An implicit requirement associated with modelling and simulation projectswithin the realm of CTDS models is a means for solving the differential equations embedded in the conceptual model. In very special cases these equations can fall into a category for which closed-formanalytic solutions can be developed and this certainly has many advantages. Far more common, however, is the case where the features of the equations preclude such a solution approach. In such situations,numerical approximation procedures provide the only solution alternative.
The first part of the course mainly considers polynomial approximations and discusses issues related to convergence, accuracy, stability and complexity. The second part introduces various current topics in the field, such as wavelets, radial basis functions, sparse grid approximations and sparse L1 approximations.
(a) Volume distributions DV(R) obtained by the different smoothing options in the EM iteration scheme. (b) Volume distributions DV(R) obtained by Tikhonov regularization. (c) Simulated experimental SAS data with noise and corresponding model scattering function. (d) The corner of the L-curve determines the optimum weighting factor for the cost function, which was chosen to be the entropy of the solution vector (blue) or the sum of its first (red) or second derivative (green), over the -test for the goodness of fit, which progresses from right to left with each iteration.
This textbook is part of the OpenIntro Statistics series and offers complete coverage of the high school AP Statistics curriculum. Real data and plenty of inline examples and exercises make this an engaging and readable book. Links to lecture slides, video overviews, calculator tutorials, and video solutions to selected end of chapter exercises make this an ideal choice for any high school or Community College teacher. In fact, Portland Community College recently adopted this textbook for its Introductory Statistics course, and it estimates that this will save their students $250,000 per year. Find out more at: openintro.org/ahss
This is a "first course" in the sense that it presumes no previous course in probability. The units are modules taken from the unpublished text: Paul E. Pfeiffer, ELEMENTS OF APPLIED PROBABILITY, USING MATLAB. The units are numbered as they appear in the text, although of course they may be used in any desired order. For those who wish to use the order of the text, an outline is provided, with indication of which modules contain the material.
This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition.
This course blends Introductory Statistics from OpenStax with other OER to offer a first course in statistics intended for students majoring in fields other than mathematics and engineering. This course assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it.The foundation of the OpenStax text is Collaborative Statistics, by Barbara Illowsky and Susan Dean. The development choices for this textbook were made with the guidance of many faculty members who are deeply involved in teaching this course. These choices led to innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility for students. We strove to make the discipline meaningful, so that students can draw from it a working knowledge that will enrich their future studies and help them make sense of the world around them.
This Statistics resource was developed under the guidance and support of experienced high school teachers and subject matter experts. It is presented here in multiple formats: PDF, online, and low-cost print. Statistics offers instruction in grade-level appropriate concepts and skills in a logical, engaging progression that begins with sampling and data and covers topics such as probability, random variables, the normal distribution, and hypothesis testing. This content was developed with students in mind, incorporating statistics labs, worked exercises, and additional opportunities for assessment that incorporate real-world statistical applications. For instructors, resources are available to support the implementation of the Statistics textbook, including a Getting Started Guide, direct instruction presentations, and a solutions manual.
This course is an introduction to data cleaning, analysis and visualization. We will teach the basics of data analysis through concrete examples. You will learn how to take raw data, extract meaningful information, use statistical tools, and make visualizations. This was offered as a non-credit course during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.
Written by authors at the forefront of their field, this Second Edition discusses problems with periodic solutions, and presents new information on initial boundary value problems and numerical methods for partial differential equations. Complete with reworked theorems, examples, and illustrations, it covers hyperbolic first order systems on structured grids; differential equations and numerical methods with a parallel development; hyperbolic equations; error bounds and estimates; artificial boundary conditions; and more. This book is an ideal reference for anyone involved in physical science, engineering, numerical analysis, and mathematical modeling.
Praise for the First Edition". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations."--SIAM ReviewTime-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-dependent problems. The book treats differential equations and difference methods with a parallel development, thus achieving a more useful analysis of numerical methods.The Second Edition presents hyperbolic equations in great detail as well as new coverage on second-order systems of wave equations including acoustic waves, elastic waves, and Einstein equations. Compared to first-order hyperbolic systems, initial-boundary value problems for such systems contain new properties that must be taken into account when analyzing stability. Featuring the latest material in partial differential equations with new theorems, examples, and illustrations,Time-Dependent Problems and Difference Methods, Second Edition also includes:* High order methods on staggered grids* Extended treatment of Summation By Parts operators and their application to second-order derivatives* Simplified presentation of certain parts and proofsTime-Dependent Problems and Difference Methods, Second Edition is an ideal reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs and to predict and investigate physical phenomena. The book is also excellent for graduate-level courses in applied mathematics and scientific computations. 2b1af7f3a8