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Principles of Turbomachineryin Air-BreathingEnginesErian BaskharoneTexas A & M University

This book begins with a review of basicthermodynamics and fluid mechanics prin-ciples to motivate their application toaerothermodynamics and real-life designissues. The approach is ideal for the readerwho will face practical situations anddesign decisions in the gas turbine industry.

Contents:1. Introduction to gas turbine engines; 2.Overview of turbomachinery nomenclature;3. Aerothermodynamics of turbomachines;4. Energy transfer between a fluid and arotor; 5. Dimensional analysis, maps andspecific speed; 6. Radial equilibrium theory;7. Polytropic (small-stage) efficiency; 8.Axial-flow turbines; 9. Axial-flow compres-sors; 10. Radial inflow turbines; 11.Centrifugal compressors; 12. Turbine-com-pressor matching.

Cambridge Aerospace Series2006/598 pp./143 exercises/396 figures

85810-0/Hb/List: $125.00

Principles of HelicopterAerodynamics2nd EditionJ. Gordon LeishmanUniversity of Maryland, College Park

“Not only is this book a good text for the graduatestudent but it is also a good book for practicalengineers and researchers...This book is an excel-lent addition to a reference library.”

AIAA Journal

This book is a modern treatment of theaerodynamic principles of helicopters androtating-wing vertical lift aircraft. It is exten-sively illustrated and contains exercises forstudents, as well as solutions for instructors.

Contents:Preface to the second edition; Preface to thefirst edition; Acknowledgements; List ofmain symbols; 1. Introduction: a history ofhelicopter flight; 2. Fundamentals of rotoraerodynamics; 3. Blade element analysis; 4.Rotating blade motion; 5. Helicopter per-formance; 6. Aerodynamics design of heli-copters; 7. Aerodynamics of rotor airfoils; 8.Unsteady airfoil behavior; 9. Dynamic stall;10. Rotor wakes and blade tip vortices; 11.Rotor-airframe interaction aerodynamics;12. Autogiros and gyroplanes; 13.Aerodynamics of wind turbines; 14.Computational methods for helicopter aero-dynamics; Appendix; Index.

Cambridge Aerospace Series2006/864 pp./11 tables/163 exercises

85860-7/Hb/List: $120.00

Introduction to StructuralDynamicsBruce DonaldsonUniversity of Maryland,College Park

This textbook provides the student of aero-space, mechanical, and civil engineeringwith all the fundamentals of linear struc-tural dynamics analysis. It is designed foran advanced undergraduate or first yeargraduate course and is a departure from theusual presentation in two importantrespects. First, descriptions of systemdynamics are based on the easier-to-useLagrange equations. Second, no organiza-tional distinctions are made between multi-degree of freedom systems andsingle-degree of freedom systems. The textcontains numerous examples and end-of-chapter exercises.

Contents:Preface for student; Preface for instructor; 1.The Lagrange equations of motion; 2.Mechanical vibrations: practice using theLagrange equations; 3. Review of the basicsof the finite element method for simple ele-ments; 4. FEM equations of motion for elas-tic systems; 5. Damped structural systems;6. Natural frequencies and mode shapes; 7.The modal transformation; 8. Continuousdynamic models; 9. Numerical integrationof the equations; Appendix I; Appendix II;Index.

Cambridge Aerospace Series2006/568 pp./2 tables/85 exercises

86574-3/Hb/List: $125.00

Dynamic Stability ofStructuresWei-Chau XieUniversity of Waterloo,Ontario

This book presents a systematic introduc-tion to the theory of parametric stability ofstructures under both deterministic andstochastic loadings. A comprehensive rangeof theories are presented and various appli-cation problems are formulated and solved,often using more than one approach. Itsemphasis is on the applications and variousanalytical and numerical methods for solv-ing engineering problems. The materialspresented are as self-contained as possible,with all of the important steps of analysisprovided, in order to make the book suit-able as a graduate level textbook as well asfor self-study.

Contents:1. Introduction; Part I. Dynamic Stability ofStructures under Deterministic Loadings: 2.Linear differential equations with periodiccoefficients; 3. Approximate methods; 4.

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Nonlinear systems under Periodic excita-tions; Part II. Dynamic Stability of Struc-tures under Stochastic Loadings: 5. Randomprocesses and stochastic differential equa-tions; 6. Almost-sure stability of systemsunder ergodic excitations; 7. Moment stabil-ity of stochastic systems; 8. Lyapunov expo-nents; 9. Moment Lyapunov exponents;Appendix A. Maple programs; Bibliography.

2006/448 pp./22 exercises85266-8/Hb/List: $120.00

Fundamental Solutions inElastodynamicsA CompendiumEduardo KauselMassachusetts Institute of Technology

This work is a compilation of fundamentalsolutions (Green’s functions) for classical orcanonical problems in elastodynamics pre-sented with a common format and nota-tion. These formulas describe thedisplacements and stresses elicited bydynamic sources in solid elastic media likefull spaces, half-spaces, strata and plates inboth two and three dimensions, using thethree major coordinate systems, and alsofor transient and harmonic motions.Formulas in the book were programmedand tested within the MATLAB environ-ment.

Contents:Preface, Part I. Preliminaries: 1. Funda-mentals; 2. Dipoles; Part II. Full Space Prob-lems: 3. Two-dimensional problems in full,homogeneous spaces; 4. Three-dimensionalproblems in full, homogeneous spaces; PartIII. Half-Space Problems: 5. Two-dimen-sional problems in homogeneous half-spaces;6. Three-dimensional problems in homoge-neous half-spaces; Part IV. Plates and Strata:7. Two-dimensional problems in homoge-neous plates and strata; Part V. Analyticaland Numerical Methods: 8. Solutions to theHelmholtz and wave equations; 9. Integraltransform method; 10. Stiffness (impedance)matrix method; Part VI. Appendices: BasicProperties of Mathematical Functions; 12.Brief table of integral transforms; 13. MAT-LAB® program listings.

2006/260 pp./17 tables85570-5/Hb/List: $75.00

Combustion PhysicsChung K. LawPrinceton University

In the past several decades,combustion has evolved from a scientificdiscipline that was largely empirical to onethat is quantitative and predictive. Theseadvances are characterized by the canonicalformulation of the theoretical foundation,the strong interplay between theory, experi-ment, and computation, and the unifieddescription of the roles of fluid mechanicsand chemical kinetics. This graduate-leveltext incorporates these advances in a com-prehensive treatment of the fundamentalprinciples of combustion physics. The pres-entation emphasizes analytical proficiencyand physical insight, with the formerachieved through complete, though abbre-viated, derivations at different levels of con-trol, and the latter through physicalinterpretations of analytical solutions,experimental observations, and computa-tional simulations. Exercises are mostlyderivative in nature in order to furtherstrengthen the student’s mastery of the the-ory. Implications of the fundamentalknowledge gained herein on practical phe-nomena are discussed whenever appropri-ate. These distinguishing features provide asolid foundation for an academic programin combustion science and engineering.

Contents:Introduction; 1. Chemical thermodynamics;2. Chemical kinetics; 3. Oxidation mecha-nisms of fuels; 4. Transport phenomena; 5.Conservation equations; 6. Laminar non-premixed flames; 7. Laminar premixedflames; 8. Limit phenomena; 9. Asymptoticstructure of flames; 10. Aerodynamics oflaminar flames; 11. Combustion in turbu-lent flows; 12. Combustion in boundarylayer flows; 13. Combustion in two-phaseflows; 14. Combustion in supersonic flows;References.

2006/736 pp./16 tables/104 exercises87052-6/Hb/List: $95.00

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Forthcoming…

Mechanical Efficiency of HeatEnginesJames R. SenftUniversity of Wisconsin, River Falls

This book presents a newly developed gen-eral conceptual and basic quantitativeanalysis of the mechanical efficiency of heatengines. It develops the theory at a levelcompatible with the treatment of thermalefficiency by classical thermodynamics.This yields wide-ranging results concerningthe overall cyclic conversion of heat intousable mechanical energy. Most notably,the work reveals intrinsic limits on theoverall performance of reciprocating heatengines.

Contents:1. Energy transfers in cyclic heat engines; 2.Mechanism effectiveness and mechanicalefficiency; 3. General efficiency limits; 4.Compression ratio and shaft work; 5.Pressurization effects; 6. Charge effects inideal Stirling engines; 7. Crossley-Stirlingengines; 8. Generalized engine cycles andvariable buffer pressure; 9. Multi-workspaceengines and heat pumps; 10. OptimumStirling engine geometry; 11. Heat transfereffects; Appendix A. General theory ofmachines, effectiveness, and efficiency;Appendix B. An ultra-low temperature dif-ferential Stirling engine; Appendix C. A tem-perature differential Stirling engine;References.

2007/148 pp./6 tables86880-7/Hb/List: $65.00*

Fundamentals of JetPropulsion with ApplicationsRonald D. FlackUniversity of Virginia

Fundamentals of JetPropulsion with Applications is an introduc-tory text in air-breathing jet propulsionincluding ramjets, turbojets, turbofans, andpropjets. Aimed at upper-level undergradu-ate and graduate students, the book pro-vides coverage of the basic operatingprinciples, from cycle analysis throughcomponent design and system matching. Abasic understanding of fluid mechanics andthermodynamics is assumed, althoughmany principles are thoroughly reviewed.Numerous examples and nearly 300 home-work problems based on modern enginesmake this book an ideal teaching tool, aswell as a valuable reference for practicingengineers. A CD included with the bookcontains example files and software to sup-port the text.

Contents:Part I. Cycle Analysis: 1. Introduction; 2.Ideal cycle analysis; 3. Non-ideal cycle analy-sis; Part II. Component Analysis: 4.Diffusers; 5. Nozzles; 6. Axial flow compres-sors and fans; 7. Centrifugal compressors; 8.Axial flow turbines; 9. Combustors andafterburners; 10. Ducts and mixers; Part III.System Matching and Analysis: 11. Match-ing of gas turbine components; Appendices;References; Answers to selected problems;Key words.

Cambridge Aerospace Series2005/658 pp./150 figures81983-0/Hb/List: $110.00

Forthcoming…

Planetary Landers and EntryProbesAndrew BallThe Open University, Milton KeynesJames GarryUniversiteit LeidenRalph LorenzThe Johns Hopkins UniversityViktor KerzhanovichNASA-Marshall Space Flight Center, Huntsville

This work is an important reference forprofessionals, academic researchers, andgraduate students involved in planetary sci-ence, aerospace engineering, and space mis-sion development.

Contents:Preface; Acknowledgements; Part I.Engineering Issues Specific to Entry Probes,Landers or Penetrators: 1. Mission goals andsystem engineering; 2. Accommodation,launch, cruise and arrival from orbit or inter-planetary trajectory; 3. Entering atmos-pheres; 4. Descent through an atmosphere;5. Descent to an airless body; 6. Planetaryballoons, aircraft, submarines and cryobots;7. Arrival at a surface; 8. Thermal control oflanders and entry probes; 9. Power systems;10. Communication and tracking of entryprobes; 11. Radiation environment; 12.Surface activities: arms, drills, moles andmobility; 13. Structures; 14. Contaminationof spacecraft and planets; Part II. PreviousAtmosphere/Surface Vehicles and TheirPayloads: 15. Destructive impact probes; 16.Atmospheric entry probes; 17. Pod landers;18. Legged landers; 19. Payload deliverypenetrators; 20. Small body surface missions;Part III. ‘Case Studies’: 21. Surveyor landers;22. Galileo probe; 23. Huygens; 24. MarsPathfinder and Sojourner; 25. Deep Space 2Mars microprobes; 26. Rosetta lander Philae;27. Mars exploration rovers: Spirit andOpportunity; Appendix: Some key parame-ters for bodies in the Solar System; List ofacronyms; Bibliography; References; Index.

2007/368 pp./41 line diagrams/58 half-tones82002-2/Hb/List: $130.00*

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Forthcoming…

Implicit Large EddySimulationComputing Turbulent Fluid DynamicsEditorsFernando F. GrinsteinLen G. MargolinWilliam J. RiderLos Alamos National Laboratory

Implicit Large Eddy Simulation (ILES) is arelatively new approach that combines gen-erality and computational efficiency withdocumented success in many areas of com-plex fluid flow. This book synthesizes thecurrent understanding of the theoreticalbasis of the ILES methodology and reviewsits accomplishments. ILES pioneers andlead researchers combine their experienceto present the first comprehensive descrip-tion of the methodology. This book shouldbe of fundamental interest to graduate stu-dents, basic research scientists, and profes-sionals involved in the design and analysisof complex turbulent flows.

Contents:Introduction; Part I. Motivation: 1.Historical introduction; 2. ILES for turbu-lent flows: a rationale; Part II. CapturingPhysics with Numerics: 3. Subgrid scalemodeling: issues and approaches; 4.Numerics for ILES; 4a. Limiting algorithms;4b. Piecewise parabolic method; 4c.Lagrangian remap method; 4d. MPDATA;4e. Vorticity confinement; 5. Numerical reg-ularization; 6. Approximate deconvolution;Part III. Verification and Validation: 7.Homogeneous turbulence; 8. Vortex dynam-ics and transition in free shear flows; 9.Symmetry bifurcation and instabilities; 10.Incompressible wall bounded flows; 11.Compressible turbulent shear flows; 12.Studies based on vorticity confinement; 13.Rayleigh-Taylor and Richtmyer-Meshkovmixing; Part IV. Frontier Flows: 14. Studiesof geophysics; 15. Studies of astrophysics;16. Complex engineering turbulent flows;17. Large scale urban simulations; 18.Outlook and open research issues.

2007/596 pp./15 tables86982-X/Hb/List: $120.00

Large-Eddy Simulation forAcousticsEditorsClaus Albrecht WagnerGerman Aerospace Center, GöttingenThomas HüttlMTU Aero Engines GmbH, MünchenPierre SagautUniversité Pierre et Marie Curie, Paris

Noise pollution around airports, trains, andindustries increasingly attracts environmen-tal concern and regulation. Designers andresearchers have intensified the use of large-eddy simulation (LES) for noise reducedindustrial design and acoustical research.This book, written by 30 experts, presentsthe theoretical background of acoustics andof LES, followed by details about numeri-cal methods, e.g., discretization schemes,boundary conditions, coupling aspects.Industrially relevant, hybrid RANS/LEStechniques for acoustic source predictionsare presented in detail.

Contents:Preface; Part I. Introduction: 1. The impor-tance of acoustic research; 2. Introduction tocomputational aeroacoustics; 3. State of theart: LES for acoustics; Part II. TheoreticalBackground: Aeroacoustics; Part III.Theoretical Background: Large-Eddy Simu-lation; Part IV. Use of Hybrid RANS/LESfor Acoustic-Source Predictions; Part V.Numerical Methods: 4. Spatial and temporaldiscretization schemes; 5. Boundary condi-tions for LES; 6. Boundary conditions:acoustics; 7. Some concepts of LES-CAAcoupling; Part VI. Applications and Resultsof Large-Eddy Simulations for Acoustics: 8.Plane and axisymmetric mixing layers; 9.Far-field jet acoustics; 10. Cavity noise; 11.Aero-elastic noise; 12. Trailing edge noise;13. Blunt bodies (cylinder, cars); 14. Internalflows; 15. Industrial aeroacoustics analyses;Part VII. Conclusions.

Cambridge Aerospace Series2006/575 pp./12 tables

87144-1/Hb/List: $110.00

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Hydrodynamics andSoundMichael HoweBoston University

This book is designed for a first graduatecourse in fluid dynamics. It focuses onknowledge and methods that find applica-tions in most branches of fluid mechanics,and aims to supply a theoretical understand-ing that will permit simplifications to bemade in the formulation of problems andenable the reader to develop analytical modelsof practical significance. The study of simpli-fied model problems can be used to guideexperimental and numerical investigations.

Contents:Preface; 1. Equations of motion; 2. Potentialflow of an incompressible fluid; 3. Ideal flowin two dimensions; 4. Rotational incom-pressible flow; 5. Surface gravity waves; 6.Introduction to acoustics; Bibliography.

2006/480 pp./12 tables/138 exercises86862-9/Hb/List: $95.00

Hydrodynamics ofHigh-Speed Marine VehiclesOdd M. FaltinsenNorwegian University of Science and Technology,Trondheim

This volume considers hydrodynamicaspects of the three main categories ofhigh-speed marine vehicles, i.e., vessels sup-ported by either the submerged hull, an aircushion, or foils. (Submerged-hull-support-ed vessels include planing and semi-dis-placement vessels.) Many illustrations,examples, and exercises are included.

Contents:1. Introduction; 2. Resistance and propul-sion; 3. Waves; 4. Wave resistance and wash;5. Surface effect ships; 6. Hydrofoil vesselsand foil theory; 7. Semi-displacement ves-sels; 8. Slamming, whipping and springing;9. Planing vessels; 10. Maneuvering; Appen-dix; References; Index.

2006/474 pp./51 line diagrams/51 half-tones/42 tables/1 map

84568-8/Hb/List: $100.00

Elements ofNumerical Methodsfor CompressibleFlowsDoyle D. KnightRutgers University, New Jersey

The purpose of this book is to present thebasic elements of numerical methods forcompressible flows. It is appropriate foradvanced undergraduate and graduate stu-dents and specialists working in high speedflows. The focus is on the unsteady one-dimensional Euler equations which formthe basis for numerical algorithms in com-pressible fluid mechanics. The text is sup-plemented by numerous end-of-chapterexercises.

Contents:1. Governing equations; 2. Mathematicalnature of 1-D Euler equations; 3. 1-D Eulerequations; 4. Reconstruction; 5. Godunovmethods; 6. Flux vector splitting methods; 7.Temporal quadrature; 8. TVD methods;Index; Notes; Bibliography.

Cambridge Aerospace Series2006/266 pp./13 tables/80 exercises

55474-8/Hb/List: $95.00

Introduction toChemical Transportin the EnvironmentJohn C. GulliverUniversity of Minnesota

Estimating the transport and fate of chemi-cals released into the environment is aninteresting and challenging task. This textapplies the mathematics of diffusion, tur-bulent diffusion and dispersion to theatmosphere, lakes, rivers, groundwater andthe ocean, as well as transport betweenthese media. A large portion of the book isdedicated to examples and case studies,from which the important principles arederived.

Contents:Prologue; 1. The global perspective on envi-ronmental transport and fate; 2. The diffu-sion equation; 3. Diffusion coefficients; 4.Mass, heat, and momentum transport analo-gies; 5. Turbulent diffusion; 6. Reactor mix-ing assumptions; 7. Computational masstransport; 8. Interfacial mass transfer; 9. Air-water mass transfer in the field; Appendices;References.

2006/425 pp./36 tables/57 exercises85850-X/Hb/List: $95.00

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Advanced TransportPhenomenaFluid Mechanics andConvective Transport ProcessesL. Gary LealUniversity of California, Santa Barbara

Advanced Transport Phenomena is ideal as agraduate textbook. It contains a detaileddiscussion of modern analytic methods forthe solution of fluid mechanics, and heatand mass transfer problems. Focusing onapproximations based upon scaling andasymptotic methods, the volume beginswith the derivation of basic equations andboundary conditions and concludes withlinear stability theory.

Contents:1. A preview; 2. Basic principles; 3.Unidirectional and one-dimensional flowand heat transfer processes; 4. An introduc-tion to asymptotic approximations; 5. Thethin gap approximation - lubrication prob-lems; 6. The thin gap approximation - filmswith a free surface; 7. Creeping flow - gener-al properties and solutions for 2D andaxisymmetric problems; 8. Creeping flow -3D problems; 9. Convection effects and heattransfer for viscous flows; 10. Boundary layertheory for laminar flows; 11. Heat and masstransfer at large Reynolds number; 12.Hydrodynamic stability; Appendices.

Cambridge Series in ChemicalEngineering

2007/936 pp./4 tables/227 exercises84910-1/Hb/List: $135.00*

Forthcoming…

Potential Flows of Viscousand Viscoelastic LiquidsDaniel JosephUniversity of Minnesota

The goal of this book is to show howpotential flows enter into the general theo-ry of motions of viscous and viscoelasticfluids. Traditionally, the theory of potentialflows is thought to apply to idealized fluidswithout viscosity. Here, the theory isapplied to real fluids that are viscous.

Contents:1. Introduction; 2. Historical notes; 3.Boundary conditions for viscous fluids; 4.Helmholtz decomposition coupling rota-tional to irrotational flow; 5. Harmonicfunctions which give rise to vorticity; 6.Radial motions of a spherical gas bubble in aviscous liquid; 7. Rise velocity of a sphericalcap bubble; 8. Ellipsoidal model of the rise ofa Taylor bubble in a round tube; 9. Rayleigh-Taylor instability of viscous fluids; 10. Theforce on a cylinder near a wall in viscouspotential flows; 11. Kelvin-Helmholtz insta-

bility; 12. Irrotational theories of gas-liquidflow: viscous potential flow (VPF), viscouspotential flow with pressure correction(VCVPF) and dissipation method (DM);13. Rising bubbles; 14. Purely irrotationaltheories of the effect of the viscosity on thedecay of waves; 15. Irrotational Faradaywaves on a viscous fluid; 16. Stability of aliquid jet into incompressible gases and liq-uids; 17. Stress induced cavitation; 18.Viscous effects of the irrotational flow out-side boundary layers on rigid solids; 19.Irrotational flows which satisfy the compress-ible Navier-Stokes equations; 20. Irrotationalflows of viscoelastic fluids; 21. Purely irrota-tional theories of stability of viscoelastic flu-ids; 22. Numerical methods for irrotationalflows of viscous fluid; Appendices;References; List of illustrations; List of tables.

Cambridge Aerospace Series2007/650 pp./57 tables

87337-1/Hb/List: $110.00*

Computational Methods forMultiphase FlowEditorsAndrea ProsperettiThe Johns Hopkins UniversityGretar TryggvasonWorcester Polytechnic Institute, Massachusetts

This book is a comprehensive and self-con-tained graduate-level introduction to thecomputational modeling of multiphaseflows. Each chapter is written by a recog-nized expert in the field and containsextensive references to current research. Itwill be welcomed by researchers and gradu-ate students in engineering, physics, andapplied mathematics.

Contents and Contributors:Preface; 1. Introduction: A computationalapproach to multiphase flow A. Prosperettiand G. Tryggvason; 2. Direct numerical sim-ulations of finite Reynolds number flows G.Tryggvason and S. Balachandar; 3. Immersedboundary methods for fluid interfaces G.Tryggvason, M. Sussman and M. Y.Hussaini; 4. Structured grid methods forsolid particles S. Balachandar; 5. Finite ele-ment methods for particulate flows H. Hu;6. Lattice Boltzmann methods for multi-phase flows S. Chen, X. He and L. S. Luo; 7.Boundary integral methods for Stokes flowsJ. Blawzdziewic; 8. Averaged equations formultiphase flows A. Prosperetti; 9. Point par-ticle methods for disperse flows K. Squires;10. Segregated methods for two-fluid modelsA. Prosperetti, S. Sundaresan, S. Pannala andD. Z. Zhang; 11. Coupled methods formulti-fluid models A. Prosperetti.2006/470 pp./77 line diagrams/5 tables/105 fig-

ures/23 color figures84764-8/Hb/List: $90.00*

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Fundamentals ofMultiphase FlowChristopher E. BrennenCalifornia Institute of Technology

This book is targeted to graduate studentsand researchers at the cutting edge of inves-tigations into the fundamental nature ofmultiphase flows. It is intended as a refer-ence book for the basic methods used inthe treatment of multiphase flows.

Contents:1. Introduction to multiphase flow; 2. Singleparticle motion; 3. Bubble or droplet trans-lation; 4. Bubble growth and collapse; 5.Cavitation; 6. Boiling and condensation; 7.Flow patterns; 8. Internal flow energy con-version; 9. Homogenous flows; 10. Flowswith bubble dynamics; 11. Flows with gasdynamics; 12. Sprays; 13. Granular flows;14. Drift flux models; 15. System instabili-ties; 16. Kinematic waves.

2005/368 pp./166 line diagrams/26 half-tones/3 tables

84804-0/Hb/List: $95.00

Molecular Models for FluidsKlaus LucasAachen University of Technology

This book presents the development ofmodern molecular models for fluids fromthe interdisciplinary fundamentals of classi-cal and statistical mechanics, of electrody-namics and of quantum mechanics. Theconcepts and working equations of the var-ious fields are briefly derived and illustratedin the context of understanding the proper-ties of molecular systems. The book is suit-ed for graduate courses in chemical andmechanical engineering, physics and chem-istry, but may also, by proper selection, befound useful on the undergraduate level.

Contents:Nomenclature; 1. Introduction; 2. Founda-tions; 3. The ideal gas; 4. Excess functionmodels; 5. Equation of state models;Appendices; Index.

2006/920 pp./18 tables/28 exercises85240-4/Hb/List: $95.00*

The Navier-Stokes EquationsA Classification of Flows and ExactSolutionsP. G. DrazinUniversity of BristolN. RileyUniversity of East Anglia

The Navier-Stokes equations were firmlyestablished in the 19th Century as the sys-tem of nonlinear partial differential equa-tions which describe the motion of mostcommonly occurring fluids in air andwater, and since that time exact solutionshave been sought by scientists. This bookdraws together exact solutions from widelydiffering sources and presents them in acoherent manner, in part by classifyingsolutions via their temporal and geometricconstraints. It will prove to be a valuableresource to all who have an interest in thesubject of fluid mechanics, and in particu-lar to those who are learning or teachingthe subject at the senior undergraduate andgraduate levels.

Contents:Preface; 1. Scope of the book; 2. Steady flowsbounded by plane boundaries; 3. Steadyaxisymmetric and related flows; 4. Unsteadyflows bounded by plane boundaries; 5.Unsteady axisymmetric and related flows.

London Mathematical Society LectureNote Series

2006/206 pp./72 line diagrams68162-6/Pb/List: $50.00

The MathematicalFoundations of MixingThe Linked Twist Map as a Paradigm inApplications: Micro to Macro, Fluids toSolidsRob SturmanUniversity of BristolJulio M. OttinoNorthwestern UniversityStephen WigginsUniversity of Bristol

This book shows how a variety of flows invery different settings possess the character-istic of streamline crossing. This notion canbe placed on firm mathematical footing viaLinked Twist Maps (LTMs), which is thecentral organizing principle of this book.The authors discuss the definition and con-struction of LTMs, provide examples ofspecific mixers that can be analyzed in theLTM framework and introduce a numberof mathematical techniques which are thenbrought to bear on the problem of fluidmixing.

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Contents:Preface; 1. Mixing: physical issues; 2. Linkedtwist maps; 3. The ergodic hierarchy; 4.Existence of a horseshoe; 5. Hyperbolicity; 6.The ergodic partition for toral LTMs; 7.Ergodicity and Bernoulli for TLTMs; 8.Linked twist maps on the plane; 9. Furtherdirections and open problems; Bibliography;Index.

Cambridge Monographs on Appliedand Computational Mathematics

2006/302 pp./110 line diagrams/17 color figures86813-0/Hb/List: $75.00

Prediction of Turbulent FlowsEditorsGeoff HewittChristos VassilicosImperial College of Science, Technology andMedicine, London

The prediction of turbulent flows is ofparamount importance in the developmentof complex engineering systems involvingflow, heat and mass transfer, and chemicalreactions. Utilizing modern computationalfluid dynamics techniques, this bookreviews current approximation methodsand their applicability to various industrialproblems.

Contents and Contributors:1. Introduction G. F. Hewitt; 2. Turbulentflows: their structure and behaviour J. C. R.Hunt, N. D. Sandham, J. C. Vassilicos, B. E.Launder, P. A. Monkewitz and G. F. Hewitt;3. The modelling of turbulent flows affectedby buoyancy and stratification B. E.Launder; 4. Turbulent flames W. P. Jones; 5.Boundary layers under strong distortion J. F.Morrison; 6. Direct and large eddy simula-tion N. D. Sandham; 7. Multiphase flows G.F. Hewitt and M. W. Reeks; 8. Guidelinesand criteria for the use of turbulence modelsin complex flows J. C. R. Hunt and A. M.Savill.

2005/350 pp./56 line diagrams/2 half-tones/74figures/16 color figures

83899-1/Hb/List: $175.00

Lagrangian Fluid DynamicsAndrew BennettOregon State University

Starting from the foundations of elemen-tary kinematics and assuming some famil-iarity of Eulerian fluid dynamics, this bookreviews the classical and new exact solu-tions of the Lagrangian framework, andthen addresses the general solvability of theresulting general equations of motion.

Contents:Part I. The Lagrangian Formulation: 1.Lagrangian kinematics; 2. Lagrangian statis-tics; 3. Lagrangian dynamics; 4. Coor-dinates; 5. Real fluids; Part II. LagrangianFlows: 6. Some analytical Lagrangian solu-tions; 7. Waves, instabilities and vortices; 8.Viscous incompressible flow; 9. Generalsolvability; Part III. Diffusion: 10. Absolutedispersion; 11. Relative dispersion; 12.Convective subranges, scalar variance spec-trum; 13. Diffusion; Part IV. Lagrangiandata: 14. Observing systems; 15. Data analy-sis: the single particle; 16. Data analysis: par-ticle clusters; References.

Cambridge Monographs on Mechanics2006/308 pp./20 line diagrams/20 figures

85310-9/Hb/List: $95.00

Nonlinear Dynamics andStatistical Theories for BasicGeophysical FlowsAndrew MajdaNew York UniversityXiaoming WangIowa State University

This introduction to the important inter-play between nonlinear dynamics and sta-tistical theories for geophysical flows isdesigned for a multi-disciplinary audienceranging from graduate students to seniorresearchers.

Contents:1. Barotropic geophysical flows and two-dimensional fluid flows: an elementaryintroduction; 2. The response to large scaleforcing; 3. The selective decay principle forbasic geophysical flows; 4. Nonlinear stabili-ty of steady geophysical flows; 5. Topo-graphic mean-flow interaction, nonlinearinstability, and chaotic dynamics; 6.Introduction to empirical statistical theory;7. Equilibrium statistical mechanics for sys-tems of ordinary differential equations; 8.Statistical mechanics for the truncated quasi-geostrophic equations; 9. Empirical statisti-cal theories for most probable states; 10.Assessing the potential applicability of equi-librium statistical theories for geophysicalflows: an overview; 11. Predictions and com-parison of equilibrium statistical theories;12. Equilibrium statistical theories and

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dynamical modeling of flows with forcingand dissipation; 13. Predicting the jets andspots on Jupiter by equilibrium statisticalmechanics; 14. Statistically relevant andirrelevant conserved quantities for truncatedquasi-geostrophic flow and the Burger-Hopfmodel; 15. A mathematical framework forquantifying predictability utilizing relativeentropy; 16. Barotropic quasi-geostrophicequations on the sphere; Bibliography;Index.

2006/564 pp./150 line diagrams/10 tables83441-4/Hb/List: $90.00

Multiple ScatteringInteraction of Time-Harmonic Waveswith N ObstaclesP. A. MartinColorado School of Mines

The mathematical theory and technologyneeded to understand the interaction ofwaves with obstacles is known as multiplescattering; this book is the first devoted tothe subject. P.A. Martin covers a variety oftechniques, describing first the single-obsta-cle methods and then extending them tothe multiple-obstacle case. This book willbe an essential reference on the topic forengineers, physicists, and applied mathe-maticians.

Contents:Preface; 1. Introduction; 2. Addition theo-rems in two dimensions; 3. Addition theo-rems in three dimensions; 4. Methods basedon separation of variables; 5. Integral equa-tion methods I: basic theory; 6. Integralequation methods II: further details; 7. Null-field and T-matrix methods; 8. Approxi-mations; Appendices; Comments on thebibliography; Bibliography; Citation index;Index.

Encyclopedia of Mathematics and itsApplications

2006/450 pp./10 line diagrams86554-9/Hb/List: $140.00

The Equations of OceanicMotionsPeter MüllerUniversity of Hawaii, Manoa

The Equations of Oceanic Motions derivesand systematically classifies the most com-mon dynamic equations used in physicaloceanography, from large scale thermoha-line circulations to those governing smallscale motions and turbulence. After estab-lishing the basic dynamical equations thatdescribe all oceanic motions, Müller thenderives approximate equations, emphasiz-ing the assumptions made and physicalprocesses eliminated. Providing the basictheoretical background for graduate stu-

dents and researchers, this book will serveas both a comprehensive text and an essen-tial reference.

Contents:1. Introduction; 2. Equilibrium thermody-namics of sea water; 3. Balance equations; 4.Molecular flux laws; 5. The gravitationalpotential; 6. The basic equations; 7.Dynamical impact of the equation state; 8.Free wave solution on a sphere; 9.Asymptotic expansions; 10. Reynoldsdecomposition; 11. Boussinesq approxima-tion; 12. Large scale motions; 13. Primitiveequations; 14. Representations of verticalstructure; 15. Ekman layers; 16. Planetarygeostrophic flows; 17. Tidal equations; 18.Medium scale motions; 19. Quasi-geostrophic flows; 20. Motions on the f-plane; 21. Small scale motions; 22. Soundwaves; Appendices; References; Index.

2006/302 pp./24 line diagrams85513-6/Hb/List: $80.00

Fundamentals ofGeophysical FluidDynamicsJames C. McWilliamsUniversity of California, Los Angeles

“...a delightfully refreshing introduction to gradu-ate-level geophysical fluid dynamics. This well-written text includes a concise review of the neededapplied mathematics, physics and fluid dynamics.The text pulls examples not only from the atmos-pheres and oceans but also from recent numericalstudies and laboratory experiments in nonlineardynamics, solitons, chaos and 2- and 3-dimension-al turbulence, with an appropriate emphasis ontheir relevance to geophysical fluid dynamics. Sometopics, for example, geostrophic adjustment, aremore clearly explained and are better physicallymotivated here than in any other text I have read.This book should not only be on the shelves of allgeophysical fluid dynamicists, but also physicists,astronomers, and applied mathematicians.”

Professor Philip Marcus, Department ofMechanical Engineering, University of

California, Berkeley

Contents:Preface; List of symbols; 1. Purposes andvalue of geophysical fluid dynamics; 2.Fundamental dynamics; 3. Barotropic andvortex dynamics; 4. Rotating shallow-waterand wave dynamics; 5. Baroclinic and jetdynamics; 6. Boundary-layer and wind-gyredynamics; Afterword; Exercises; Bibliog-raphy; Index.

2006/266 pp./64 line diagrams/18 half-tones/7 color plates

85637-X/Hb/List: $75.00

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Introduction toComputationalFluid DynamicsAnil W. DateIndian Institute of Technology, Bombay

This textbook is directed to advancedundergraduate and first-year graduate stu-dents in mechanical, aerospace, and chemi-cal engineering. The book emphasizesunderstanding CFD through physical prin-ciples and examples. Practicing engineerswill also find this book useful for referenceand for continuing education.

Contents:Preface; Nomenclature; 1. Introduction; 2.1D heat conduction; 3. 1D conduction-con-vection; 4. 2D boundary layers; 5. 2D con-vection - Cartesian grids; 6. 2D convection -complex domains; 7. Phase change; 8.Numerical grid generation; 9. Convergenceenhancement; Appendices.

2005/398 pp./131 line diagrams/35 tables/126exercises

85326-5/Hb/List: $80.00

Measurement in FluidMechanicsStavros TavoularisUniversity of Ottawa

This graduate textbook and reference inexperimental fluid mechanics is intendedfor anyone wishing to understand theproperties of fluid-containing systems, todesign improved systems, predict the oper-ation of such fluid systems, and monitorand control physical processes.

Contents:Part I. General Concepts: 1. Flow propertiesand basic principles; 2. Measuring systems;3. Measurement uncertainty; 4. Signal con-ditioning, discretization and analysis; 5.Background for optical experimentation; 6.Fluid mechanical apparatus; 7. Towards asound experiment; Part II. MeasurementTechniques: 8. Measurement of flow pres-sure; 9. Measurement of flow rate; 10. Flowvisualization techniques; 11. Measurementof local flow velocity; 12. Measurement oftemperature; 13. Measurement of composi-tion; 14. Measurement of wall shear stress;15. Outlook.

2005/384 pp./97 line diagrams/3 half-tones/21 tables/106 exercises81518-5/Hb/List: $85.00

Statistical ThermodynamicsFundamentals and ApplicationsNormand LaurendeauPurdue University, Indiana

Contents:1. Introduction; Part I. Fundamentals ofStatistical Thermodynamics: 2. Probabilityand statistics; Problem Set I: Probability theo-ry and statistical mathematics; 3. The statisticsof independent particles; 4. Thermodynamicsproperties in the dilute limit; Problem Set II:Statistical modeling for thermodynamics; PartII. Quantum Mechanics and Spectroscopy: 5.Basics of quantum mechanics; 6. Quantumanalysis of internal energy modes; 7. The spec-troscopy of diatomic molecules; Problem SetIII: Quantum mechanics and spectroscopy; 8.Interlude: from particle to assembly; 9.Thermodynamic properties of the ideal gas;Problem Set IV: Thermodynamic propertiesof the ideal gas; 10. Statistical thermodynam-ics for ideal gas mixtures; 11. Concentrationand temperature measurements; Problem SetV: Chemical equilibrium and diagnostics;Part IV. Statistical Thermodynamics Beyondthe Dilute Limit: 12. Thermodynamics andinformation; 13. Elements of the solid state;14. Equilibrium radiation; Problem Set VI:The Solid state and radiation; Part V. Non-Equilibrum Statistical Thermodynamics: 15.Elementary kinetic theory; 16. Kinetics ofmolecular transport; 17. Chemical kinetics;Problem Set VII: Kinetic theory and molecu-lar transport; Part VI. The Ensemble Methodof Statistical Thermodynamics: 18. Thecanonical and grand canonical ensembles; 19.Applications of ensemble theory to real gases;Problem Set VIII: Ensemble theory and thenon-ideal gas; 20. Whence and whither; PartVII. Appendices.

2005/464 pp./92 line diagrams/64 tables/117 exercises

84635-8/Hb/List: $90.00

ThermodynamicsConcepts and ApplicationsStephen R. TurnsPennsylvania State University

Although the focus of this textbook is ontraditional thermodynamics topics, thebook is concerned with introducing thethermal-fluid sciences as well. It is designedfor the instructor to select topics and seam-lessly combine them with material fromother chapters. Pedagogical devices include:learning objectives, chapter overviews andsummaries, historical perspectives, andnumerous examples, questions, problemsand lavish illustrations.

Contents:Preface; 1. Beginnings; 2. Thermodynamicproperties, property relationships andprocesses; 3. Conservation of mass; 4. Ener-gy and energy transfer; 5. Conservation ofenergy; 6. Second law of thermodynamics

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and some of its consequences; 7. Steady-flowdevices; 8. Systems for power production,propulsion, heating and cooling; Appen-dices; Answers to Selected Problems; Index.

2006/756 pp./690 line diagrams/321 color plates/41 tables/1107 exercises

85042-8/Hb/List: $95.00

Thermal-Fluid SciencesAn Integrated ApproachStephen TurnsPennsylvania State University

“The book can easily be adopted as a courseresource in undergraduate engineering fluiddynamics courses and even in a self-studyapproach. Highly recommended.”

Choice

This integrated textbook for an engineeringcourse covering thermodynamics, heattransfer, and fluid mechanics is based onthe fundamental conservation principles ofmass, energy, and momentum. It featuresmany full color illustrations, and includeschapter learning objectives, overviews, his-torical vignettes, numerous examples ofproblem-solving, and a format enhanced byinnovative self tests and color coding tohighlight significant equations andadvanced topics. Integrated tutorials showthe student how to use modern software,including the NIST Database on CD, toobtain thermodynamic and transport prop-erties.

Contents:Preface; Part I. Fundamentals: 1. Beginnings;2. Thermodynamic properties, property rela-tionships and processes; 3. Conservation ofmass; 4. Energy and energy transfer; 5.Conservation of energy; 6. Conservation ofmomentum; 7. Second law of thermody-namics and some of its consequences; 8.Similitude and dimensionless parameters;Part II. Beyond the Fundamentals; 9.External flows: friction, drag and heat trans-fer; 10. Internal flows: friction, pressure dropand heat transfer; 11. Thermal-fluid analysisof steady-flow devices; 12. Systems for powerproduction, propulsion, heating and cool-ing; Appendices; Selected answers; Index.

2006/1218 pp./1120 line diagrams/557 colorplates/61 tables/1836 exercises

85043-6/Hb/List: $105.00

Multimedia Fluid Mechanics—Multilingual Version CD-ROMG. M. HomsyUniversity of California, Santa BarbaraH. ArefVirginia Polytechnic Institute and State UniversityK. S. BreuerBrown University, Rhode IslandS. HochgrebSandia National Laboratories, PeruJ. R. KoseffStanford University, CaliforniaB. R. MunsonIowa State UniversityK. G. PowellMichigan State UniversityC. R. RobertsonStanford University, CaliforniaS. T. ThoroddsenUniversity of Illinois, Urbana-Champaign

“Homsy and his colleagues have now provided uswith a new and powerful teaching aid...This CDis an ambitious project, and, in my view, it hasbeen accomplished with remarkable success...I haveno doubt that this CD-ROM should be regardedas a ‘set text’ for viscous fluid mechanics courses atthe undergraduate or starting graduate levels.”

Journal of Fluid Mechanics

This CD-ROM offers an interactive toolfor teaching undergraduate fluid mechan-ics. It features experiments that demon-strate fluid mechanical phenomena,animations of important principles andconcepts, virtual laboratories in which stu-dents acquire data from the images, inter-active computational exercises in whichparameters can be varied, and otherdescriptive and illuminating material onapplications.

200460476-1/CD-ROM/List: $21.00

Thermal-Fluid Sciences withMultimedia FluidMechanicsStephen TurnsPennsylvania State University

This special package combines Turns:Thermal Fluid Sciences: An IntegratedApproach with a copy of Homsy et al,Multimedia Fluid Mechanics - MultilingualVersion CD-ROM to enhance the fluidmechanics presentation.

2006/1,218 pp./CD-ROM68241-X/Hb and CD-ROM/List: $105.00

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ThermodynamicsFundamentals for ApplicationsJ. P. O’ConnellUniversity of VirginiaJ. M. HaileMacatea Productions, South Carolina

“O’Connell and Haile are weathered experts in thefield, and in teaching thermodynamics. This clear-ly shows in their new textbook, which is primarilyintended for beginning graduate students in chem-ical engineering. Their experience is visiblethrough the special care they take to graduallybuild up the subject with the utmost attention todetails…As excellent writers, they are able to con-vey their deep understanding to us, and their bookshould make many students enthusiastic aboutthermodynamics. To bring classical thermodynam-ics to life in such an appealingly vivid, yet alsomathematically rigorous, way is an accomplish-ment that makes this book highly recommend-able.”

Angewandte Chemie

Contents:Introduction. Part I. The Basics: 1. Primi-tives; 2. The first and second laws; 3. Funda-mental relations; Part II. Single-PhaseSystems: 4. Properties relative to ideal gases;5. Properties relative to ideal solutions; 6.Relations among relations; Part III.Multiphase and Reacting Systems: 7.Transfers, transformations, and equilibria; 8.Criteria for observability; 9. Phase diagramsfor real systems; Part IV. EngineeringCalculations: 10. Options for equilibriumcalculations; 11. Elementary computationalprocedures; 12. Selected applications;Afterword; Appendices; Notation; Index.

2005/672 pp./148 line diagrams/24 tables/287 exercises

58206-7/Hb/List: $100.00

Forthcoming…

Dynamic Modeling andControl of EngineeringSystems3rd EditionBohdan KulakowskiPennsylvania State UniversityJohn GardnerBoise State University

This textbook is appropriate for anadvanced undergraduate course inEngineering System Dynamics andControls. The third edition features manynew and expanded sections on such topicsas: Solving Stiff Systems, OperationalAmplifiers, Electrohydraulic Servovalves,Using Matlab with Transfer Functions,Using Matlab with Frequency Response,Matlab Tutorial and an expanded SimulinkTutorial. The work includes 40% moreend-of-chapter exercises and 30% moreexamples than the previous edition.

Contents:Preface; 1. Introduction; 2. Mechanical sys-tems; 3. Mathematical models; 4. Analyticalsolutions of system input-output equations;5. Numerical solutions of ordinary differen-tial equations; 6. Simulation of dynamic sys-tems; 7. Electrical systems; 8. Thermalsystems; 9. Fluid systems; 10. Mixed sys-tems; 11. Transfer functions; 12. Frequencyanalysis; 13. Closed-loop systems and systemstability; 14. Control systems; 15. Analysis ofdiscrete-time systems; 16. Digital controlsystems; Appendices; Index.

2007/432 pp./31 tables/204 exercises86435-6/Hb/List: $90.00*

A Guide to MATLAB®

For Beginners and Experienced Users2nd EditionBrian R. HuntRonald L. LipsmanJonathan M. RosenbergUniversity of Maryland, College ParkKevin R. CoombesUniversity of TexasJohn E. OsbornGarrett J. StuckUniversity of Maryland, College Park

This guide presents a short, focused intro-duction to MATLAB, a comprehensivesoftware system for mathematical and tech-nical computing. It contains concise expla-nations of essential MATLAB commands,as well as easily understood instructions forusing MATLAB’s programming features,graphical capabilities, simulation models,and rich desktop interface. Written forMATLAB 7, it can also be used with earlier(and later) versions of MATLAB.

Contents:Preface; 1. Getting started; 2. MATLABbasics; 3. Interacting with MATLAB; 4.Beyond the basics; 5. MATLAB graphics; 6.M-Books; 7. MATLAB programming; 8.SIMULINK and GUIs; 9. Applications; 10.MATLAB and the Internet; 11. Trouble-shooting; Solutions to the practice sets; Glos-sary; Index.

2006/416 pp./145 line diagrams/39 exercises/9 worked examples

85068-1/Hb/List: $125.0061565-8/Pb/List: $50.00

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Numerical Methods inEngineering with MATLAB®

Jaan KiusalaasPennsylvania State University

Numerical Methods in Engineering withMATLAB® is a text for engineering stu-dents and a reference for practicing engi-neers. Examples and applications werechosen for their relevance to real worldproblems, and where numerical solutionsare most efficient. Numerical methods arediscussed thoroughly and illustrated withproblems involving both hand computa-tion and programming. MATLAB® mfilesaccompany each method and are availableon www.cambridge.org/0521852889.

Contents:1. Introduction to MATLAB®; 2. Systems oflinear algebraic equations; 3. Interpolationand curve fitting; 4. Roots of equations; 5.Numerical differentiation; 6. Numericalintegration; 7. Initial value problems; 8.Two-point boundary value problems; 9.Symmetric Matrix Eigenvalue problems; 10.Introduction to optimization; Appendices.

2005/434 pp./133 line diagrams/12 tables/346 exercises

85288-9/Hb/List: $85.00

Also available with Python code…

Numerical Methods inEngineering with PythonJaan KiusalaasPennsylvania StateUniversity

2005/432 pp./133 line diagrams/12 tables/346 exercises

85287-0/Hb/List: $85.00

Mathematical Methods forPhysics and EngineeringA Comprehensive Guide3rd EditionK. F. RileyM. P. HobsonUniversity of CambridgeS. J. Bence

The third edition of this highly acclaimedundergraduate textbook is suitable forteaching the necessary mathematics for anundergraduate course in any of the physicalsciences.

Contents:Prefaces; 1. Preliminary algebra; 2. Prelim-inary calculus; 3. Complex numbers andhyperbolic functions; 4. Series and limits; 5.Partial differentiation; 6. Multiple integrals;7. Vector algebra; 8. Matrices and vectorspaces; 9. Normal modes; 10. Vector calcu-

lus; 11. Line, surface and volume integrals;12. Fourier series; 13. Integral transforms;14. First-order ordinary differential equa-tions; 15. Higher-order ordinary differentialequations; 16. Series solutions of ordinarydifferential equations; 17. Eigenfunctionmethods for differential equations; 18.Special functions; 19. Quantum operators;20. Partial differential equations: general andparticular; 21. Partial differential equations:separation of variables; 22. Calculus of varia-tions; 23. Integral equations; 24. Complexvariables; 25. Application of complex vari-ables; 26. Tensors; 27. Numerical methods;28. Group theory; 29. Representation theo-ry; 30. Probability; 31. Statistics; Index.2006/1362 pp./235 line diagrams/820 exercises

86153-5/Hb/List: $160.0067971-0/Pb/List: $80.00

Writing ScientificSoftwareA Guide to Good StyleSuely OliveiraDavid E. StewartUniversity of Iowa

Contents:Part I. Numerical Software: 1. Why numeri-cal software?; 2. Scientific computation andnumerical analysis; 3. Priorities; 4. Famousdisasters; 5. Exercises; Part II. DevelopingSoftware: 6. Basics of computer organiza-tion; 7. Software design; 8. Modularity andall that; 9. Data structures; 10. Design fortesting and debugging; 11. Exercises; PartIII. Efficiency in Time, Efficiency inMemory: 12. Be algorithm aware; 13.Computer architecture and efficiency; 14.Global vs. local optimization; 15. Grabbingmemory when you need it; 16. Memorybugs and leaks; Part IV. Tools: 17. Sources ofscientific software; 18. Unix tools; 19. Cubicspline function library; 20. Multigrid algo-rithms; A. Review of vectors and matrices; B.Trademarks; Bibliography; Index.

2006/316 pp.85896-8/Hb/List: $85.0067595-2/Pb/List: $34.99

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Simulation........................................................................Hb $120.00

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___ 68241X Turns/Therml Fld Sci with Multim Fld Mech....................Hb/CD $105.00

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