Exponential Fitting
Exponential Fitting

Author: Liviu Gr. Ixaru

Publisher: Springer Science & Business Media

Published: 2004-05-26

Total Pages: 328

ISBN-13: 9781402020995

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Exponential Fitting is a procedure for an efficient numerical approach of functions consisting of weighted sums of exponential, trigonometric or hyperbolic functions with slowly varying weight functions. This book is the first one devoted to this subject. Operations on the functions described above like numerical differentiation, quadrature, interpolation or solving ordinary differential equations whose solution is of this type, are of real interest nowadays in many phenomena as oscillations, vibrations, rotations, or wave propagation. The authors studied the field for many years and contributed to it. Since the total number of papers accumulated so far in this field exceeds 200 and the fact that these papers are spread over journals with various profiles (such as applied mathematics, computer science, computational physics and chemistry) it was time to compact and to systematically present this vast material. In this book, a series of aspects is covered, ranging from the theory of the procedure up to direct applications and sometimes including ready to use programs. The book can also be used as a textbook for graduate students.

Practical Handbook of Curve Fitting
Practical Handbook of Curve Fitting

Author: Sandra Arlinghaus

Publisher: CRC Press

Published: 2023-06-14

Total Pages: 261

ISBN-13: 1000943283

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Practical Handbook of Curve Fitting is a reference work assembled by Arlinghaus and a set of editors with well over a century of combined experience in various disciplines and activities related to curve fitting. The book demonstrates how to analyze World data bases and graph and map the results. Default settings in software packages can produce attractive graphs of data imported into the software. Often, however, the default graph has no equation associated with it and cannot therefore be used as a tool for further analysis or projection of the data. The same software can often be used to generate curves from equations. The reader is shown directly, and in a series of steps, how to fit curves to data using Lotus 1-2-3. There are traditional unbounded curve fitting techniques-lines of least squares, exponentials, logistic curves, and Gompertz curves. There is the bounded curve fitting technique of cubic spline interpolation. Beyond these, there is a detailed application of Feigenbaum's graphical analysis from chaos theory, and there is a hint as to how fractal geometry might come into play. Curve fitting algorithms take on new life when they are actually used on real-world data. They are used in numerous worked examples drawn from electronic data bases of public domain information from the Stars data base of The World Bank and from the WRD data base of the World Resources Institute. The applications are current and reflect a state-of-the-art interest in the human dimensions of global change.

Precalculus
Precalculus

Author: Jay P. Abramson

Publisher:

Published: 2014-10-23

Total Pages: 2000

ISBN-13: 9781938168345

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"Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of OpenStax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. OpenStax will also be releasing College Algebra and Algebra and trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses."--Preface.

Numerical Data Fitting in Dynamical Systems
Numerical Data Fitting in Dynamical Systems

Author: Klaus Schittkowski

Publisher: Springer Science & Business Media

Published: 2013-06-05

Total Pages: 406

ISBN-13: 1441957626

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Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.

Mathematical Modeling
Mathematical Modeling

Author: Antonio Palacios

Publisher: Springer Nature

Published: 2022-09-19

Total Pages: 575

ISBN-13: 303104729X

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This book provides qualitative and quantitative methods to analyze and better understand phenomena that change in space and time. An innovative approach is to incorporate ideas and methods from dynamical systems and equivariant bifurcation theory to model, analyze and predict the behavior of mathematical models. In addition, real-life data is incorporated in the derivation of certain models. For instance, the model for a fluxgate magnetometer includes experiments in support of the model. The book is intended for interdisciplinary scientists in STEM fields, who might be interested in learning the skills to derive a mathematical representation for explaining the evolution of a real system. Overall, the book could be adapted in undergraduate- and postgraduate-level courses, with students from various STEM fields, including: mathematics, physics, engineering and biology.

Practical Numerical Methods with C#
Practical Numerical Methods with C#

Author: Jack Xu

Publisher: UniCAD

Published: 2019

Total Pages: 470

ISBN-13: 1695895576

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The second edition of this book builds all the code example within a single project by incorporating new advancements in C# .NET technology and open-source math libraries. It also uses C# Interactive Window to test numerical computations without compiling or running the complete project code. The second edition includes three new chapters, including "Plotting", Fourier Analysis" and "Math Expression Parser". As in the first edition, this book presents an in-depth exposition of the various numerical methods used in real-world scientific and engineering computations. It emphasizes the practical aspects of C# numerical methods and mathematical functions programming, and discusses various techniques in details to enable you to implement these numerical methods in your .NET application. Ideal for scientists, engineers, and students who would like to become more adept at numerical methods, the second edition of this book covers the following content: - Overview of C# programming. - The mathematical background and fundamentals of numerical methods. - plotting the computation results using a 3D chart control. - Math libraries for complex numbers and functions, real and complex vector and matrix operations, and special functions. - Numerical methods for generating random numbers and random distribution functions. - Various numerical methods for solving linear and nonlinear equations. - Numerical differentiation and integration. - Interpolations and curve fitting. - Optimization of single-variable and multi-variable functions with a variety of techniques, including advanced simulated annealing and evolutionary algorithms. - Numerical techniques for solving ordinary differential equations. - Numerical methods for solving boundary value problems. - Eigenvalue problems. - Fourier analysis. - mathematical expression parser and evaluator. In addition, this book provides testing examples for every math function and numerical method to show you how to use these functions and methods in your own .NET applications in a manageable and step-by-step fashion. Please visit the author's website for more information about this book at https://drxudotnet.com https://drxudotnet.com and https://gincker.com.

Rhodopsin
Rhodopsin

Author: Valentin Gordeliy

Publisher: Springer Nature

Published: 2022-07-20

Total Pages: 371

ISBN-13: 107162329X

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This volume provides readers with the latest information on the advances made in the field of rhodopsins. The chapters in this book cover topics such as new discoveries and developments; new ways to search for rhodopsins; methods to characterize the function and structure of rhodopsins on a molecular level; nano volume high throughput in meso crystallization, and fourth generation x-ray synchrotron sources. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Cutting-edge and thorough, Rhodopsin: Methods and Protocols is a valuable resource for any scientist and researcher interested in learning more about this developing field.

Intermediate Statistics For Dummies
Intermediate Statistics For Dummies

Author: Deborah J. Rumsey

Publisher: John Wiley & Sons

Published: 2007-02-26

Total Pages: 386

ISBN-13: 0470147741

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Need to know how to build and test models based on data? Intermediate Statistics For Dummies gives you the knowledge to estimate, investigate, correlate, and congregate certain variables based on the information at hand. The techniques you’ll learn in this book are the same techniques used by professionals in medical and scientific fields. Picking up right where Statistics For Dummies left off, this straightforward, easy-to-follow book guides you beyond Central Limit Theorem and hypothesis tests and immerses you in flavors of regression, ANOVA, and nonparametric procedures. Unlike regular statistics books, this guide provides full explanations of intermediate statistical ideas; computer input dissection; an extensive number of examples, tips, strategies, and warnings; and clear, concise step-by-step procedures—all in a language you can understand. You’ll soon discover how to: Analyze data and base models off of your data Make predictions using regression Compare many means with ANOVA Test models using Chi-square Dealing with abnormal data In addition, this book includes a list of wrong statistical conclusions and common questions that professors ask using computer output. This book also adopts a nonlinear approach, making it possible to skip to the information you need without having to read previous chapters. With Intermediate Statistics For Dummies, you’ll have all the tools you need to make important decisions in all types of professional areas—from biology and engineering to business and politics!

Single-Molecule Biophysics
Single-Molecule Biophysics

Author: Tamiki Komatsuzaki

Publisher: John Wiley & Sons

Published: 2011-11-16

Total Pages: 403

ISBN-13: 111813138X

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Discover the experimental and theoretical developments in optical single-molecule spectroscopy that are changing the ways we think about molecules and atoms The Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. This latest volume explores the advent of optical single-molecule spectroscopy, and how atomic force microscopy has empowered novel experiments on individual biomolecules, opening up new frontiers in molecular and cell biology and leading to new theoretical approaches and insights. Organized into two parts—one experimental, the other theoretical—this volume explores advances across the field of single-molecule biophysics, presenting new perspectives on the theoretical properties of atoms and molecules. Single-molecule experiments have provided fresh perspectives on questions such as how proteins fold to specific conformations from highly heterogeneous structures, how signal transductions take place on the molecular level, and how proteins behave in membranes and living cells.This volume is designed to further contribute to the rapid development of single-molecule biophysics research. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.