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Exterior Differential Systems

Exterior Differential Systems

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Δημοσιεύθηκε 3 Μαι 2009

This book gives a treatment of exterior differential systems. It will include both the general theory and various applications.

An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i.e., submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems.

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Differential Equations

Differential Equations

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Paul Dawkins

Δημοσιεύθηκε 8 Μαρ 2009

Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my “class notes” they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher on differential equations.

I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from a Calculus or Algebra class or contained in other sections of the notes.

Paul Dawkins

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Ordinary Differential Equations

Ordinary Differential Equations

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Peter R. Wolenski

Δημοσιεύθηκε 24 Νοε 2006

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Lecture Notes for Partial Differential Equations
Differential Equations of Mathematical Physics
Hilbert Space Methods for Partial Differential Equations

Hilbert Space Methods for Partial Differential Equations

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R. E. Showalter

Δημοσιεύθηκε 24 Νοε 2006

This book is an outgrowth of a course which we have given almost periodically over the last eight years.

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Partial Differential Equations
Difference Equations to Differential Equations
Notes on Differential Equations
Linear Partial Differential Equations and Fourier Theory