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100 results in Cambridge Textbooks

Page 1 of 5

Measurement in Fluid Mechanics

Fundamentals of Dispersed Multiphase Flows
  • S. Balachandar
  • Coming soon
  • Expected online publication date: March 2024
  • Print publication: 31 March 2024
  • Dispersed multiphase flows are at the heart of many geophysical, environmental, industrial, and energy applications. Volcanic eruption, rain formation, powder snow avalanches, sediment transport, and dust storms are some of the classic examples from the environment, while industrial applications include fluidized beds, slurry transport, fuel injection, cyclone separators, and plasma coating, to name a few. Although each application is unique, they share significant commonalities in the underlying dispersed multiphase flow physics that govern their dynamics. This book takes a rigorous approach to explaining the complex interconnected physical processes that are at play, before developing different classes of mathematical models and numerical techniques that are appropriate for different regimes of dispersed multiphase flows. Containing many examples and over 100 exercises, it is suitable for use as a graduate-level textbook as well as a reference for researchers who want to model and simulate a multiphase flow phenomenon in their application.

How to Think about Algorithms
  • 2nd edition
  • Jeff Edmonds
  • Coming soon
  • Expected online publication date: February 2024
  • Print publication: 29 February 2024
  • Understand algorithms and their design with this revised student-friendly textbook. Unlike other algorithms books, this one is approachable, the methods it explains are straightforward, and the insights it provides are numerous and valuable. Without grinding through lots of formal proof, students will benefit from step-by-step methods for developing algorithms, expert guidance on common pitfalls, and an appreciation of the bigger picture. Revised and updated, this second edition includes a new chapter on machine learning algorithms, and concise key concept summaries at the end of each part for quick reference. Also new to this edition are more than 150 new exercises: selected solutions are included to let students check their progress, while a full solutions manual is available online for instructors. No other text explains complex topics such as loop invariants as clearly, helping students to think abstractly and preparing them for creating their own innovative ways to solve problems.

Quantitative Risk and Portfolio Management
  • Theory and Practice
  • Kenneth J. Winston
  • Coming soon
  • Expected online publication date: November 2023
  • Print publication: 21 September 2023
  • A comprehensive modern introduction to risk and portfolio management for quantitatively adept advanced undergraduate and beginning graduate students who will become practitioners in the field of quantitative finance. With a focus on real-world application, but providing a background in academic theory, this text builds a firm foundation of rigorous but practical knowledge. Extensive live data and Python code are provided as online supplements, allowing a thorough understanding of how to manage risk and portfolios in practice. With its detailed examination of how mathematical techniques are applied to finance, this is the ideal textbook for giving students with a background in engineering, mathematics or physics a route into the field of quantitative finance.

Matrix Mathematics
  • A Second Course in Linear Algebra
  • 2nd edition
  • Stephan Ramon Garcia, Roger A. Horn
  • Coming soon
  • Expected online publication date: September 2023
  • Print publication: 25 May 2023
  • Using a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student's understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor's resources are available.

Online Algorithms
  • Rahul Vaze
  • Coming soon
  • Expected online publication date: August 2023
  • Print publication: 31 October 2023
  • Online algorithms are a rich area of research with widespread applications in scheduling, combinatorial optimization, and resource allocation problems. This lucid textbook provides an easy but rigorous introduction to online algorithms for graduate and senior undergraduate students. In-depth coverage of most of the important topics is presented with special emphasis on elegant analysis. The book starts with classical online paradigms like the ski-rental, paging, list-accessing, bin packing, where performance of online algorithms is studied under the worst-case input and moves on to newer paradigms like 'beyond worst case', where online algorithms are augmented with predictions using machine learning algorithms. The book goes on to cover multiple applied problems such as routing in communication networks, server provisioning in cloud systems, communication with energy harvested from renewable sources, and sub-modular partitioning. Finally, a wide range of solved examples and practice exercises are included, allowing hands-on exposure to the concepts.

Fundamentals of Transport Processes with Applications
  • V. Kumaran
  • Coming soon
  • Expected online publication date: August 2023
  • Print publication: 16 February 2023
  • 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.

Functional Analysis
  • Prahlad Vaidyanathan
  • Coming soon
  • Expected online publication date: August 2023
  • Print publication: 21 September 2023
  • Since its inception in the early 20th century, Functional Analysis has become a core part of modern mathematics. This accessible and lucid textbook will guide students through the basics of Functional Analysis and the theory of Operator Algebras. The text begins with a review of Linear Algebra and Measure Theory. It progresses to concepts like Banach spaces, Hilbert spaces, Dual spaces and Weak Topologies. Subsequent chapters introduce the theory of operator algebras as a guide to study linear operators on a Hilbert space and cover topics such as Spectral Theory and C*-algebras. Theorems have been introduced and explained through proofs and examples, and historical background to the mathematical concepts have been provided wherever appropriate. At the end of chapters, practice exercises have been segregated in a topic-wise manner for targeted practice, making the book ideal both for classroom teaching as well as self-study.

Calculus
  • Amber Habib
  • Coming soon
  • Expected online publication date: August 2023
  • Print publication: 16 February 2023
  • Calculus is important for first-year undergraduate students pursuing mathematics, physics, economics, engineering, and other disciplines where mathematics plays a significant role. The book provides a thorough reintroduction to calculus with an emphasis on logical development arising out of geometric intuition. The author has restructured the subject matter in the book by using Tarski's version of the completeness axiom, introducing integration before differentiation and limits, and emphasizing benefits of monotonicity before continuity. The standard transcendental functions are developed early in a rigorous manner and the monotonicity theorem is proved before the mean value theorem. Each concept is supported by diverse exercises which will help the reader to understand applications and take them nearer to real and complex analysis.

Computing in Scilab
  • Chetana Jain
  • Coming soon
  • Expected online publication date: August 2023
  • Print publication: 05 January 2023
  • 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
  • Joseph M. Powers
  • Published online: 14 July 2023
  • Print publication: 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.

Introduction to Proofs and Proof Strategies
  • Shay Fuchs
  • Published online: 08 June 2023
  • Print publication: 22 June 2023
  • 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.

The Atmospheric General Circulation
  • John M. Wallace, David S. Battisti, David W. J. Thompson, Dennis L. Hartmann
  • Published online: 26 May 2023
  • Print publication: 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.

Stochastic Finance
  • An Introduction with Examples
  • Amanda Turner, Dirk Zeindler
  • Published online: 16 February 2023
  • Print publication: 09 February 2023
  • 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.

Actions of Groups
  • A Second Course in Algebra
  • John McCleary
  • Published online: 03 May 2023
  • Print publication: 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.

Finite Element and Finite Volume Methods for Heat Transfer and Fluid Dynamics
  • J. N. Reddy, N. K. Anand, P. Roy
  • Published online: 27 January 2023
  • Print publication: 27 October 2022
  • 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.

Modern Mathematical Logic
  • Joseph Mileti
  • Published online: 08 December 2022
  • Print publication: 22 September 2022
  • This textbook gives a complete and modern introduction to mathematical logic. The author uses contemporary notation, conventions, and perspectives throughout, and emphasizes interactions with the rest of mathematics. In addition to covering the basic concepts of mathematical logic and the fundamental material on completeness, compactness, and incompleteness, it devotes significant space to thorough introductions to the pillars of the modern subject: model theory, set theory, and computability. Requiring only a modest background of undergraduate mathematics, the text can be readily adapted for a variety of one- or two-semester courses at the upper-undergraduate or beginning-graduate level. Numerous examples reinforce the key ideas and illustrate their applications, and a wealth of classroom-tested exercises serve to consolidate readers' understanding. Comprehensive and engaging, this book offers a fresh approach to this enduringly fascinating and important subject.

An Elementary Course on Partial Differential Equations
  • Aftab Alam, Mohammad Imdad
  • Published online: 15 September 2022
  • Print publication: 05 January 2023
  • 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.

Connecting Discrete Mathematics and Computer Science
  • 2nd edition
  • David Liben-Nowell
  • Published online: 16 December 2022
  • Print publication: 04 August 2022
  • Computer science majors taking a non-programming-based course like discrete mathematics might ask 'Why do I need to learn this?' Written with these students in mind, this text introduces the mathematical foundations of computer science by providing a comprehensive treatment of standard technical topics while simultaneously illustrating some of the broad-ranging applications of that material throughout the field. Chapters on core topics from discrete structures – like logic, proofs, number theory, counting, probability, graphs – are augmented with around 60 'computer science connections' pages introducing their applications: for example, game trees (logic), triangulation of scenes in computer graphics (induction), the Enigma machine (counting), algorithmic bias (relations), differential privacy (probability), and paired kidney transplants (graphs). Pedagogical features include 'Why You Might Care' sections, quick-reference chapter guides and key terms and results summaries, problem-solving and writing tips, 'Taking it Further' asides with more technical details, and around 1700 exercises, 435 worked examples, and 480 figures.

Mathematical Methods and Physical Insights
  • An Integrated Approach
  • Alec J. Schramm
  • Published online: 15 July 2022
  • Print publication: 16 June 2022
  • Mathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students' physical intuition as he guides them through the mathematical methods required to study upper-level physics. Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material. It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions ('By the Ways') as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, many taking advantage of Mathematica, to test and deepen comprehension.

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