Modern computational tools for solving thermodynamic problems are explored, and the student is assured that he or she will gain knowledge of practical usefulness. This essential text is suitable for mechanical or aerospace engineering graduate students who have a strong background in engineering thermodynamics, those entering advanced fields such as combustion, high temperature gas dynamics, environmental sciences, or materials processing, and those who wish to build a background for understanding advanced experimental diagnostic techniques in these or similar fields.
Statistical Thermodynamics: An Engineering Approach covers in a practical, readily understandable manner the underlying meaning of entropy, temperature and other thermodynamic concepts, the foundations of quantum mechanics, and the physical basis of gas, liquid and solid phase properties. It presents simply the relationship between macroscopic and microscopic thermodynamics. In addition, the molecular basis of transport phenomena and chemical kinetics are explored, as are basic concepts in spectroscopy. Modern computational tools for solving thermodynamic problems are explored, and the student is assured that he or she will gain knowledge of practical usefulness. This essential text is suitable for mechanical or aerospace engineering graduate students who have a strong background in engineering thermodynamics, those entering advanced fields such as combustion, high temperature gas dynamics, environmental sciences, or materials processing, and those who wish to build a background for understanding advanced experimental diagnostic techniques in these or similar fields.
Optimization in Practice with MATLAB®
For Engineering Students and Professionals
, Mississippi State University
Online ISBN: 9781316271391
Online publication date:
28 May 2018
Hardback ISBN: 9781107109186
Hardback publication date: 23 March 2015
Optimization in Practice with MATLAB® provides a unique approach to optimization education. It is accessible to both junior and senior undergraduate and graduate students, as well as industry practitioners. It provides a strongly practical perspective that allows the student to be ready to use optimization in the workplace. It covers traditional materials, as well as important topics previously unavailable in optimization books (e.g. numerical essentials - for successful optimization). Written with both the reader and the instructor in mind, Optimization in Practice with MATLAB® provides practical applications of real-world problems using MATLAB®, with a suite of practical examples and exercises that help the students link the theoretical, the analytical, and the computational in each chapter. Additionally, supporting MATLAB® m-files are available for download via www.cambridge.org.messac. Lastly, adopting instructors will receive a comprehensive solution manual with solution codes along with lectures in PowerPoint with animations for each chapter, and the text's unique flexibility enables instructors to structure one- or two-semester courses.
Optimization in Practice with MATLAB® provides a unique approach to optimization education. It is accessible to both junior and senior undergraduate and graduate students, as well as industry practitioners. It provides a strongly practical perspective that allows the student to be ready to use optimization in the workplace. It covers traditional materials, as well as important topics previously unavailable in optimization books (e.g. numerical essentials - for successful optimization). Written with both the reader and the instructor in mind, Optimization in Practice with MATLAB® provides practical applications of real-world problems using MATLAB®, with a suite of practical examples and exercises that help the students link the theoretical, the analytical, and the computational in each chapter. Additionally, supporting MATLAB® m-files are available for download via www.cambridge.org.messac. Lastly, adopting instructors will receive a comprehensive solution manual with solution codes along with lectures in PowerPoint with animations for each chapter, and the text's unique flexibility enables instructors to structure one- or two-semester courses.
A First Course in Analysis
, George Washington University, Washington DC
Online ISBN: 9781316779811
Online publication date:
28 May 2018
Hardback ISBN: 9781107173149
Hardback publication date: 25 July 2017
This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.
This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.
Chance, Strategy, and Choice
An Introduction to the Mathematics of Games and Elections
, St Joseph's University, Philadelphia
Online ISBN: 9781316026786
Online publication date:
11 May 2018
Hardback ISBN: 9781107084520
Hardback publication date: 29 June 2015
- Textbook
Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague–Grundy theorem and Arrow's impossibility theorem.Uses an integrative approach to probability, game, and social choice theoryProvides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studiesContains numerous exercises and examples of varying levels of difficultyRequires only a high school mathematical background.
Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague–Grundy theorem and Arrow's impossibility theorem.Uses an integrative approach to probability, game, and social choice theoryProvides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studiesContains numerous exercises and examples of varying levels of difficultyRequires only a high school mathematical background.
Linear Algebra: Concepts and Methods
, London School of Economics and Political Science, , London School of Economics and Political Science
Online ISBN: 9780511844249
Online publication date:
05 June 2012
Paperback ISBN: 9780521279482
Paperback publication date: 29 June 2012
- Textbook
Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book.
Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book.