Download and read online Numerical Methods with MATLAB in PDF and EPUB This thorough, modern exposition of classic numerical methods using MATLAB briefly develops the fundamental theory of each method. Rather than providing a detailed numerical analysis, the behavior of the methods is exposed by carefully designed numerical experiments. The methods are then exercised on several nontrivial example problems from engineering practice. This structured, concise, and efficient book contains a large number of examples of two basic types—One type of example demonstrates a principle or numerical method in the simplest possible terms. Another type of example demonstrates how a particular method can be used to solve a more complex practical problem. The material in each chapter is organized as a progression from the simple to the complex. Contains an extensive reference to using MATLAB. This includes interactive (command line) use of MATLAB, MATLAB programming, plotting, file input and output. For a practical and rigorous introduction to the fundamentals of numerical computation.
Download and read online Numerical Methods with MATLAB in PDF and EPUB
Download and read online Numerical Methods for Chemical Engineering in PDF and EPUB Applications of numerical mathematics and scientific computing to chemical engineering.
Download and read online Numerical Methods in PDF and EPUB Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online
Download and read online Numerical Methods for Engineers and Scientists Using MATLAB in PDF and EPUB Designed to benefit scientific and engineering applications, Numerical Methods for Engineers and Scientists Using MATLAB® focuses on the fundamentals of numerical methods while making use of MATLAB software. The book introduces MATLAB early on and incorporates it throughout the chapters to perform symbolic, graphical, and numerical tasks. The text covers a variety of methods from curve fitting to solving ordinary and partial differential equations. Provides fully worked-out examples showing all details Confirms results through the execution of the user-defined function or the script file Executes built-in functions for re-confirmation, when available Generates plots regularly to shed light on the soundness and significance of the numerical results Created to be user-friendly and easily understandable, Numerical Methods for Engineers and Scientists Using MATLAB® provides background material and a broad introduction to the essentials of MATLAB, specifically its use with numerical methods. Building on this foundation, it introduces techniques for solving equations and focuses on curve fitting and interpolation techniques. It addresses numerical differentiation and integration methods, presents numerical methods for solving initial-value and boundary-value problems, and discusses the matrix eigenvalue problem, which entails numerical methods to approximate a few or all eigenvalues of a matrix. The book then deals with the numerical solution of partial differential equations, specifically those that frequently arise in engineering and science. The book presents a user-defined function or a MATLAB script file for each method, followed by at least one fully worked-out example. When available, MATLAB built-in functions are executed for confirmation of the results. A large set of exercises of varying levels of difficulty appears at the end of each chapter. The concise approach with strong, up-to-date MATLAB integration provided by this book affords readers a thorough knowledge of the fundamentals of numerical methods utilized in various disciplines.
Download and read online Uncertainty Quantification and Stochastic Modeling with Matlab in PDF and EPUB Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences. Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does not lead to a unified presentation of the methods. Moreover, this description does not consider either deterministic problems or infinite dimensional ones. This book gives a unified, practical and comprehensive presentation of the main techniques used for the characterization of the effect of uncertainty on numerical models and on their exploitation in numerical problems. In particular, applications to linear and nonlinear systems of equations, differential equations, optimization and reliability are presented. Applications of stochastic methods to deal with deterministic numerical problems are also discussed. Matlab® illustrates the implementation of these methods and makes the book suitable as a textbook and for self-study. Discusses the main ideas of Stochastic Modeling and Uncertainty Quantification using Functional Analysis Details listings of Matlab® programs implementing the main methods which complete the methodological presentation by a practical implementation Construct your own implementations from provided worked examples
Download and read online Numerical Methods with Chemical Engineering Applications in PDF and EPUB Designed primarily for undergraduates, but also graduates and practitioners, this textbook integrates numerical methods and programming with applications from chemical engineering. Combining mathematical rigor with an informal writing style, it thoroughly introduces the theory underlying numerical methods, its translation into MATLAB programs, and its use for solving realistic problems. Specific topics covered include accuracy, convergence and numerical stability, as well as stiffness and ill-conditioning. MATLAB codes are developed from scratch, and their implementation is explained in detail, all while assuming limited programming knowledge. All scripts employed are downloadable, and built-in MATLAB functions are discussed and contextualised. Numerous examples and homework problems - from simple questions to extended case studies - accompany the text, allowing students to develop a deep appreciation for the range of real chemical engineering problems that can be solved using numerical methods. This is the ideal resource for a single-semester course on numerical methods, as well as other chemical engineering courses taught over multiple semesters.
Download and read online Numerical Methods for Chemical Engineers with MATLAB Applications in PDF and EPUB Master numerical methods using MATLAB, today's leading software for problem solving. This complete guide to numerical methods in chemical engineering is the first to take full advantage of MATLAB's powerful calculation environment. Every chapter contains several examples using general MATLAB functions that implement the method and can also be applied to many other problems in the same category. The authors begin by introducing the solution of nonlinear equations using several standard approaches, including methods of successive substitution and linear interpolation; the Wegstein method, the Newton-Raphson method; the Eigenvalue method; and synthetic division algorithms. With these fundamentals in hand, they move on to simultaneous linear algebraic equations, covering matrix and vector operations; Cramer's rule; Gauss methods; the Jacobi method; and the characteristic-value problem. Additional coverage includes: Finite difference methods, and interpolation of equally and unequally spaced points Numerical differentiation and integration, including differentiation by backward, forward, and central finite differences; Newton-Cotes formulas; and the Gauss Quadrature Two detailed chapters on ordinary and partial differential equations Linear and nonlinear regression analyses, including least squares, estimated vector of parameters, method of steepest descent, Gauss-Newton method, Marquardt Method, Newton Method, and multiple nonlinear regression The numerical methods covered here represent virtually all of those commonly used by practicing chemical engineers. The focus on MATLAB enables readers to accomplish more, with less complexity, than was possible with traditional FORTRAN. For those unfamiliar with MATLAB, a brief introduction is provided as an Appendix. Over 60+ MATLAB examples, methods, and function scripts are covered, and all of them are included on the book's CD
Download and read online Financial Modelling in PDF and EPUB Financial Modelling - Theory, Implementation and Practice is a unique combination of quantitative techniques, the application to financial problems and programming using Matlab. The book enables the reader to model, design and implement a wide range of financial models for derivatives pricing and asset allocation, providing practitioners with complete financial modelling workflow, from model choice, deriving prices and Greeks using (semi-) analytic and simulation techniques, and calibration even for exotic options. The book is split into three parts. The first part considers financial markets in general and looks at the complex models needed to handle observed structures, reviewing models based on diffusions including stochastic-local volatility models and (pure) jump processes. It shows the possible risk neutral densities, implied volatility surfaces, option pricing and typical paths for a variety of models including SABR, Heston, Bates, Bates-Hull-White, Displaced-Heston, or stochastic volatility versions of Variance Gamma, respectively Normal Inverse Gaussian models and finally, multi-dimensional models. The stochastic-local-volatility Libor market model with time-dependent parameters is considered and as an application how to price and risk-manage CMS spread products is demonstrated. The second part of the book deals with numerical methods which enables the reader to use the models of the first part for pricing and risk management, covering methods based on direct integration and Fourier transforms, and detailing the implementation of the COS, CONV, Carr-Madan method or Fourier-Space-Time Stepping. This is applied to pricing of European, Bermudan and exotic options as well as the calculation of the Greeks. The Monte Carlo simulation technique is outlined and bridge sampling is discussed in a Gaussian setting and for Lévy processes. Computation of Greeks is covered using likelihood ratio methods and adjoint techniques. A chapter on state-of-the-art optimization algorithms rounds up the toolkit for applying advanced mathematical models to financial problems and the last chapter in this section of the book also serves as an introduction to model risk. The third part is devoted to the usage of Matlab, introducing the software package by describing the basic functions applied for financial engineering. The programming is approached from an object-oriented perspective with examples to propose a framework for calibration, hedging and the adjoint method for calculating Greeks in a Libor Market model. Source code used for producing the results and analysing the models is provided on the author’s dedicated website, http://www.mathworks.de/matlabcentral/fileexchange/authors/246981
Download and read online Nodal Discontinuous Galerkin Methods in PDF and EPUB This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.
Download and read online Numerical Analysis and Graphic Visualization with MATLAB in PDF and EPUB PREFACE WHAT THIS BOOK DESCRIBES This book is intended to introduce numerical analysis and graphic visualization using MATLAB to college students majoring in engineering and science.It can also be a handbook of MATLAB applications for professional engi-neers and scientists. The goal is not to teach the mathematics of numericalanalysis, but rather to teach the knowledge and skills of solving equationsand presenting them graphically so that readers can easily handle equationsand results of the computations. With its unique and fascinating capabilities, MATLAB has changed theconcept of programming for numerical and mathematical analyses. Therefore, MATLAB is a superb vehicle to achieve our goal. This book fullyimplements the mathematical and graphic tools in the most recent versionof MATLAB. The following four fundamental elements are integrated in this book: (1)programming in MATLAB, (2) mathematical basics of numerical analysis,(3) application of numerical methods to engineering, scientific, and mathematical problems, and (4) scientific graphics with MATLAB. The first two chapters are comprehensive tutorials of MATLAB commands and graphic tools, particularly for the beginner or entry-level collegestudent. Indeed, these two chapters have been most significantly enhancedin this edition compared to the first edition. In Chapter 1, understandingand developing programming skills on MATLAB are emphasized particularlybecause, unless the reader has knowledge and experience with another pro-gramming language, these are tough hurdles for the beginner to overcome.To acquire the knowledge and skills necessary to read the rest of the book,solving the problems at the end of each chapter is very important. Chapter 2 starts out with the elements of graphics on MATLAB, whichis easy to follow. Yet, toward the end of the chapter, three-dimensionalgraphics on the professional level are achieved. Not only is the programmingtechnique of plotting functions mentioned, but also skills of presenting mathematical and scientific material using graphics are developed throughout thechapter. The graphics knowledge acquired in this chapter are foundationsin learning and applying the numerical methods described in the remainderof the book. Again, practice on the computer is important. Some studentstry to memorize scripts without understanding why and how they work,but such an effort is utterly meaningless. More important is to play with afew new commands, understand how they work and how they may fail, andfinally become a master of the commands. Chapters 3 through 11 cover numerical methods and their implementations with MATLAB. All the numerical methods described are illustratedwith applications on MATLAB. Appendices describe special topics, including advanced three-dimensional graphics with colors, motion pictures, imageprocessing, and graphical user interface. Readers should feel free to use thescripts in this book in any way desired. However, the beginning studentsare advised not to u se these scripts blindly. The students should write theirown scripts. Using the lists of the scripts and function, readers can run most examples and figures on their own computers. The m-files of the scripts can bedownloaded as mentioned later. WHAT IS UNIQUE ABOUT MATLAB? MATLAB may be regarded as a programming language like Fortran or C,although describing it in a few words is difficult. Some of its outstandingfeatures for numerical analyses, however, are: Significantly simpler programming Continuity among integer, real, and complex values Extended range of numbers and their accuracy A comprehensive mathematical library Extensive graphic tools including graphic user interface functions Capability of linking with traditional programming languages Transportability of MATLAB programs An extraordinary feature of MATLAB is that there is no distinction amongreal, complex, and integer numbers. All numbers are in double precision. InMATLAB, all kinds of numbers are continuously connected, as they should be. It means that in MATLAB, any variable can take any type of numberwithout special declaration in programming. This makes programming fasterand more productive. In Fortran, a different subroutine is necessary for eachsingle, double, real or complex, or integer variable, while in MATLAB thereis no need to separate them. The mathematical library in MATLAB makes mathematical analyseseasy. Yet the user can develop additional mathematical routines significantlymore easily than in other programming languages because of the continuitybetween real and complex variables. Among numerous mathematical functions, linear algebra solvers play central roles. Indeed, the whole MATLABsystem is founded upon linear algebra solvers. IMPORTANCE OF GRAPHICS Graphic presentation of mathematical analysis helps the reader to under-stand mathematics and makes it enjoyable. Although this advantage hasbeen well known, presenting computed results with computer graphics wasnot without substantial extra effort in the past. With MATLAB, however,graphic presentations of mathematical material is possible with just a fewcommands. Scientific and even artistic graphic objects can be created on thescreen using mathematical expressions. It has been found that MATLABgraphics motivate and excite students to learn mathematical and numericalmethods that could otherwise be dull. MATLAB graphics are easy and great fun for readers. This book alsoillustrates image processing and production of motion pictures for scientific computing as well as for artistic or hobby material. WILL MATLAB ELIMINATE THE NEED FOR FORTRAN OR C? The answer is no. Fortran and C are still important for high-performancecomputing that requires a large memory or long computing time. The speedof MATLAB computation is significantly slower than that with Fortran orC because MATLAB is paying the high price for the nice features. Learn-ing Fortran or C, however, is not a prerequisite for understanding MATLAB. REFERENCE BOOKS THAT ARE HELPFUL TO LEARN MATLAB This book explains many MATLAB commands but is not intended to be acomplete guide to MATLAB. Readers interested in further information onMATLAB are advised to read User's Guide and Reference Guide. Also, youshould know that over 400 books for use with MATLAB, Simulink, Tool-boxes, and Blocksets have been written. See http://www.mathworks.com/support/books WEB SITE FOR READERS OF THIS BOOK A Web site for readers of this book has been opened at http://olen.eng.ohio-state.ed/matlab This Web site includes additional examples, hints, and color graphics thatcannot be printed in the book. If there are corrections to the text material,they will appear on this Web site. Links to other relevant sites are alsoprovided. HOW TO OBTAIN M-FILES PACKAGE The m-files package that includes all the scripts and functions developed inthe present book are available from the download site of the publisher, whichcan be accessed via the Web site in the foregoing paragraph. The packageincludes the following files: All m-files listed at the end of chapters. All scripts illustrated in the book (except short ones). Scripts to plot typical figures in the book. SOLUTION KEYS Solution keys for the problems for each chapter are available at the end ofthis book. Further help may also be available at the Web site for the readers. HOW TO OBTAIN MORE INFORMATION ABOUT MATLAB The best way to start collecting more information about MATLAB is to visitthe Web site of MATHWORKS athttp://www.mathworks.com For other communication with MathWorks, their address is: The MathWorks, Inc., 3 Apple Hill Drive, Natick ,MA 01760-2098, United StatesPhone: 508-647-7000, Fax: 508-647-7001. LIST OF REVIEWERS The first edition of this book was reviewed by: Professor T. Aldemir, Nuclear Engineering, The Ohio State University, Columbus, Ohio Professor M. Darwish, Mechanical Engineering Department, American University of Beirut, Beirut, Lebanon The MathWorks Inc., Natick, Massacusetts Professor J.K. Shultis, Nuclear Engineering, Kansas State University, Manhattan, Kansas Professor S.V. Sreenivasan, Department of Mechanical Engineering, University of Texas, Austin, Texas
Download and read online Wind Turbine Aerodynamics and Vorticity Based Methods in PDF and EPUB The book introduces the fundamentals of fluid-mechanics, momentum theories, vortex theories and vortex methods necessary for the study of rotors aerodynamics and wind-turbines aerodynamics in particular. Rotor theories are presented in a great level of details at the beginning of the book. These theories include: the blade element theory, the Kutta-Joukowski theory, the momentum theory and the blade element momentum method. A part of the book is dedicated to the description and implementation of vortex methods. The remaining of the book focuses on the study of wind turbine aerodynamics using vortex-theory analyses or vortex-methods. Examples of vortex-theory applications are: optimal rotor design, tip-loss corrections, yaw-models and dynamic inflow models. Historical derivations and recent extensions of the models are presented. The cylindrical vortex model is another example of a simple analytical vortex model presented in this book. This model leads to the development of different BEM models and it is also used to provide the analytical velocity field upstream of a turbine or a wind farm under aligned or yawed conditions. Different applications of numerical vortex methods are presented. Numerical methods are used for instance to investigate the influence of a wind turbine on the incoming turbulence. Sheared inflows and aero-elastic simulations are investigated using vortex methods for the first time. Many analytical flows are derived in details: vortex rings, vortex cylinders, Hill's vortex, vortex blobs etc. They are used throughout the book to devise simple rotor models or to validate the implementation of numerical methods. Several Matlab programs are provided to ease some of the most complex implementations.
Download and read online Meshfree Approximation Methods with Matlab in PDF and EPUB Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.
Download and read online Uncertainty Quantification in PDF and EPUB The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.
Download and read online The Finite Element Method Theory Implementation and Applications in PDF and EPUB This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.