Differential calculus and equations

For introductory courses in Differential Equations.

Elementary Number Theory, 6th Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets.

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Straightforward introduction for non-specialists and experts alike.

Straightforward introduction for non-specialists and experts alike.

This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.

This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.

This book contains a comprehensive collection of chapters on recent and original research, along with review articles, on mathematical modeling of dynamical systems described by various types of differential equations.

This book provides a well-balanced and comprehensive picture based on clear physics, solid mathematical formulation, and state-of-the-art useful numerical methods in deterministic, stochastic, deep neural network machine learning approaches for computer simulations of electromagnetic and transport processes in biology, microwave and optical wave devices, and nano-electronics.

This book discusses the generalized Duffing equation and its periodic perturbations, with special emphasis on the existence and multiplicity of periodic solutions, subharmonic solutions and different approaches to prove rigorously the presence of chaotic dynamics.

Each volume in the Notre Dame Series on Quantitative Methodology features leading methodologists and substantive experts who provide instruction on innovative techniques designed to enhance quantitative skills in a substantive area.

Each volume in the Notre Dame Series on Quantitative Methodology features leading methodologists and substantive experts who provide instruction on innovative techniques designed to enhance quantitative skills in a substantive area.

"e;Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus.

Modern Computational Methods for Fractional Differential Equations provides a comprehensive introduction to the fundamentals of fractional calculus.

This book addresses the issue of uniqueness of a solution to a problem - a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon.

Input-to-State Stability presents the dominating stability paradigm in nonlinear control theory that revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, and stability of nonlinear interconnected control systems.

Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type.

Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type.

Bessel functions are associated with a wide range of problems in important areas of mathematical physics.

Bessel functions are associated with a wide range of problems in important areas of mathematical physics.

This book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems.

This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies.

This book introduces an original fractional calculus methodology ('the infinite state approach') which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs).

This book introduces an original fractional calculus methodology ('the infinite state approach') which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs).

GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces.

GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces.

The purpose of this book is to introduce and study numerical methods basic and advanced ones for scientific computing.

The purpose of this book is to introduce and study numerical methods basic and advanced ones for scientific computing.

Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems.

A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics.

A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics.

Presents the methodology and applications of ODE and PDE models within biomedical science and engineering With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE).

Presents the methodology and applications of ODE and PDE models within biomedical science and engineering With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE).

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universit s, UPMC - Universit Paris 6, France A comprehensive overview of techniques for the computational solution of PDE'sNumerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method.

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universit s, UPMC - Universit Paris 6, France A comprehensive overview of techniques for the computational solution of PDE'sNumerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method.

Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications details newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty.

Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications details newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty.

Solutions Manual to Accompany http://www.

Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer.

Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer.

Solutions Manual to Accompany http://www.

Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically.

Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically.

A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible, combination of techniques, applications, and introductory theory on the subjectof partial differential equations.

A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEsSymmetry Analysis of Differential Equations: An Introduction presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs).

A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEsSymmetry Analysis of Differential Equations: An Introduction presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs).

Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-world ODE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology.

Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology.

Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology.