Data-Driven Modeling & Scientific Computation

Methods for Complex Systems & Big Data

Author: J. Nathan Kutz

Publisher: OUP Oxford

ISBN: 019163588X

Category: Mathematics

Page: 608

View: 1102


The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from: · statistics, · time-frequency analysis, and · low-dimensional reductions The blend of these ideas provides meaningful insight into the data sets one is faced with in every scientific subject today, including those generated from complex dynamical systems. This is a particularly exciting field and much of the final part of the book is driven by intuitive examples from it, showing how the three areas can be used in combination to give critical insight into the fundamental workings of various problems. Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences. An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

From Calculus to Computers

Using the Last 200 Years of Mathematics History in the Classroom

Author: Amy Shell-Gellasch,Dick Jardine

Publisher: Cambridge University Press

ISBN: 9780883851784

Category: Mathematics

Page: 255

View: 3823


To date, much of the literature prepared on the topic of integrating mathematics history into undergraduate teaching contains, predominantly, ideas from the 18th century and earlier. This volume focuses on nineteenth- and twentieth-century mathematics, building on the earlier efforts but emphasizing recent history in the teaching of mathematics, computer science, and related disciplines. From Calculus to Computers is a resource for undergraduate teachers that provides ideas and materials for immediate adoption in the classroom and proven examples to motivate innovation by the reader. Contributions to this volume are from historians of mathematics and college mathematics instructors with years of experience and expertise in these subjects. Examples of topics covered are probability in undergraduate statistics courses, logic and programming for computer science, undergraduate geometry to include non-Euclidean geometries, numerical analysis, and abstract algebra.

Elementary Calculus

Author: P.R. Masani,R. C. Patel,D. J. Patil

Publisher: Elsevier

ISBN: 1483274896

Category: Mathematics

Page: 352

View: 3086


Elementary Calculus presents a three semester introductory course on calculus. This book reveals the conceptual development of the calculus, taking into cognizance the technical and applied sides and standards of clarity and rigor that prevail in mathematics. The topics discussed include the basic laws of numbers, classification of real functions, and concept of instantaneous velocity. The limits of functions defined on intervals, derivatives of the trigonometric functions, and standard logarithmic function are also reviewed. This text likewise considers integration by substitution, lengths of plane curves, and simple harmonic motion. This publication is designed for students who have a knowledge of elementary trigonometry, and either have had a one semester course on analytic or coordinate geometry or might take such a course with calculus.

Calculus with Analytic Geometry

Author: Harley Flanders,Justin J. Price

Publisher: Academic Press

ISBN: 1483262405

Category: Mathematics

Page: 1054

View: 4739


Calculus with Analytic Geometry presents the essentials of calculus with analytic geometry. The emphasis is on how to set up and solve calculus problems, that is, how to apply calculus. The initial approach to each topic is intuitive, numerical, and motivated by examples, with theory kept to a bare minimum. Later, after much experience in the use of the topic, an appropriate amount of theory is presented. Comprised of 18 chapters, this book begins with a review of some basic pre-calculus algebra and analytic geometry, paying particular attention to functions and graphs. The reader is then introduced to derivatives and applications of differentiation; exponential and trigonometric functions; and techniques and applications of integration. Subsequent chapters deal with inverse functions, plane analytic geometry, and approximation as well as convergence, and power series. In addition, the book considers space geometry and vectors; vector functions and curves; higher partials and applications; and double and multiple integrals. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

CliffsTestPrep CSET: Mathematics

Author: Janet B Andreasen,Enrique Ortiz

Publisher: Houghton Mifflin Harcourt

ISBN: 0544185811

Category: Study Aids

Page: 240

View: 2025


Your complete guide to a higher score on the CSET: Mathematics. Features information about certification requirements, an overview of the test - with a scoring scale, description of the test structure and format and proven test-taking strategies Approaches for answering the three types of questions: multiple-choice enhanced multiple-choice constructed-response. Reviews and Practice Focused reviews of all areas tested: algebra, number theory, geometry, probability, calculus, and history of mathematics Practice problems for selected difficult areas and domains 2 Full-Length Practice Tests are structured like the actual exam and are complete with answers and explanations The Glossary of Terms has description of Key Formulas and Properties Test-Prep Essentials from the Experts at CliffsNotes

Research in Collegiate Mathematics Education VII

Author: Fernando Hitt,Derek Allan Holton,Patrick W. Thompson

Publisher: American Mathematical Soc.

ISBN: 0821849964

Category: Mathematics

Page: 261

View: 4445


The present volume of Research in Collegiate Mathematics Education, like previous volumes in this series, reflects the importance of research in mathematics education at the collegiate level. The editors in this series encourage communication between mathematicians and mathematics educators, and as pointed out by the International Commission of Mathematics Instruction (ICMI), much more work is needed in concert with these two groups. Indeed, editors of RCME are aware of this need and the articles published in this series are in line with that goal. Nine papers constitute this volume. The first two examine problems students experience when converting a representation from one particular system of representations to another. The next three papers investigate students learning about proofs. In the next two papers, the focus is instructor knowledge for teaching calculus. The final two papers in the volume address the nature of ``conception'' in mathematics. Whether they are specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas that they can use.