Differential Equations, Maps, and Chaotic Behaviour
Author: D. Arrowsmith,C.M. Place
Publisher: CRC Press
This text discusses the qualitative properties of dynamical systems including both differential equations and maps. The approach taken relies heavily on examples (supported by extensive exercises, hints to solutions and diagrams) to develop the material, including a treatment of chaotic behavior. The unprecedented popular interest shown in recent years in the chaotic behavior of discrete dynamic systems including such topics as chaos and fractals has had its impact on the undergraduate and graduate curriculum. However there has, until now, been no text which sets out this developing area of mathematics within the context of standard teaching of ordinary differential equations. Applications in physics, engineering, and geology are considered and introductions to fractal imaging and cellular automata are given.
Modern Techniques and Applications
Author: Edward E. Qian,Ronald H. Hua,Eric H. Sorensen
Publisher: CRC Press
Quantitative equity portfolio management combines theories and advanced techniques from several disciplines, including financial economics, accounting, mathematics, and operational research. While many texts are devoted to these disciplines, few deal with quantitative equity investing in a systematic and mathematical framework that is suitable for quantitative investment students. Providing a solid foundation in the subject, Quantitative Equity Portfolio Management: Modern Techniques and Applications presents a self-contained overview and a detailed mathematical treatment of various topics. From the theoretical basis of behavior finance to recently developed techniques, the authors review quantitative investment strategies and factors that are commonly used in practice, including value, momentum, and quality, accompanied by their academic origins. They present advanced techniques and applications in return forecasting models, risk management, portfolio construction, and portfolio implementation that include examples such as optimal multi-factor models, contextual and nonlinear models, factor timing techniques, portfolio turnover control, Monte Carlo valuation of firm values, and optimal trading. In many cases, the text frames related problems in mathematical terms and illustrates the mathematical concepts and solutions with numerical and empirical examples. Ideal for students in computational and quantitative finance programs, Quantitative Equity Portfolio Management serves as a guide to combat many common modeling issues and provides a rich understanding of portfolio management using mathematical analysis.
Author: Drumi D. Bainov,Snezhana G. Hristova
Publisher: CRC Press
Differential equations with "maxima"—differential equations that contain the maximum of the unknown function over a previous interval—adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval. More and more, these equations model and regulate the behavior of various technical systems on which our ever-advancing, high-tech world depends. Understanding and manipulating the theoretical results and investigations of differential equations with maxima opens the door to enormous possibilities for applications to real-world processes and phenomena. Presenting the qualitative theory and approximate methods, Differential Equations with Maxima begins with an introduction to the mathematical apparatus of integral inequalities involving maxima of unknown functions. The authors solve various types of linear and nonlinear integral inequalities, study both cases of single and double integral inequalities, and illustrate several direct applications of solved inequalities. They also present general properties of solutions as well as existence results for initial value and boundary value problems. Later chapters offer stability results with definitions of different types of stability with sufficient conditions and include investigations based on appropriate modifications of the Razumikhin technique by applying Lyapunov functions. The text covers the main concepts of oscillation theory and methods applied to initial and boundary value problems, combining the method of lower and upper solutions with appropriate monotone methods and introducing algorithms for constructing sequences of successive approximations. The book concludes with a systematic development of the averaging method for differential equations with maxima as applied to first-order and neutral equations. It also explores different schemes for averaging, partial averaging, partially additive averaging, and partially multiplicative averaging. A solid overview of the field, this book guides theoretical and applied researchers in mathematics toward further investigations and applications of these equations for a more accurate study of real-world problems.
Author: T.S.L Radhika,T. K.V. Iyengar,T. Raja Rani
Publisher: CRC Press
Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods. The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete description of the methods without going deep into rigorous mathematical aspects. Detailed examples illustrate the application of the methods to solve real-world problems. The authors introduce the classical power series method for solving differential equations before moving on to asymptotic methods. They next show how perturbation methods are used to understand physical phenomena whose mathematical formulation involves a perturbation parameter and explain how the multiple-scale technique solves problems whose solution cannot be completely described on a single timescale. They then describe the Wentzel, Kramers, and Brillown (WKB) method that helps solve both problems that oscillate rapidly and problems that have a sudden change in the behavior of the solution function at a point in the interval. The book concludes with recent nonperturbation methods that provide solutions to a much wider class of problems and recent analytical methods based on the concept of homotopy of topology.
An Application-Oriented Exposition Using Differential Operators of Caputo Type
Author: Kai Diethelm
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Author: Valentin F. Zaitsev,Andrei D. Polyanin
Publisher: CRC Press
Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handbook now contains the exact solutions to more than 6200 ordinary differential equations. The authors have made significant enhancements to this edition, including: An introductory chapter that describes exact, asymptotic, and approximate analytical methods for solving ordinary differential equations The addition of solutions to more than 1200 nonlinear equations An improved format that allows for an expanded table of contents that makes locating equations of interest more quickly and easily Expansion of the supplement on special functions This handbook's focus on equations encountered in applications and on equations that appear simple but prove particularly difficult to integrate make it an indispensable addition to the arsenals of mathematicians, scientists, and engineers alike.
Author: Sergio Blanes,Fernando Casas
Publisher: CRC Press
Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.
Author: D.S. Jones,Michael Plank,B.D. Sleeman
Publisher: CRC Press
Deepen students’ understanding of biological phenomena Suitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeling and analytical techniques used to understand biological phenomena. In this edition, many of the chapters have been expanded to include new and topical material. New to the Second Edition A section on spiral waves Recent developments in tumor biology More on the numerical solution of differential equations and numerical bifurcation analysis MATLAB® files available for download online Many additional examples and exercises This textbook shows how first-order ordinary differential equations (ODEs) are used to model the growth of a population, the administration of drugs, and the mechanism by which living cells divide. The authors present linear ODEs with constant coefficients, extend the theory to systems of equations, model biological phenomena, and offer solutions to first-order autonomous systems of nonlinear differential equations using the Poincaré phase plane. They also analyze the heartbeat, nerve impulse transmission, chemical reactions, and predator–prey problems. After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behavior. It concludes with problems of tumor growth and the spread of infectious diseases.
Author: George F. Simmons
Publisher: CRC Press
Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one’s own time. An unfortunate effect of the predominance of fads is that if a student doesn’t learn about such worthwhile topics as the wave equation, Gauss’s hypergeometric function, the gamma function, and the basic problems of the calculus of variations—among others—as an undergraduate, then he/she is unlikely to do so later. The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author—a highly respected educator—advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter. With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss’s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity—i.e., identifying why and how mathematics is used—the text includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout. Provides an ideal text for a one- or two-semester introductory course on differential equations Emphasizes modeling and applications Presents a substantial new section on Gauss’s bell curve Improves coverage of Fourier analysis, numerical methods, and linear algebra Relates the development of mathematics to human activity—i.e., identifying why and how mathematics is used Includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout Uses explicit explanation to ensure students fully comprehend the subject matter Outstanding Academic Title of the Year, Choice magazine, American Library Association.
Author: Andrei D. Polyanin,Valentin F. Zaitsev
Publisher: CRC Press
New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM, Mathematica®, and MATLAB® Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.
A Structure-Preserving Numerical Method for Partial Differential Equations
Author: Daisuke Furihata,Takayasu Matsuo
Publisher: CRC Press
Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of "structure-preserving numerical equations" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineers and physicists with a basic knowledge of numerical analysis. Topics discussed include: "Conservative" equations such as the Korteweg–de Vries equation (shallow water waves) and the nonlinear Schrödinger equation (optical waves) "Dissipative" equations such as the Cahn–Hilliard equation (some phase separation phenomena) and the Newell-Whitehead equation (two-dimensional Bénard convection flow) Design of spatially and temporally high-order schemas Design of linearly-implicit schemas Solving systems of nonlinear equations using numerical Newton method libraries
introduction and qualitative theory
Author: Jane Cronin
Publisher: Marcel Dekker Inc
Existence theorems; Linear systems; Autonomous systems; Stability; The lyapunov second method; Periodic solutions; Bifurcation and branching of periodic solutions.
Author: John Strikwerda
A unified and accessible introduction to the basic theory of finite difference schemes.
Introduction and Qualitative Theory, Third Edition
Author: Jane Cronin
Publisher: CRC Press
Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of nonlinear equations. Requiring only a background in advanced calculus and linear algebra, the text is appropriate for advanced undergraduate and graduate students in mathematics, engineering, physics, chemistry, or biology. This third edition of a highly acclaimed textbook provides a detailed account of the Bendixson theory of solutions of two-dimensional nonlinear autonomous equations, which is a classical subject that has become more prominent in recent biological applications. By using the Poincaré method, it gives a unified treatment of the periodic solutions of perturbed equations. This includes the existence and stability of periodic solutions of perturbed nonautonomous and autonomous equations (bifurcation theory). The text shows how topological degree can be applied to extend the results. It also explains that using the averaging method to seek such periodic solutions is a special case of the use of the Poincaré method.
Theory and Numerical Solution
Author: J. Necas
As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs). This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control. The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.
Author: Fred Brauer,Dawn Bies
Publisher: Springer Science & Business Media
The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.
Author: Zhe-wei Zhou
Publisher: DEStech Publications, Inc
Novel mathematical and modeling approaches to problems in graded materials, biological materials, fluid mechanics and more Covers nanomechanics, multi-scale modeling, interface mechanics and microstructure This series volume contains 128 not previously published research presentations on using nonlinear mechanics to understand and model a wide variety of materials, including polymers, metals and composites, as well as subcellular and cellular tissues. Focus is on numerical and physics approaches to representing multiscale relationships within complex solids and fluids systems, with applications in materials science, energy storage, medical diagnostics and treatment, and biotechnology. TABLE OF CONTENTS Preface Committees SESSION 1: INVITED LECTURES Micro-Macro Analysis of Creep and Damage Behavior of Multi-Pass Welds Some New Developments in Non-Linear Solid Mechanics Design of Material Systems: Mathematics and Physics of the Archetype-Genome Exemplar Criticism of Generally Accepted Fundamentals and Methodologies of Traffic and Transportation Theory SESSION 2: NONLINEAR CONTINUUM MECHANICS Geometrically Nonlinear Analysis of Simple Plane Frames of Functionally Graded Materials Thermal Post-Buckling of FG Circular Plates Under Transversely Point-Space Constraint Tunability of Longitudinal Wave Band Gap in One Dimensional Magneto-Elastic Phononic Crystal Teaching Nonlinear Mechanics at the Undergraduate and Graduate Level—Two Examples Geometrically Nonlinear FE Instability Simulations of Hinged Composite Laminated Cylindrical Shells Constitutive Relation of Martensitic Transformation in CuAlNi Based on Atomistic Simulations Soft Behaviors of Beam Shaped Liquid Crystal Elastomers Under Light Actuations XFEM Based Discontinuity Simulation for Saturated Soil Numerical Algorithm of Solving the Problem of Large Elastic-Plastic Deformation by FEM Finite Deformation for Everted Compressible Hypereleastic Cylindrical Tubes Modelling and Non-Linear Free Vibrations of Cable-Stayed Beam Wavelet Solution of a Class of Nonlinear Boundary Value Problems Axial Compression of a Rectangular Rubber Ring Composed of an Incompressible Mooney-Rivlin Material Influence of Concentration-Dependent Elastic Modulus and Charge or Discharge Rate on Tensile Stress in Anode An Integral Equation Approach to the Fully Nonlinear Fluid Flow Problem in an Infinite Channel Over Arbitrary Bottom Topography Analysis of Nonlinear Dynamical Characteristics for Thermoelastic Half-Plane with Voids Tensor Model for Dynamic Damage of Ductile Metals Over a Wide Range of Strain Rates SESSION 3: MULTI-SCALE MECHANICS AND MULTI-PHYSICS MODELING The Nonlinear Magnetoelectric Effect of Layered Magnetoelectric Composite Cylinder with an Imperfect Interface A Solution for Nonlinear Poisson-Neumann Problem of Nb3Sn Superconducting Transport Current Temperature Effect on the Tensile Mechanical Properties of Graphene Nanoribbons Square Inclusion with a Nonlinear Eigenstrain in an Anisotropic Piezoelectric Full Plane Nonlinear Analysis of the Threaded Connection with Three-Dimensional Finite Element Model Effects of Particle Volume Fraction on the Macro-Thermo-Mechanical Behaviors in Plate-Type Dispersion Nuclear Fuel Elements Mechanics of Semiflexible Polymer Chains Under Confinements Study on the Solution of Reynolds Equation for Micro Gas Bearings Using the Alternating-Direction Implication Algorithm Atomistic Study of Li Concentration Dependence of the Mechanical Properties of Graphite Anode in Li-ion Battery 3D Extrusion Simulation of the Single Screw Head and Optimization Design Buckling Behavior of Defective Carbon Nanotubes Elastic Properties of Single-Stranded DNA Biofilm with Strong Interactions Analysis on Thickness Dependence of Jc Caused by Dislocations and Grain Boundaries in YBCO Superconducting Films Operating Strain Response in CICC Coils Through Nonlinear Finite Element Modeling Dynamics Analysis of a Multi-Degree-of-Freedom Electro-Hydraulic Mix-Drive Motion Simulator by KANE Equation Multiscale 3D Fracture Simulation Integrating Tomographic Characterization Research into Compressive Mechanical Properties of Special Piezomagnetic Material Sheets A Numerical Study on Detonation Wave Propagation Using High-Precision and High-Resolution Schemes SESSION 4: STRUCTURAL DYNAMIC AND STRUCTURE-FLUID INTERACTIONS A Study on Pure IL VIV of a Marine Riser in Shear Current Parametric Studies on Nonlinear Flutter of High-Aspect-Ratio Flexible Wings Model Reduction of a Flexible Beam Rotating at High Speed Considering Dynamic Stiffening Vibration Modal Analysis of Cantilever Beams with Complicated Elasticity Boundary Constraint Numerical Simulation of Ahmed Model in Consideration of the FSI Effect Aerodynamic Damping of a Hammerhead Launch Vehicle in Transonic Flow Symmetry Reductions and Explicit Solutions of (3 + 1)-Dimensional Kadomtsev-Petviashvili (KP) Equation Nonlinear Behaviors of an Isotropic Incompressible Hyperelastic Spherical Membrane Under Different Dynamic Loads Creep Buckling of Viscoelastic Plate Consdering Higher Order Modes SESSION 5: COMPLEX FLUID FLOW AND NONLINEAR STABILITY Homotopy Analysis of Korteweg-de Vries Equation with Time Delay Homotopy Analysis Method for Bubble Pulsation Equation with Nonlinear Term of Fractional Power Chebyshev Finite Spectral Method for Boussinesq-Type Equations on Staggered Grids Twin Jets in Crossflow Application of Fixed Point Method to Obtain a Semi-Analytical Solution of Stagnation Flow On the Nonlinear Stability of Laminar Flow Between Parallel Planes Boundary Treatments in Lattice Boltzmann Method A Lattice Boltzmann Based Immersed Boundary Method for Fluid-Structure Interaction Numerical Solutions of Convection-Diffusion Equations by Hybrid Discontinuous Galerkin Methods Steady-State Solutions of the Wave-Bottom Resonant Interaction Lattice Boltzmann Simulation of the Shock Damping and the Shock Increased by Means of Lorentz Force Analysis of the Effects of Nonlinear Characteristics of Lag Dampers on Helicopter Ground Resonance Flow Structures and Sound Radiation in Supersonic Mixing Layers with Nonlinear PSE Method Turbulent Structures in Subsonic Jet Flow Forced by Random Disturbances Exponential p-Stability for a Delayed Recurrent Neural Networks with Impulses Spatial Variation of Scaling Exponents for Structure Functions in a Decaying Turbulence SESSION 6: NONLINEAR DYNAMIC OF STRUCTURE Analysis of Chaos Behavior of Single Mode Vibration of Cable-Stayed Chaotification of Fractional Maps Nonlinear Finite Element Analysis of the Dynamic Axial Crushing of Empty Hexagonal Tube Active Control of a Nonlinear Aeroelastic System Using the Receptance Method Dynamics Analysis of the FHN Neuronal Model Analyzing the Effect of the Axial Force to the Natural Frequencies of Arch Stable Periodic Response of One-Way Clutches in a Two-Pulley Belt-Drive Model Supercritical Nonlinear Dynamics of an Axially Moving Viscoelastic Beam with Speed Fluctuation Nonlinear Dynamic Response to a Moving Force of Timoshenko Beams Resting on Pasternak Foundations An Improved Method for the Construction of Nonlinear Operator in Homotopy Analysis Method A Nonlinear Integration Scheme for Evolutionary Differential Equations A Comparative Study of Civil Aircraft Crashworthiness with Different Ground Conditions Improved Dynamic Analysis of Development of Pulmonary Edema The Timescale Function Method for Solving Free Vibration of Nonlinear Oscillator Nonlinear Aeroelastic Analysis of Flexible Wings with High-Aspect-Ratio Considering Large Deflection Differential Quadrature Method for Vibration Analysis of Finite Beams on Nonlinear Viscoelastic Foundations Numerical Simulation on the Strength and Sealing Performance for High-Pressure Isolating Flange Nonlinear Dynamical Stability of the Lattices with Initial Material and Geometric Imperfection Nonlinear Vibration of Symmetric Angle-Ply Laminated Piezoelectric Plates with Linearly Varying Thickness An Exact Free Vibration Frequency Formula for Oscillator with Single-Term Positive-Power Restoring Force An Exact Solution of Synchronization State for a Class of Networked Mass-Spring-Damper Oscillator Systems SESSION 7: INTERFACE MECHANICS AND ENGINEERING APPLICATION Numerical Simulation of Free Surface Collapse in Propellant Tank Restudy on the Adaptive Mesh Technique for Seepage Problems High-Order Series Solutions of Wave and Current Interactions Deformation and Stress Distribution of Arterial Walls of the Aged A p53-Mdm2 Dynamical Model Induced by Laminar Shear Stress in Endothelial Cells Optimized Image Processing Based on CUDA in a Combined Measurement Technique of PIV and Shadowgraph 3D Visualization of the Flow Fields Using Digital In-Line Holography Analysis and Experimental Study on Air Foam Flooding Seepage Flow Mechanics Experimental Measurements for Mechanical and Electrical Conductive Properties of CNT Bundles Analysis on Dynamic Response of Bedding Rock Slope with Bolts under Earthquakes Numerical Prediction of Aerodynamic Noise Radiated from High Speed Train Pantograph Effects of Length on Aerodynamics of High Speed Train Models Free Convection Nanofluid Flow in the Stagnation-Point Region of a Three Dimensional Body Vertical Distribution and Dynamic Release Characteristics of Pollutants from Resuspended Sediment Numerical Simulation of the Contaminant Release Through the Sediment-Overlying Water Interface Analysis on the Aerodynamic and Aero-Noise of MIRA Model Radial Squeeze Force of MR Fluid Between Two Cylinders Nonlinear Buckling Analysis and Ultimate Extended Capacity Research of Downhole Pipe Strings in Ultra-Deep Horizontal Wells A Novel Method of Generating Nonlinear Internal Wave in a Stratified Fluid Tank and Its Theoretical Model SESSION 8: MINI-SYMPOSIUM ON TRAFFIC FLUID Study on Correlation Analysis of Synchronized Flow in the Kerner-Klenov-Wolf Cellular Automation Model Numerical Simulation of Traffic Flow in the Rain or Snow Weather Condition First Order Phase Transitions in the Brake Light Cellular Automation Model Within the Fundamental Diagram Approach The Leader-Follower Winding Behavior of Pedestrians in a Queue Effect of Overpasses in Two-Dimensional Traffic Flow Model with Random Update Rule Analysis of the Density Wave in a New Continuum Model The Phenomenon of High-Speed-Car-Following on Chinese Highways A Lattice Hydrodynamic Model Considering the Difference of Density and its Analysis Experimental Feature of Car-Following Behaviors in a Platoon of 25 Vehicles Car-Following Model for Manual Transmission Vehicles The Mechanism of Synchronized Flow in Traffic Flow Modeling An Asymmetric Stochastic Car-Following Model Based on Extended Tau Theory A Gaussian Distribution Based Dual-Cognition Driver Behavior Model at Cross Traffic A New Traffic Kinetic Model Considering Potential Influence The Effect of Marks on the Pedestrian Evacuation Equilibrium Velocity Distribution Function for Traffic Flow Effects of Antilock Braking System on Driving Behavior Under Emergent Stability Analysis of Pedestrian Flow in Two-Dimensional Optimal Velocity Model with Asymmetric Interaction Simulation-Based Stability Analysis of Car-Following Models Under Heterogeneous Traffic Crossing Speed of Pedestrian at an Unsignalized Intersection Modeling Mixed Traffic Flow at a Crosswalk with Push Button Effects of Game Strategy Update on Pedestrian Evacuation in a Hall Study on Long-Term Correlation of CO and CO2 from Vehicle Emissions on Roadsides with the Detrended Fluctuation Analysis Method Bottleneck Effect on a Bidirectional Two-Lane Mixed Traffic Flow
Author: Hans Petter Langtangen
The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science. From the reviews: Langtangen ... does an excellent job of introducing programming as a set of skills in problem solving. He guides the reader into thinking properly about producing program logic and data structures for modeling real-world problems using objects and functions and embracing the object-oriented paradigm. ... Summing Up: Highly recommended. F. H. Wild III, Choice, Vol. 47 (8), April 2010 Those of us who have learned scientific programming in Python ‘on the streets’ could be a little jealous of students who have the opportunity to take a course out of Langtangen’s Primer.” John D. Cook, The Mathematical Association of America, September 2011 This book goes through Python in particular, and programming in general, via tasks that scientists will likely perform. It contains valuable information for students new to scientific computing and would be the perfect bridge between an introduction to programming and an advanced course on numerical methods or computational science. Alex Small, IEEE, CiSE Vol. 14 (2), March /April 2012 “This fourth edition is a wonderful, inclusive textbook that covers pretty much everything one needs to know to go from zero to fairly sophisticated scientific programming in Python...” Joan Horvath, Computing Reviews, March 2015
Essays in Honour of Eckhard Platen
Author: Carl Chiarella,Alexander Novikov
Publisher: Springer Science & Business Media
This volume contains a collection of papers dedicated to Professor Eckhard Platen to celebrate his 60th birthday, which occurred in 2009. The contributions have been written by a number of his colleagues and co-authors. All papers have been - viewed and presented as keynote talks at the international conference “Quantitative Methods in Finance” (QMF) in Sydney in December 2009. The QMF Conference Series was initiated by Eckhard Platen in 1993 when he was at the Australian - tional University (ANU) in Canberra. Since joining UTS in 1997 the conference came to be organised on a much larger scale and has grown to become a signi?cant international event in quantitative ?nance. Professor Platen has held the Chair of Quantitative Finance at the University of Technology, Sydney (UTS) jointly in the Faculties of Business and Science since 1997. Prior to this appointment, he was the Founding Head of the Centre for Fin- cial Mathematics at the Institute of Advanced Studies at ANU, a position to which he was appointed in 1994. Eckhard completed a PhD in Mathematics at the Technical University in Dresden in 1975 and in 1985 obtained his Doctor of Science degree (Habilitation degree in the German system) from the Academy of Sciences in Berlin where he headed the Stochastics group at the Weierstrass Institute.