The second edition of Reverse Engineering of Algebraic Inequalities is a comprehensively updated new edition demonstrating the exploration of new physical realities in various unrelated domains of human activity through reverse engineering of algebraic inequalities. This book introduces a groundbreaking method for generating new knowledge in science and technology that relies on reverse engineering of algebraic inequalities. By using this knowledge, the purpose is to optimize systems and processes in diverse fields such as mechanical engineering, structural engineering, physics, electrical engineering, reliability engineering, risk management and economics. This book will provide the reader with methods to enhance the reliability of systems in total absence of knowledge about the reliabilities of the components building the systems; to develop light-weight structures with very big materials savings; to develop structures with very big load-bearing capacity; to enhance process performance and decision-making; to obtain new useful physical properties; and to correct serious flaws in the current practice for predicting system reliability. This book will greatly benefit professionals and mathematical modelling researchers working on optimising processes and systems in diverse disciplines. It will also benefit undergraduate students introduced to mathematical modelling, post-graduate students and post-doctoral researchers working in the area of mathematical modelling, mechanical engineering, reliability engineering, structural engineering, risk management, and engineering design. .

This book introduces a new method based on algebraic inequalities for optimising engineering systems and processes, with applications in mechanical engineering, materials science, electrical engineering, reliability engineering, risk management and operational research. This book shows that the application potential of algebraic inequalities in engineering and technology is far-reaching and certainly not restricted to specifying design constraints. Algebraic inequalities can handle deep uncertainty associated with design variables and control parameters. With the method presented in this book, powerful new knowledge about systems and processes can be generated through meaningful interpretation of algebraic inequalities. This book demonstrates how the generated knowledge can be put into practice through covering the algebraic inequalities suitable for interpretation in different contexts and describing how to apply this knowledge to enhance system and process performance. Depending on the specific interpretation, knowledge, applicable to different systems from different application domains, can be generated from the same algebraic inequality. Furthermore, an important class of algebraic inequalities has been introduced that can be used for optimising systems and processes in any area of science and technology provided that the variables and the separate terms of the inequalities are additive quantities. With the presented various examples and solutions, this book will be of interest to engineers, students and researchers in the field of optimisation, engineering design, reliability engineering, risk management and operational research.

A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.

This unique collection of new and classical problems provides full coverage of algebraic inequalities. Many of the exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. Algebraic Inequalities can be considered a continuation of the book Geometric Inequalities: Methods of Proving by the authors. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving algebraic inequalities.

Over the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inverse problems, or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman Inequalities, driven by applications to various questions of unique continuation. Beginning with an elementary introduction to the topic, including examples accessible to readers without prior knowledge of advanced mathematics, the book's first five chapters contain a thorough exposition of the most classical results, such as Calderón's and Hörmander's theorems. Later chapters explore a selection of results of the last four decades around the themes of continuation for elliptic equations, with the Jerison-Kenig estimates for strong unique continuation, counterexamples to Cauchy uniqueness of Cohen and Alinhac & Baouendi, operators with partially analytic coefficients with intermediate results between Holmgren's and Hörmander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more. With examples and special cases motivating the general theory, as well as appendices on mathematical background, this monograph provides an accessible, self-contained basic reference on the subject, including a selection of the developments of the past thirty years in unique continuation.

Intermediate Algebra: A Text/Workbook, Second Edition focuses on the principles, operations, and approaches involved in intermediate algebra. The publication first takes a look at basic properties and definitions, first-degree equations and inequalities, and exponents and polynomials. Discussions focus on properties of exponents, polynomials, sums, and differences, multiplication of polynomials, inequalities involving absolute value, word problems, first-degree inequalities, real numbers, opposites, reciprocals, and absolute value, and addition and subtraction of real numbers. The text then examines rational expressions, quadratic equations, and rational expressions and roots. Topics include completing the square, quadratic formula, multiplication and division of radical expressions, equations with radicals, basic properties and reducing to lowest terms, and addition and subtraction of rational expression. The book takes a look at logarithms, relations and functions, conic sections, and systems of linear equations, including introduction to determinants, systems of linear equations in three variables, ellipses and hyperbolas, nonlinear systems, function notation, inverse of a function, and exponential equations and change of base. The publication is a valuable reference for students and researchers interested in intermediate algebra.

Algebra I Essentials For Dummies (9781119590965) was previously published as Algebra I Essentials For Dummies (9780470618349). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, Algebra I Essentials For Dummies provides content focused on key topics only, with discrete explanations of critical concepts taught in a typical Algebra I course, from functions and FOILs to quadratic and linear equations. This guide is also a perfect reference for parents who need to review critical algebra concepts as they help students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts. The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Algebra II For Dummies, 2nd Edition (9781119543145) was previously published as Algebra II For Dummies, 2nd Edition (9781119090625). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Your complete guide to acing Algebra II Do quadratic equations make you queasy? Does the mere thought of logarithms make you feel lethargic? You're not alone! Algebra can induce anxiety in the best of us, especially for the masses that have never counted math as their forte. But here's the good news: you no longer have to suffer through statistics, sequences, and series alone. Algebra II For Dummies takes the fear out of this math course and gives you easy-to-follow, friendly guidance on everything you'll encounter in the classroom and arms you with the skills and confidence you need to score high at exam time. Gone are the days that Algebra II is a subject that only the serious 'math' students need to worry about. Now, as the concepts and material covered in a typical Algebra II course are consistently popping up on standardized tests like the SAT and ACT, the demand for advanced guidance on this subject has never been more urgent. Thankfully, this new edition of Algebra II For Dummies answers the call with a friendly and accessible approach to this often-intimidating subject, offering you a closer look at exponentials, graphing inequalities, and other topics in a way you can understand. Examine exponentials like a pro Find out how to graph inequalities Go beyond your Algebra I knowledge Ace your Algebra II exams with ease Whether you're looking to increase your score on a standardized test or simply succeed in your Algebra II course, this friendly guide makes it possible.