Newton Cotes Formula Derivation
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Numerical Methods for Engineering and Data Science
Numerical Methods for Engineering and Data Science guides students in implementing numerical methods in engineering and in assessing their limitations and accuracy, particularly using algorithms from the field of machine learning. The textbook presents key principles building upon the fundamentals of engineering mathematics. It explores classical techniques for solving linear and nonlinear equations, computing definite integrals and differential equations. Emphasis is placed on the theoretical underpinnings, with an in-depth discussion of the sources of errors, and in the practical implementation of these using Octave. Each chapter is supplemented with examples and exercises designed to reinforce the concepts and encourage hands-on practice. The second half of the book transitions into the realm of machine learning. The authors introduce basic concepts and algorithms, such as linear regression and classification. As in the first part of this book, a special focus is on the solid understanding of errors and practical implementation of the algorithms. In particular, the concepts of bias, variance, and noise are discussed in detail and illustrated with numerous examples. This book will be of interest to students in all areas of engineering, alongside mathematicians and scientists in industry looking to improve their knowledge of this important field.
Numerical Methods in Biomedical Engineering
Numerical Modeling in Biomedical Engineering brings together the integrative set of computational problem solving tools important to biomedical engineers. Through the use of comprehensive homework exercises, relevant examples and extensive case studies, this book integrates principles and techniques of numerical analysis. Covering biomechanical phenomena and physiologic, cell and molecular systems, this is an essential tool for students and all those studying biomedical transport, biomedical thermodynamics & kinetics and biomechanics. - Supported by Whitaker Foundation Teaching Materials Program; ABET-oriented pedagogical layout - Extensive hands-on homework exercises
Applied Numerical Methods for Chemical Engineers
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