The main objective of this book is to extend the scope of the q-calculus based on the definition of q-derivative [Jackson (1910)] to make it applicable to dense domains. As a matter of fact, Jackson's definition of q-derivative fails to work for impulse points while this situation does not arise for impulsive equations on q-time scales as the domains consist of isolated points covering the case of consecutive points. In precise terms, we study quantum calculus on finite intervals. In the first part, we discuss the concepts of qk-derivative and qk-integral, and establish their basic properties. As applications, we study initial and boundary value problems of impulsive qk-difference equations and inclusions equipped with different kinds of boundary conditions. We also transform some classical integral inequalities and develop some new integral inequalities for convex functions in the context of qk-calculus. In the second part, we develop fractional quantum calculus in relation to a new qk-shifting operator and establish some existence and qk uniqueness results for initial and boundary value problems of impulsive fractional qk-difference equations. Contents:PreliminariesQuantum Calculus on Finite IntervalsInitial Value Problems for Impulsive qk-Difference Equations and InclusionsBoundary Value Problems for First-Order Impulsive qk-Integro-Difference Equations and InclusionsImpulsive qk-Difference Equations with Different Kinds of Boundary ConditionsNonlinear Second-Order Impulsive qk-Difference Langevin Equation with Boundary ConditionsQuantum Integral Inequalities on Finite IntervalsImpulsive Quantum Difference Systems with Boundary ConditionsNew Concepts of Fractional Quantum Calculus and Applications to Impulsive Fractional qk-Difference EquationsIntegral Inequalities via Fractional Quantum CalculusNonlocal Boundary Value Problems for Impulsive Fractional qk-Difference EquationsExistence Results for Impulsive Fractional qk-Difference Equations with Anti-periodic Boundary ConditionsImpulsive Fractional qk-Integro-Difference Equations with Boundary ConditionsImpulsive Hybrid Fractional Quantum Difference Equations Readership: Mathematics and physics researchers.
This new edition introduces more problem-solving strategies and new conceptual and challenge problems. Also, each Chapter Review has been enhanced with Learning Goals to reinforce the mastery of concepts for students.
This laboratory manual contains 42 experiments for the standard sequence of topics in general, organic, and biological chemistry.
The book guides students through basic chemistry problem solving with engaging visuals and a focus on developing the math skills necessary to be successful in the course.
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Basic Chemistry
Basic Chemistry, Books a la Carte Edition
Essential Laboratory Manual for General, Organic and Biological Chemistry
The main objective in writing this text is to make the study of chemistry an engaging and a positive experience for students by relating the structure and behaviour of matter to real life.
The eText pages look exactly like the printed text, and include powerful interactive and customization functions. This is the product access code card for MasteringChemistry with Pearson eText and does not include the actual bound book.
Health, Environmental, and Green Chemistry Notes throughout the text relate chemistry chapters to real-life topics in health, the environment, and medicine that are interesting and motivating to students.