This volume resulted from presentations given at the international "Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", that took place at the Instituto de Ciencias Matematicas (ICMAT) in Madrid, Spain. It combines overview and research articles on recent and ongoing developments, as well as new research directions. Why geometric numerical integration? In their article of the same title Arieh Iserles and Reinout Quispel, two renowned experts in numerical analysis of differential equations, provide a compelling answer to this question. After this introductory chapter a collection of high-quality research articles aim at exploring recent and ongoing developments, as well as new research directions in the areas of geometric integration methods for differential equations, nonlinear systems interconnections, and discrete mechanics. One of the highlights is the unfolding of modern algebraic and combinatorial structures common to those topics, which give rise to fruitful interactions between theoretical as well as applied and computational perspectives. The volume is aimed at researchers and graduate students interested in theoretical and computational problems in geometric integration theory, nonlinear control theory, and discrete mechanics.

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This sixth volume collects authoritative chapters covering several applications of fractional calculus in control theory, including fractional controllers, design methods and toolboxes, and a large number of engineering applications of control.

Over a career that spanned 60 years, Ronald L. Graham (known to all as Ron) made significant contributions to the fields of discrete mathematics, number theory, Ramsey theory, computational geometry, juggling and magical mathematics, and many more. Ron also was a mentor to generations of mathematicians, he gave countless talks and helped bring mathematics to a wider audience, and he held signifi cant leadership roles in the mathematical community. This volume is dedicated to the life and memory of Ron Graham, and includes 20-articles by leading scientists across a broad range of subjects that refl ect some of the many areas in which Ron worked.

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fifth volume collects authoritative chapters covering several applications of fractional calculus in physics, including electrodynamics, statistical physics and physical kinetics, and quantum theory.

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fourth volume collects authoritative chapters covering several applications of fractional calculus in physics, including classical and continuum mechanics.

The relaxation method has enjoyed an intensive development during many decades and this new edition of this comprehensive text reflects in particular the main achievements in the past 20 years. Moreover, many further improvements and extensions are included, both in the direction of optimal control and optimal design as well as in numerics and applications in materials science, along with an updated treatment of the abstract parts of the theory.

Rooted in a pedagogically successful problem-solving approach to linear algebra, this work fills a gap in the literature that is sharply divided between, on the one end, elementary texts with only limited exercises and examples, and, at the other end, books too advanced in prerequisites and too specialized in focus to appeal to a wide audience. Instead, it clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science.Key features: * Intertwined discussion of linear algebra and geometry* Example-driven exposition; each section starts with a concise overview of important concepts, followed by a selection of fully-solved problems* Over 500 problems are carefully selected for instructive appeal, elegance, and theoretical importance; roughly half include complete solutions* Two or more solutions provided to many of the problems; paired solutions range from step-by-step, elementary methods whose purpose is to strengthen basic comprehension to more sophisticated, self-study manual for professional scientists and mathematicians. Complete with bibliography and index, this work is a natural bridge between pure/ applied mathematics and the natural/social sciences, appropriate for any student or researcher who needs a strong footing in the theory, problem-solving, and model-building that are the subject's hallmark. I

This book gives a self-contained account of applications of category theory to the theory of representations of algebras. Its main focus is on 2-categorical techniques, including 2-categorical covering theory. The book has few prerequisites beyond linear algebra and elementary ring theory, but familiarity with the basics of representations of quivers and of category theory will be helpful. In addition to providing an introduction to category theory, the book develops useful tools such as quivers, adjoints, string diagrams, and tensor products over a small category; gives an exposition of new advances such as a 2-categorical generalization of Cohen-Montgomery duality in pseudo-actions of a group; and develops the moderation level of categories, first proposed by Levy, to avoid the set theoretic paradox in category theory. The book is accessible to advanced undergraduate and graduate students who would like to study the representation theory of algebras, and it contains many exercises. It can be used as the textbook for an introductory course on the category theoretic approach with an emphasis on 2-categories, and as a reference for researchers in algebra interested in derived equivalences and covering theory.

The main reason I write this book was just to fullfil my long time dream to be able to tutor students. Most students do not bring their text books at home from school. This makes it difficult to help them. This book may help such students as this can be used as a reference in understanding Algebra and Geometry.

The Tobey/Slater/Blair/Crawford series builds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical "building block" organization makes it easy for students to understand each topic and gain confidence as they move through each section. Students will find many opportunities to check and reinforce their understanding of concepts throughout the text and its MyMathLab course. With this revision, the author team has added a new Math Coach feature that provides students with an office hour experience by helping them to avoid commonly made mistakes. With Tobey/Slater/Blair/Crawford, students have a tutor, a study companion, and now a coach, with them every step of the way.

The Tobey/Slater/Blair/Crawford series builds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical "building block" organization makes it easy for students to understand each topic and gain confidence as they move through each section. Students will find many opportunities to check and reinforce their understanding of concepts throughout the text and its MyMathLab course. With this revision, the author team has added a new Math Coach feature that provides students with an office hour experience by helping them to avoid commonly made mistakes. With Tobey/Slater/Blair/Crawford, students have a tutor, a study companion, and now a coach, with them every step of the way.

Is there anything more beautiful than an "A" in Algebra? Not to the Lial team! Marge Lial, John Hornsby, and Terry McGinnis write their textbooks and accompanying resources with one goal in mind: giving students and teachers all the tools they need to achieve success. With this revision, the Lial team has further refined the presentation and exercises throughout the text. They offer several exciting new resources for students and teachers that will provide extra help when needed, regardless of the learning environment (classroom, lab, hybrid, online, etc)-new study skills activities in the text, an expanded video program available in MyMathLab and on the Video Resources on DVD, and more!

Linear Algebra and Differential Equations has been written for a one-semester combined linear algebra and differential equations course, yet it contains enough material for a two-term sequence in linear algebra and differential equations. By introducing matrices, determinants, and vector spaces early in the course, the authors are able to fully develop the connections between linear algebra and differential equations. The book is flexible enough to be easily adapted to fit most syllabi, including separate courses that that cover linear algebra in the first followed by differential equations in the second. Technology is fully integrated where appropriate, and the text offers fresh and relevant applications to motivate student interest.

This book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.

This book presents, in a uniform way, several problems in applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors. It reveals that various problems and studies in mechanical engineering produce certain patterns that can be treated in a similar way. Accordingly, the same mathematical apparatus allows us to study not only mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems. In addition, the book explores a wealth of engineering applications.

Algebra, Second Edition, by Michael Artin, is ideal for the honors undergraduate or introductory graduate course. The second edition of this classic text incorporates twenty years of feedback and the author's own teaching experience. The text discusses concrete topics of algebra in greater detail than most texts, preparing students for the more abstract concepts; linear algebra is tightly integrated throughout.

The Bittinger Worktext Series changed the face of developmental education with the introduction of objective-based worktexts that presented math one concept at a time. This approach allowed students to understand the rationale behind each concept before practicing the associated skills and then moving on to the next topic. With this revision, Marv Bittinger continues to focus on building success through conceptual understanding, while also supporting students with quality applications, exercises, and new review and study materials to help them apply and retain their knowledge.

Beecher, Penna, and Bittinger's Algebra and Trigonometry is known for enabling students to "see the math" through its focus on visualization and early introduction to functions. With the Fourth Edition, the authors continue to innovate by incorporating more ongoing review to help students develop their understanding and study effectively. Mid-chapter Mixed Review exercise sets have been added to give students practice in synthesizing the concepts, and new Study Guide summaries provide built-in tools to help them prepare for tests. MyMathLab has been expanded so that the online content is even more integrated with the text's approach, with the addition of Vocabulary, Synthesis, and Mid-chapter Mixed Review exercises from the text, as well as example-based videos created by the authors.

College Algebra in Context, Fourth Edition is ideal for students majoring in business, social sciences, and life sciences. The authors use modeling, applications, and real-data problems to develop skills, giving students the practice they need to become adept problem solvers in their future courses and careers. This revision maintains the authors' focus on applying math in the real world through updated real-data applications. Features such as Group Activities and Extended Applications promote collaborative learning, improve communication and research skills, and foster critical thinking. MyMathLab has increased exercise coverage, pre-built sample assignments, and Ready-to-Go course options that make it easier to get started with online homework.

An introduction to elementary linear algebra - designed especially for those interested in computer science, business and economics, the natural and social sciences, engineering, or mathematics.

Is there anything more beautiful than an "A" in Algebra? Not to the Lial team! Marge Lial, John Hornsby, and Terry McGinnis write their textbooks and accompanying resources with one goal in mind: giving students and teachers all the tools they need to achieve success. With this revision, the Lial team has further refined the presentation and exercises throughout the text. They offer several exciting new resources for students and teachers that will provide extra help when needed, regardless of the learning environment (classroom, lab, hybrid, online, etc)-new study skills activities in the text, an expanded video program available in MyMathLab and on the Video Resources on DVD, and more!