This book explores the fundamental concepts of derivatives and integrals in calculus, extending their classical definitions to more advanced forms such as fractional derivatives and integrals.
This impressive compilation of the material presented at the International Conference on Partial Differential Equations held in Fez, Morocco, represents an integrated discussion of all major topics in the area of partial differential equations--highlighting recent progress and new trends for real-world applications.
Mathematical Analysis: Theory and Applications provides an overview of the most up-to-date developments in the field, presenting original contributions and surveys from a spectrum of respected academics.
"e;Presents new approaches to qualitative analysis of continuous, discreteptime, and impulsive nonlinear systems via Liapunov matrix-valued functions that introduce more effective tests for solving problems of estimating the domains of asymptotic stability.
Suitable for a one- or two-semester course, Advanced Calculus: Theory and Practice expands on the material covered in elementary calculus and presents this material in a rigorous manner.
A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems.
Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group.
A Powerful Methodology for Solving All Types of Differential EquationsDecomposition Analysis Method in Linear and Non-Linear Differential Equations explains how the Adomian decomposition method can solve differential equations for the series solutions of fundamental problems in physics, astrophysics, chemistry, biology, medicine, and other scientif
Offering in-depth analyses of current theories and approaches related to Sobolev-type equations and systems, this reference is the first to introduce a classification of equations and systems not solvable with respect to the highest order derivative, and it studies boundary value problems for these classes of equations.
"e;Illuminates the most important results of the Lyapunov and Lagrange stability theory for a general class of dynamical systems by developing topics in a metric space independantly of equations, inequalities, or inclusions.
Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few.
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type.
Presents Real & Complex Analysis Together Using a Unified ApproachA two-semester course in analysis at the advanced undergraduate or first-year graduate levelUnlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together.
Functions of a Complex Variable provides all the material for a course on the theory of functions of a complex variable at the senior undergraduate and beginning graduate level.
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability.
More than ever before, complicated mathematical procedures are integral to the success and advancement of technology, engineering, and even industrial production.
Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions.
This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations.
With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures.
The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation.
With special emphasis on engineering and science applications, this textbook provides a mathematical introduction to the field of partial differential equations (PDEs).
Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems.
Bridging the gap between procedural mathematics that emphasizes calculations and conceptual mathematics that focuses on ideas, Mathematics: A Minimal Introduction presents an undergraduate-level introduction to pure mathematics and basic concepts of logic.
Offers Both Standard and Novel Approaches for the Modeling of SystemsExamines the Interesting Behavior of Particular Classes of ModelsChaotic Modelling and Simulation: Analysis of Chaotic Models, Attractors and Forms presents the main models developed by pioneers of chaos theory, along with new extensions and variations of these models.
