Classical mechanics Books
Springer Vectored Propulsion Supermaneuverability and Robot Aircraft Ifip Series on Computer Graphics
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Springer New York Brownian Motion and Stochastic Calculus
Book Synopsis1 Martingales, Stopping Times, and Filtrations.- 1.1. Stochastic Processes and ?-Fields.- 1.2. Stopping Times.- 1.3. Continuous-Time Martingales.- 1.4. The DoobMeyer Decomposition.- 1.5. Continuous, Square-Integrable Martingales.- 1.6. Solutions to Selected Problems.- 1.7. Notes.- 2 Brownian Motion.- 2.1. Introduction.- 2.2. First Construction of Brownian Motion.- 2.3. Second Construction of Brownian Motion.- 2.4. The SpaceC[0, ?), Weak Convergence, and Wiener Measure.- 2.5. The Markov Property.- 2.6. The Strong Markov Property and the Reflection Principle.- 2.7. Brownian Filtrations.- 2.8. Computations Based on Passage Times.- 2.9. The Brownian Sample Paths.- 2.10. Solutions to Selected Problems.- 2.11. Notes.- 3 Stochastic Integration.- 3.1. Introduction.- 3.2. Construction of the Stochastic Integral.- 3.3. The Change-of-Variable Formula.- 3.4. Representations of Continuous Martingales in Terms of Brownian Motion.- 3.5. The Girsanov Theorem.- 3.6. Local Time and a Generalized Itô Rule for Brownian Motion.- 3.7. Local Time for Continuous Semimartingales.- 3.8. Solutions to Selected Problems.- 3.9. Notes.- 4 Brownian Motion and Partial Differential Equations.- 4.1. Introduction.- 4.2. Harmonic Functions and the Dirichlet Problem.- 4.3. The One-Dimensional Heat Equation.- 4.4. The Formulas of Feynman and Kac.- 4.5. Solutions to selected problems.- 4.6. Notes.- 5 Stochastic Differential Equations.- 5.1. Introduction.- 5.2. Strong Solutions.- 5.3. Weak Solutions.- 5.4. The Martingale Problem of Stroock and Varadhan.- 5.5. A Study of the One-Dimensional Case.- 5.6. Linear Equations.- 5.7. Connections with Partial Differential Equations.- 5.8. Applications to Economics.- 5.9. Solutions to Selected Problems.- 5.10. Notes.- 6 P. Lévy's Theory of Brownian Local Time.-6.1. Introduction.- 6.2. Alternate Representations of Brownian Local Time.- 6.3. Two Independent Reflected Brownian Motions.- 6.4. Elastic Brownian Motion.- 6.5. An Application: Transition Probabilities of Brownian Motion with Two-Valued Drift.- 6.6. Solutions to Selected Problems.- 6.7. Notes.Trade ReviewSecond Edition I. Karatzas and S.E. Shreve Brownian Motion and Stochastic Calculus "A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."—MATHEMATICAL REVIEWSTable of Contents1 Martingales, Stopping Times, and Filtrations.- 1.1. Stochastic Processes and ?-Fields.- 1.2. Stopping Times.- 1.3. Continuous-Time Martingales.- A. Fundamental inequalities.- B. Convergence results.- C. The optional sampling theorem.- 1.4. The Doob—Meyer Decomposition.- 1.5. Continuous, Square-Integrable Martingales.- 1.6. Solutions to Selected Problems.- 1.7. Notes.- 2 Brownian Motion.- 2.1. Introduction.- 2.2. First Construction of Brownian Motion.- A. The consistency theorem.- B. The Kolmogorov—?entsov theorem.- 2.3. Second Construction of Brownian Motion.- 2.4. The SpaceC[0, ?), Weak Convergence, and Wiener Measure.- A. Weak convergence.- B. Tightness.- C. Convergence of finite-dimensional distributions.- D. The invariance principle and the Wiener measure.- 2.5. The Markov Property.- A. Brownian motion in several dimensions.- B. Markov processes and Markov families.- C. Equivalent formulations of the Markov property.- 2.6. The Strong Markov Property and the Reflection Principle.- A. The reflection principle.- B. Strong Markov processes and families.- C. The strong Markov property for Brownian motion.- 2.7. Brownian Filtrations.- A. Right-continuity of the augmented filtration for a strong Markov process.- B. A “universal” filtration.- C. The Blumenthal zero-one law.- 2.8. Computations Based on Passage Times.- A. Brownian motion and its running maximum.- B. Brownian motion on a half-line.- C. Brownian motion on a finite interval.- D. Distributions involving last exit times.- 2.9. The Brownian Sample Paths.- A. Elementary properties.- B. The zero set and the quadratic variation.- C. Local maxima and points of increase.- D. Nowhere differentiability.- E. Law of the iterated logarithm.- F. Modulus of continuity.- 2.10. Solutions to Selected Problems.- 2.11. Notes.- 3 Stochastic Integration.- 3.1. Introduction.- 3.2. Construction of the Stochastic Integral.- A. Simple processes and approximations.- B. Construction and elementary properties of the integral.- C. A characterization of the integral.- D. Integration with respect to continuous, local martingales.- 3.3. The Change-of-Variable Formula.- A. The Itô rule.- B. Martingale characterization of Brownian motion.- C. Bessel processes, questions of recurrence.- D. Martingale moment inequalities.- E. Supplementary exercises.- 3.4. Representations of Continuous Martingales in Terms of Brownian Motion.- A. Continuous local martingales as stochastic integrals with respect to Brownian motion.- B. Continuous local martingales as time-changed Brownian motions.- C. A theorem of F. B. Knight.- D. Brownian martingales as stochastic integrals.- E. Brownian functionals as stochastic integrals.- 3.5. The Girsanov Theorem.- A. The basic result.- B. Proof and ramifications.- C. Brownian motion with drift.- D. The Novikov condition.- 3.6. Local Time and a Generalized Itô Rule for Brownian Motion.- A. Definition of local time and the Tanaka formula.- B. The Trotter existence theorem.- C. Reflected Brownian motion and the Skorohod equation.- D. A generalized Itô rule for convex functions.- E. The Engelbert—Schmidt zero-one law.- 3.7. Local Time for Continuous Semimartingales.- 3.8. Solutions to Selected Problems.- 3.9. Notes.- 4 Brownian Motion and Partial Differential Equations.- 4.1. Introduction.- 4.2. Harmonic Functions and the Dirichlet Problem.- A. The mean-value property.- B. The Dirichlet problem.- C. Conditions for regularity.- D. Integral formulas of Poisson.- E. Supplementary exercises.- 4.3. The One-Dimensional Heat Equation.- A. The Tychonoff uniqueness theorem.- B. Nonnegative solutions of the heat equation.- C. Boundary crossing probabilities for Brownian motion.- D. Mixed initial/boundary value problems.- 4.4. The Formulas of Feynman and Kac.- A. The multidimensional formula.- B. The one-dimensional formula.- 4.5. Solutions to selected problems.- 4.6. Notes.- 5 Stochastic Differential Equations.- 5.1. Introduction.- 5.2. Strong Solutions.- A. Definitions.- B. The Itô theory.- C. Comparison results and other refinements.- D. Approximations of stochastic differential equations.- E. Supplementary exercises.- 5.3. Weak Solutions.- A. Two notions of uniqueness.- B. Weak solutions by means of the Girsanov theorem.- C. A digression on regular conditional probabilities.- D. Results of Yamada and Watanabe on weak and strong solutions.- 5.4. The Martingale Problem of Stroock and Varadhan.- A. Some fundamental martingales.- B. Weak solutions and martingale problems.- C. Well-posedness and the strong Markov property.- D. Questions of existence.- E. Questions of uniqueness.- F. Supplementary exercises.- 5.5. A Study of the One-Dimensional Case.- A. The method of time change.- B. The method of removal of drift.- C. Feller’s test for explosions.- D. Supplementary exercises.- 5.6. Linear Equations.- A. Gauss—Markov processes.- B. Brownian bridge.- C. The general, one-dimensional, linear equation.- D. Supplementary exercises.- 5.7. Connections with Partial Differential Equations.- A. The Dirichlet problem.- B. The Cauchy problem and a Feynman—Kac representation.- C. Supplementary exercises.- 5.8. Applications to Economics.- A. Portfolio and consumption processes.- B. Option pricing.- C. Optimal consumption and investment (general theory).- D. Optimal consumption and investment (constant coefficients).- 5.9. Solutions to Selected Problems.- 5.10. Notes.- 6 P. Lévy’s Theory of Brownian Local Time.- 6.1. Introduction.- 6.2. Alternate Representations of Brownian Local Time.- A. The process of passage times.- B. Poisson random measures.- C. Subordinators.- D. The process of passage times revisited.- E. The excursion and downcrossing representations of local time.- 6.3. Two Independent Reflected Brownian Motions.- A. The positive and negative parts of a Brownian motion.- B. The first formula of D. Williams.- C. The joint density of (W(t), L(t), ? +(t)).- 6.4. Elastic Brownian Motion.- A. The Feynman—Kac formulas for elastic Brownian motion.- B. The Ray—Knight description of local time.- C. The second formula of D. Williams.- 6.5. An Application: Transition Probabilities of Brownian Motion with Two-Valued Drift.- 6.6. Solutions to Selected Problems.- 6.7. Notes.
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Springer New York A Mathematical Introduction to Fluid Mechanics
Book SynopsisThe text illustrates the physical background and motivation for some constructions used in recent mathematical and numerical work on the Navier- Stokes equations and on hyperbolic systems, so as to interest students in this at once beautiful and difficult subject.Trade Review From the reviews: "… The book contains some of the basic ideas of fluid mechanics in a mathematically attractive manner...has the very advantage of providing the solution of the differential equations using the new and modern techniques...the material is very well presented both the mathematical arguments as well as the physical input." PhysicaliaTable of ContentsPreface.- 1. The Equations of Motion: 1.1. Euler's Equations. 1.2. Rotation and Vorticity. 1.3. The Navier-Stokes Equations.- 2. Potential Flow and Slightly Viscous Flow: 2.1. Potential Flow. 2.2. Boundary Layers. 2.3. Vortex Sheets. 2.4. Remarks on Stability and Bifurcation.- 3. Gas Flow in One Dimension: 3.1. Characteristics. 3.2. Shocks. 3.3. The Riemann Problem. 3.4. Combustion Waves.
£75.99
Springer Microcontinuum Field Theories I Foundations and Solids
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Springer Introduction to Classical Mechanics
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Springer Engineering Thermodynamics
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Springer Introduction to Thermodynamics
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Springer Heat Transfer in Fluidized Beds 11 Particle Technology Series
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Springer Rheological Measurement
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Springer Deformationenhanced Fluid Transport in the Earths Crust and Mantle Mineralogical Society 8 The Mineralogical Society Series
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Springer Handbook of Compressed Gases
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Springer Cavity Expansion Methods in Geomechanics
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Springer Mechanical Properties and Testing of Polymers An AZ Reference 3 Polymer Science and Technology Series
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Springer Rheology of Filled Polymer Systems Rheological Principles
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Springer Modern Prestressed Concrete
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Wiley Friction and Wear of Materials
Book SynopsisFriction and Wear of Materials Second Edition Written by one of the world''s foremost authorities on friction, this classic book offers a lucid presentation of the theory of mechanical surface interactions as it applies to friction, wear, adhesion, and boundary lubrication. To aid engineers in design decisions, Friction and Wear of Materials evaluates the properties of materials which, under specified conditions, cause one material to function better as a bearing material than another. Featured also are thorough treatments of lubricants and the sizes and shapes of wear particles. This updated Second Edition includes new material on erosive wear, impact wear, and friction. Professor Rabinowicz''s book will be especially welcomed by mechanical and design engineers, surface scientists, tribologists and others who design, produce and operate products, machines and equipment which involve friction and its effects.Table of ContentsMaterial Properties That Influence Surface Interactions. Surface Interactions. Friction. Types of Wear. Adhesive Wear. Abrasive and Other Types of Wear. Lubrication. Adhesion. Appendix. Sample Problems. Index.
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iUniverse Forces of Nature The Principles of Rotation
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Springer Instrumentation for Combustion and Flow in Engines Proceedings 154 Nato Science Series E
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Springer Homogenisation Averaging Processes in Periodic Media Mathematical Problems in the Mechanics of Composite Materials 36 Mathematics and its Applications
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Springer Advances in Fatigue Science and Technology International Proceedings 159 Nato Science Series E
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Springer Recent Advances in Hydraulic Physical Modelling Conference Proceedings 165 Nato Science Series E
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Springer The Practical Use of Fracture Mechanics
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Springer Variational Principles in Topology Multidimensional Minimal Surface Theory 42 Mathematics and its Applications
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Springer Proceedings of the Second Workshop on RoadVehicleSystems and Related Mathematics 4 European Consortium for Mathematics in Industry
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Springer Plasticity and failure behavior of solids Memorial volume dedicated to the late Professor Yuriy Nickolaevich Rabotnov 3 Fatigue and Fracture
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Springer The Behaviour of Nonlinear Vibrating Systems Volume I Fundamental Concepts and Methods Applications to Single DegreeofFreedom Systems Volume II Systems 1213 Mechanics Dynamical Systems
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Springer The Behaviour of Nonlinear Vibrating Systems Volume II Advanced Concepts and Applications to MultiDegreeofFreedom Systems 1213 Mechanics Dynamical Systems
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Springer Oscillations and Waves in Linear and Nonlinear Systems 50 Mathematics and its Applications
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Springer Asymptotic Distribution of Eigenvalues of Differential Operators 53 Mathematics and its Applications
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Springer The Numerical Modelling of Nonlinear Stellar Pulsations Problems and Prospects 302 Nato Science Series C
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Springer Turbulence and Coherent Structures 2 Fluid Mechanics and Its Applications
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Springer Integration of Theory and Applications in Applied Mechanics Choice of papers presented at the First National Mechanics Congress April 24 1990 Netherlands Chemistry and Biochemistry 23
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Springer Problems of Nonlinear Deformation The Continuation Method Applied to Nonlinear Problems in Solid Mechanics
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Springer Basic Elements of Differential Geometry and Topology 60 Mathematics and its Applications
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Springer Turbulence Control by Passive Means Proceedings of the 4th European Drag Reduction Meeting Fluid Mechanics and Its Applications
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Springer Nematics Mathematical and Physical Aspects 332 Nato Science Series C
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Springer Finite Element Analysis of Composite Laminates 7 Solid Mechanics and Its Applications
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Springer Advances in Rockfill Structures 200 Nato Science Series E
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Springer Finite Element Methods in Dynamics
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Springer Dynamic Structure of Detonation in Gaseous and Dispersed Media 5 Fluid Mechanics and Its Applications
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Springer Computational Fluid Dynamics for the Petrochemical Process Industry
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Springer Current Trends in Concrete Fracture Research
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Springer Modelling and Applications of Transport Phenomena in Porous Media 5 Theory and Applications of Transport in Porous Media
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Springer Spontaneous Formation of SpaceTime Structures and Criticality 349 Nato Science Series C
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Springer Elements of Structural Optimization 11 Solid Mechanics and Its Applications
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Springer Elements of Structural Optimization 11 Solid Mechanics and Its Applications
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Springer Energy Dissipators and Hydraulic Jump 8 Water Science and Technology Library
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Springer Averaging in Stability Theory A Study of Resonance MultiFrequency Systems 79 Mathematics and its Applications
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