Partial Differential Equations – Mathematical Association of America

Featured Resources

How Internships Helped Me Find My Path

By Jocelyn Ornelas-Munoz Throughout graduate school, I’ve been told repeatedly, “Focus on your research.” While I agree that graduate school is a time of deep academic exploration, it’s also a stepping stone to broader career opportunities and professional growth. One of the most valuable—and even life-changing—experiences of my PhD was participating in summer internships. These...

Calculus for Teachers: The Fundamental Theorem of Integral Calculus

By David Bressoud @dbressoud As of 2024, new Launchings columns appear on the third Tuesday of the month. The first step is to turn the definite integral into a function. This can be done by turning the upper limit into a variable, Since this is a function, one can seek to differentiate it. This tells...

Introduction to Traveling Waves

The authors wrote this book to provide students with enough background to study traveling waves and simultaneously enable them to develop some research experience of their own in that area. They had found that very little published material on traveling waves was accessible to students at the undergraduate and masters level. Accordingly, they prepared a...

Invitation to Partial Differential Equations

This text offers an introduction to linear partial differential equations (PDEs) with topics that include classical and modern approaches. It is based on notes for a course the author gave at Moscow State University. He worked for several years to finish a book derived from that course, but he died before it was completed. His...

Maximal Function Methods for Sobolev Spaces

This book concerns maximal functions and their use in the theory of Sobolev spaces and partial differential equations. Maximal functions have well-known uses in harmonic analysis and function theory, but their use in Sobolev-type inequalities and estimates is less familiar, which provides the motivation for this work. This book makes a valuable and expansive contribution...

Partial Differential Equations in Action

This is the fourth edition of a book whose third edition was reviewed here. Much of the book remains the same, but there has been some re-ordering of topics and a few additions. The treatment of first-order equations has been supplemented by additional discussion of complete, general, and singular solutions. Later on, a treatment of the...

Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs

This is the second edition of a book first reviewed here. It continues to be a very attractive text. Its subject is at the crossroads of an amazing collection of mathematical areas including partial differential equations, elliptic curves, and the algebra of differential operators, as well as striking applications in science and engineering. All of this...

Differential Equations: A First Course on ODE and a Brief Introduction to PDE

This is the second edition of a book previously reviewed here. The preface to the new edition suggests that the first edition might have been rushed into publication because of the pandemic. The goals in the new edition include the usual correction of errors and misprints, as well as inclusion of new examples and exercises,...

Cover of "Differential Equations" by Antonio Ambrosetti and Shair Ahmad, 2nd edition, with abstract wave-like patterns.

Shock Waves

The aim of this book is to present the fundamentals of shock wave theory. In most respects this is a subject within the scope of partial differential equations, but this text goes well beyond the standard theory. Stokes and Riemann were pioneers in this area. Their efforts, as with much of the succeeding work, were...

Partial Differential Equations

James Kennedy has translated the textbook Partial Differential Equations by Wolfgang Arendt and Karsten Urban from German into English. Are there so few PDE textbooks in English that it is worth translating a German PDE text? There are indeed many PDE textbooks, particularly in English, but hardly any that present analytic and numerical methods on an equal...

Analytical Methods for Solving Nonlinear Partial Differential Equations

An introductory course in differential equations can easily give students the false impression that all differential equations have closed-form solutions. After all, all the differential equations given in homework assignments do have closed-form solutions. An instructor can say that this is not the norm, but homework assignments speak louder than words. A more advanced course...

Book Cover of Analytical Methods for Solving Nonlinear Partial Differential Equations ...

Accuracy of Mathematical Models: Dimension Reduction, Homogenization, and Simplification

Unambiguous determination of the accuracy and reliability of mathematical models is a complex problem, very difficult without the kind of complete quantitative verification that is rarely possible. Even when experimental data are compared to the results of a computation based on a mathematical model, differences can arise that are not due to the model itself,...