Differential calculus and equations

Although some examples of phase portraits of quadratic systems can already be found in the work of Poincare, the first paper dealing exclusively with these systems was published by Buchel in 1904.

This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications.

Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2.

This book discusses the mathematical simulation of biological systems, with a focus on the modeling of gene expression, gene regulatory networks and stem cell regeneration.

Addressing algebraic problems found in biomathematics and energy, Free and Moving Boundaries: Analysis, Simulation and Control discusses moving boundary and boundary control in systems described by partial differential equations (PDEs).

This book contains the papers presented at the ICM2002 Satellite Conference on Nonlinear Evolution Equations and Dynamical Systems.

**2025 Textbook and Academic Authors Association (TAA) McGuffey Longevity Award Winner**Introductory Differential Equations, Sixth Edition provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies.

This book is devoted to stochastic Navier-Stokes equations and more generally to stochasticity in fluid mechanics.

Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models.

The study of isoperimetric inequalities involves a fascinating interplay of analysis, geometry and the theory of partial differential equations.

In this book the authors show that it is possible to construct efficient computationally oriented models of multi-parameter complex systems by using asymptotic methods, which can, owing to their simplicity, be directly used for controlling processes arising in connection with composite material systems.

Nobel prize winner Ilya Prigogine writes in his preface: "e;Irreversibility is a challenge to mathematics.

The book includes theoretical and applied results of a generalization of the numerical method of lines.

This proceedings volume originates from a conference held in Herrnhut in June 2013.

In this fully-illustrated textbook, the author examines the spectral theory of self-adjoint elliptic operators.

Sparse grids are a popular tool for the numerical treatment of high-dimensional problems.

'An Introduction to Integral Transforms' is meant for students pursuing graduate and post graduate studies in Science and Engineering.

This book collects original research papers and survey articles presented at the International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), held at Delhi Technological University, India, on 23-25 October 2018.

Multivariate calculus, as traditionally presented, can overwhelm students who approach it directly from a one-variable calculus background.

This monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes.

This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincare and Darboux to basic tools of modern mathematics.

Second Order Differential Equations presents a classical piece of theory concerning hypergeometric special functions as solutions of second-order linear differential equations.

This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations.

This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes - non-orientable objects with a stratified structure.

This Research Note aims to provide an insight into recent developments in the theory of pattern formation.

This book discusses numerical methods for solving partial differential and integral equations, as well as ordinary differential and integral equations, involving fractional differential and integral operators.

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In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples.

This contributed volume presents some recent theoretical advances in mathematics and its applications in various areas of science and technology.

The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces.

This book provides a systematic and thorough overview of the classical bending members based on the theory for thin beams (shear-rigid) according to Euler-Bernoulli, and the theories for thick beams (shear-flexible) according to Timoshenko and Levinson.

Sparse grids are a popular tool for the numerical treatment of high-dimensional problems.

In this book we describe the basic principles, problems, and methods of cl- sical mechanics.

Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations.

This two-volume set presents combinatorial functional equations using an algebraic approach, and illustrates their applications in combinatorial maps, graphs, networks, etc.

This book not only presents essential material to understand fuzzy metric fixed point theory, but also enables the readers to appreciate the recent advancements made in this direction.

This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years.

Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods.

This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy, addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs).

This book provides analytical solutions to a number of classical problems in transport processes, i.

The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis.

This monograph presents  the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations.

Several distinctive aspects make Dynamical Systems unique, including:treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas through examples and at a level accessible to a beginning graduate student<

Since the publication of our first book [80], there has been a real resiu-gence of interest in the study of almost automorphic functions and their applications ([16, 17, 28, 29, 30, 31, 32, 40, 41, 42, 46, 51, 58, 74, 75, 77, 78, 79]).