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.
Fitting and Pattern Alteration: A Multi-Method Approach to the Art of Style Selection, Fitting, and Alteration, Third Edition, shows readers how to recognize, evaluate, and correct fit for 88 figure variations. This comprehensive guide presents proven methods of style selection, fitting, and alteration. The authors use a multi-level approach that is both logical and easy to follow, and each procedure is clearly identified and fully illustrated with a second color added to clarify the procedure and show directional measuring. Each figure is drawn to scale ensuring consistency and accuracy. The cause for the fitting problem is clearly identified and explained--giving readers the why behind each fitting procedure. Highlights of this edition include new photographs of common fit problems, as well as instructions for working with multi-sized patterns and correcting garments that have more than one fit problem...New to this Edition..~ Chapters open with added key terms and chapter objectives.~ End-of-chapter discussion questions allow the reader to fully engage with the content.~ New 2-color graded pattern illustrations, measurement illustrations, photos of actual body types and illustrations of advanced bodice and pant fitting patterns.~ Updated Reality Check boxes present further details on the topic at hand and reinforce the learning experience..Introducing Fitting and Pattern Alteration STUDIO--an online tool for more effective study!.- Study smarter with self-quizzes featuring scored results and personalized study tips.- Review concepts with flashcards of terms and definitions ..PLEASE NOTE: Purchasing or renting this ISBN does not include access to the STUDIO resources that accompany this text. To receive free access to the STUDIO content with new copies of this book, please refer to the book + STUDIO access card bundle ISBN 9781501318207.
Throughout the physical and social sciences, researchers face the challenge of fitting statistical distributions to their data. Although the study of statistical modelling has made great strides in recent years, the number and variety of distributions to choose from-all with their own formulas, tables, diagrams, and general properties-continue to create problems. For a specific application, which of the dozens of distributions should one use? What if none of them fit well?