Calculus of variations

This is based on the course 'Calculus of Variations' taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics.

The concept of equilibrium plays a central role in various applied sciences, such as physics (especially, mechanics), economics, engineering, transportation, sociology, chemistry, biology and other fields.

A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.

This is based on the course 'Calculus of Variations' taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics.

Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas.

A comprehensive guide to using energy principles and variational methods for solving problems in solid mechanics This book provides a systematic, highly practical introduction to the use of energy principles, traditional variational methods, and the finite element method for the solution of engineering problems involving bars, beams, torsion, plane elasticity, trusses, and plates.

This book introduces the concept of Polya property for holomorphic functions of two and several variables.

In this modern treatment of the topic, Rolland Trapp presents an accessible introduction to the topic of multivariable calculus, supplemented by the use of fully interactive three-dimensional graphics throughout the text.

This book deals with the new class of one-dimensional variational problems - the problems with branching solutions.

Mathematical control theory has evolved from the study of practical problems in engineering and sciences to the elaboration of deep, important concepts in mathematics and applied sciences.

Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.

This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.

The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form.

This monograph deals with cases where optimal control either does not exist or is not unique, cases where optimality conditions are insufficient of degenerate, or where extremum problems in the sense of Tikhonov and Hadamard are ill-posed, and other situations.

Optimal Control is a modern development of the calculus of variations and classical optimization theory.

An engaging graduate-level introduction that bridges analysis and geometry.

The book Sequences and Series in Calculus is designed as the first college/university calculus course for students who take and do well on the AP AB exam in high school and who are interested in a more proof-oriented treatment of calculus.

This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.

This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps.

The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form.

The book Sequences and Series in Calculus is designed as the first college/university calculus course for students who take and do well on the AP AB exam in high school and who are interested in a more proof-oriented treatment of calculus.

This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps.

An engaging graduate-level introduction that bridges analysis and geometry.

This monograph deals with problems of dynamical reconstruction of unknown variable characteristics (distributed or boundary disturbances, coefficients of operator etc.

In recent years, technological progress created a great need for complex mathematical models.

Philosophiæ Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy), often referred to as simply the Principia, is a work in three books by Isaac Newton, in Latin, first published 5 July 1687.

Fractional calculus has emerged as a powerful and effective mathematical tool in the study of several phenomena in science and engineering.

A comprehensive guide to using energy principles and variational methods for solving problems in solid mechanics This book provides a systematic, highly practical introduction to the use of energy principles, traditional variational methods, and the finite element method for the solution of engineering problems involving bars, beams, torsion, plane elasticity, trusses, and plates.

Calculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimal methods.

The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains.

This problem book contains exercises for courses in differential equations and calculus of variations at universities and technical institutes.

Fractional calculus has emerged as a powerful and effective mathematical tool in the study of several phenomena in science and engineering.

This hands-on guide is primarily intended to be used in undergraduate laboratories in the physical sciences and engineering.

A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.