The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.
This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors and transformations using matrices. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines.
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)
Previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB® Approach, Fourth Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computed results so that the main steps are easily visualized and interpreted. This edition also includes a new chapter on Dynamical Systems and Chaos. Features Covers the most common numerical methods encountered in science and engineering Illustrates the methods using MATLAB Presents numerous examples and exercises, with selected answers at the back of the book
MATLAB stands for Matrix Laboratory. It is a term used in technical computing of high efficiency. Cleve Molar of MathWorks.Inc built this system in 1984. In 1984. It's in the C, C++, and Java. It permits matrix manipulation, function detection, algorithm implementation, and user interface design.
This book introduces fundamental concepts and principles of 2D and 3D graphics and is written for undergraduate and postgraduate students of computer science, graphics, multimedia, and data science. It demonstrates the use of MATLAB® programming for solving problems related to graphics and discusses a variety of visualization tools to generate graphs and plots. The book covers important concepts like transformation, projection, surface generation, parametric representation, curve fitting, interpolation, vector representation, and texture mapping, all of which can be used in a wide variety of educational and research fields. Theoretical concepts are illustrated using a large number of practical examples and programming codes, which can be used to visualize and verify the results. Key Features: Covers fundamental concepts and principles of 2D and 3D graphics Demonstrates the use of MATLAB® programming for solving problems on graphics Provides MATLAB® codes as answers to specific numerical problems Provides codes in a simple copy and execute format for the novice learner Focuses on learning through visual representation with extensive use of graphs and plots Helps the reader gain in-depth knowledge about the subject matter through practical examples Contains review questions and practice problems with answers for self-evaluation
The purpose of this book is to reveal the foundations and major features of several basic methods for curve and surface fitting that are currently in use.
The first edition of ‘Basics of MATLAB Programming’ offers a brief glimpse of the power and flexibility of MATLAB. This book is intended to assist undergraduates with learning in programming, specifically in MATLAB. The MATLAB codes are given in Courier New font [MATLAB font] to get the feel of MATLAB environment. It combines engineering mathematics with MATLAB. This book has around ten chapters comprising Arrays, Functions, Control statements, Plotting, Simulink and other miscellaneous concepts. It consists of many real-life examples which help in better understanding of MATLAB.
Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relatively focused need of an extraordinarily broad range of scientists.
This new edition provides an updated approach for students, engineers, and researchers to apply numerical methods for solving problems using MATLAB® This accessible book makes use of MATLAB® software to teach the fundamental concepts for applying numerical methods to solve practical engineering and/or science problems. It presents programs in a complete form so that readers can run them instantly with no programming skill, allowing them to focus on understanding the mathematical manipulation process and making interpretations of the results. Applied Numerical Methods Using MATLAB®, Second Edition begins with an introduction to MATLAB usage and computational errors, covering everything from input/output of data, to various kinds of computing errors, and on to parameter sharing and passing, and more. The system of linear equations is covered next, followed by a chapter on the interpolation by Lagrange polynomial. The next sections look at interpolation and curve fitting, nonlinear equations, numerical differentiation/integration, ordinary differential equations, and optimization. Numerous methods such as the Simpson, Euler, Heun, Runge-kutta, Golden Search, Nelder-Mead, and more are all covered in those chapters. The eighth chapter provides readers with matrices and Eigenvalues and Eigenvectors. The book finishes with a complete overview of differential equations. Provides examples and problems of solving electronic circuits and neural networks Includes new sections on adaptive filters, recursive least-squares estimation, Bairstow's method for a polynomial equation, and more Explains Mixed Integer Linear Programing (MILP) and DOA (Direction of Arrival) estimation with eigenvectors Aimed at students who do not like and/or do not have time to derive and prove mathematical results Applied Numerical Methods Using MATLAB®, Second Edition is an excellent text for students who wish to develop their problem-solving capability without being involved in details about the MATLAB codes. It will also be useful to those who want to delve deeper into understanding underlying algorithms and equations.
