Application of Numerical Methods in Engineering Problems Using MATLAB® presents an analysis of structures using numerical methods and mathematical modeling. This structural analysis also includes beam, plate, and pipe elements, and examines deflection and frequency or buckling loads. The various engineering theories of beams/plates/shells are comprehensively presented, and the relationships between stress and strain, and the governing equations of the structure are extracted. To solve governing equations with numerical methods, there are two general types, including methods based on derivatives or integrals. Derivative-based methods have the advantage of flexibility in modeling boundary conditions, low analysis time, and a very high degree of accuracy. Therefore, the book explains numerical methods based on derivatives, especially the differential quadrature method. Features: Examines the application of numerical methods to obtain the deflection, frequency, and buckling loads. Discusses the application of numerical methods for solving motion equations. Includes numerous practical and applicable examples throughout.

In recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems. Over the years, many textbooks have been written on the subject of numerical methods. Based on their course experience, the authors use a more practical approach and link every method to real engineering and/or science problems. The main benefit is that engineers don't have to know the mathematical theory in order to apply the numerical methods for solving their real-life problems. An Instructor's Manual presenting detailed solutions to all the problems in the book is available online.

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.

The fourth edition of Numerical Methods Using MATLAB® provides a clear and rigorous introduction to a wide range of numerical methods that have practical applications. The authors' approach is to integrate MATLAB® with numerical analysis in a way which adds clarity to the numerical analysis and develops familiarity with MATLAB®. MATLAB® graphics and numerical output are used extensively to clarify complex problems and give a deeper understanding of their nature. The text provides an extensive reference providing numerous useful and important numerical algorithms that are implemented in MATLAB® to help researchers analyze a particular outcome. By using MATLAB® it is possible for the readers to tackle some large and difficult problems and deepen and consolidate their understanding of problem solving using numerical methods. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization and many other fields. The text will be a valuable aid to people working in a wide range of fields, such as engineering, science and economics. - Features many numerical algorithms, their fundamental principles, and applications - Includes new sections introducing Simulink, Kalman Filter, Discrete Transforms and Wavelet Analysis - Contains some new problems and examples - Is user-friendly and is written in a conversational and approachable style - Contains over 60 algorithms implemented as MATLAB® functions, and over 100 MATLAB® scripts applying numerical algorithms to specific examples

An Introduction to Numerical Methods using MATLAB is designed to be used in any introductory level numerical methods course. It provides excellent coverage of numerical methods while simultaneously demonstrating the general applicability of MATLAB to problem solving. This textbook also provides a reliable source of reference material to practicing engineers, scientists, and students in other junior and senior-level courses where MATLAB can be effectively utilized as a software tool in problem solving. The principal goal of this book is to furnish the background needed to generate numerical solutions to a variety of problems. Specific applications involving root-finding, interpolation, curve-fitting, matrices, derivatives, integrals and differential equations are discussed and the broad applicability of MATLAB demonstrated. This book employs MATLAB as the software and programming environment and provides the user with powerful tools in the solution of numerical problems. Although this book is not meant to be an exhaustive treatise on MATLAB, MATLAB solutions to problems are systematically developed and included throughout the book. MATLAB files and scripts are generated, and examples showing the applicability and use of MATLAB are presented throughout the book. Wherever appropriate, the use of MATLAB functions offering shortcuts and alternatives to otherwise long and tedious numerical solutions is also demonstrated. At the end of every chapter a set of problems is included covering the material presented. A solutions manual to these exercises is available to instructors.

This undergraduate textbook integrates the teaching of numerical methods and programming with problems from core chemical engineering subjects.

Numerical, analytical and statistical computations are routine affairs for chemical engineers. They usually prefer a single software to solve their computational problems, and at present, MATLAB has emerged as a powerful computational language, which is preferably used for this purpose, due to its built-in functions and toolboxes. Considering the needs and convenience of the students, the author has made an attempt to write this book, which explains the various concepts of MATLAB in a systematic way and makes its readers proficient in using MATLAB for computing. It mainly focuses on the applications of MATLAB, rather than its use in programming basic numerical algorithms. Commencing with the introduction to MATLAB, the text covers vector and matrix computations, solution of linear and non-linear equations, differentiation and integration, and solution of ordinary and partial differential equations. Next, analytical computations using the Symbolic Math Toolbox and statistical computations using the Statistics and Machine Learning Toolbox are explained. Finally, the book describes various curve fitting techniques using the Curve Fitting Toolbox. Inclusion of all these advanced-level topics in the book stands it out from the rest. KEY FEATURES  Numerous worked-out examples to enable the readers understand the steps involved in solving the chemical engineering problems  MATLAB codes to explain the computational techniques  Several snapshots to help the readers understand the step-by-step procedures of using the toolboxes  Chapter-end exercises, including short-answer questions and numerical problems  Appendix comprising the definitions of some important and special matrices  Supplemented with Solutions Manual containing complete detailed solutions to the unsolved analytical problems  Accessibility of selected colour figures (including screenshots and results/outputs of the programs) cited in the text at www.phindia.com/Pallab_Ghosh. TARGET AUDIENCE • BE/B.Tech (Chemical Engineering) • ME/M.Tech (Chemical Engineering)

Applied Numerical Methods for Chemical Engineers emphasizes the derivation of a variety of numerical methods and their application to the solution of engineering problems, with special attention to problems in the chemical engineering field. These algorithms encompass linear and nonlinear algebraic equations, eigenvalue problems, finite difference methods, interpolation, differentiation and integration, ordinary differential equations, boundary value problems, partial differential equations, and linear and nonlinear regression analysis. MATLAB is adopted as the calculation environment throughout the book because of its ability to perform all the calculations in matrix form, its large library of built-in functions, its strong structural language, and its rich graphical visualization tools. Through this book, students and other users will learn about the basic features, advantages and disadvantages of various numerical methods, learn and practice many useful m-files developed for different numerical methods in addition to the MATLAB built-in solvers, develop and set up mathematical models for problems commonly encountered in chemical engineering, and solve chemical engineering related problems through examples and after-chapter problems with MATLAB by creating application m-files. - Clearly and concisely develops a variety of numerical methods and applies them to the solution of chemical engineering problems. These algorithms encompass linear and nonlinear algebraic equations, eigenvalue problems, finite difference methods, interpolation, linear and nonlinear regression analysis, differentiation and integration, ordinary differential equations, boundary value problems, and partial differential equations - Includes systematic development of the calculus of finite differences and its application to the integration of differential equations, and a detailed discussion of nonlinear regression analysis, with powerful programs for implementing multivariable nonlinear regression and statistical analysis of the results - Makes extensive use of MATLAB and Excel, with most of the methods discussed implemented into general MATLAB functions. All the MATLAB-language scripts developed are listed in the text and included in the book's companion website - Includes numerous real-world examples and homework problems drawn from the field of chemical and biochemical engineering

The book is designed to cover all major aspects of applied numerical methods, including numerical computations, solution of algebraic and transcendental equations, finite differences and interpolation, curve fitting, correlation and regression, numerical differentiation and integration, matrices and linear system of equations, numerical solution of ordinary differential equations, and numerical solution of partial differential equations. MATLAB is incorporated throughout the text and most of the problems are executed in MATLAB code. It uses a numerical problem-solving orientation with numerous examples, figures, and end of chapter exercises. Presentations are limited to very basic topics to serve as an introduction to more advanced topics. FEATURES: Integrates MATLAB throughout the text Includes over 600 fully-solved problems with step-by-step solutions Limits presentations to basic concepts of solving numerical methods

This interdisciplinary book presents numerical techniques needed for chemical and biological engineers using Matlab. The book begins by exploring general cases, and moves on to specific ones. The text includes a large number of detailed illustrations, exercises and industrial examples. The book provides detailed mathematics and engineering background in the appendixes, including an introduction to Matlab. The text will be useful to undergraduate students in chemical/biological engineering, and in applied mathematics and numerical analysis.