Differential Equations – Mathematical Association of America

Featured Resources

How do you respond when you are asked to use your expertise to help your nation?

By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social In the 1940s, American mathematicians faced that question. (Enough said “yes” to create the atomic bomb. These can be hard questions, with overwhelming consequences.) Post-9/11/2001, I (as a freshly naturalized American) found myself pondering the same question. Now, as a retiree, my younger American colleagues are likely going to face that question...

Lighting the EMBER: A New Initiative to Transform Introductory Mathematics

By Dave Kung Change is hard, especially for us humans. As much as we want to believe that we evaluate options on their merits, the truth is that we are deeply conservative (small “c”), regularly defaulting to the status quo. Change at scale is even harder. Policy experts posit that real tectonic plate shifts require...

Fast Track to Differential Equations

Fast Track to Differential Equations fits squarely within a long tradition of accessible introductions to applied mathematics, and it sets itself apart through a steady emphasis on why solutions work instead of how to compute them. I found this focus surprisingly refreshing. Many introductory texts rely heavily on symbolic routines, but this volume slows the...

Bifurcation Theory

Bifurcation theory is a component of the study of dynamical systems that analyzes the changes in dynamics that occur when there is a qualitative change of behavior arising from varying parameters. Poincaré introduced the term bifurcation in the late nineteenth century to mean the splitting of equilibria for a family of differential equations. A great...

Introduction to Differential Equations

There are a very large number of introductory differential equations textbooks on the market, and they largely cover the same topics. So the task of the reviewer is to explain how the book under review is different, and what the potential audience is. The main difference is that the book assumes a higher level of...

Delay Differential Equations and Applications to Biology

The second part of the book includes applications and examples of delay differential equations in six areas of biology. Three of these describe models for the spread of disease (including Hepatitis C and Covid19), two treat ecological models, and one describes a model of the interaction between tumors and the immune system. One of the...

Differential Equations: A Toolbox for Modeling the World

This textbook was written for a first course in ordinary differential equations for undergraduate students pursuing majors in mathematics, engineering, and science. The approach of the book is to use real-world phenomena to construct mathematical models based on differential equations in such a way that undergraduate students are motivated to learn the material and understand the usefulness of...

Cover of the book "Differential Equations: A Toolbox for Modeling the World" by Kurt Bryan. The background features a soft, watercolor-style blend of green and white. A hand-drawn spiral graph is overlaid in the center, marked with equations and labeled axes, representing mathematical modeling.

Partial Differential Equations

The book under review, Partial Differential Equations : Methods, Applications and Theories is intended for a university-level course on PDEs. It contains 12 chapters which can be covered in a one semester course. It is intended to present the main tools used in PDEs in view of studying more advanced subjects from other disciplines. Within the 12 chapters,...

Cover of the book "Partial Differential Equations: Methods, Applications and Theories (Second Edition)" by Harumi Hattori. The background is red with a grid design and features a 3D plot graphic of a geometric surface labeled with x-axis, y-axis, and z-axis. The title is in bold white and yellow text, and the publisher "World Scientific" is displayed at the bottom.

Differential Equations: Techniques, Theory, and Applications

This book can serve as a textbook for various types of introductory differential equations courses. As the title suggests, there is a balance between theory, techniques and applications (of which there are many in this book!). A large number of problems and applications are in the life sciences in addition to the physical sciences. The tone is more conversational...

Differential Equations: A Modern Approach with Wavelets

The author describes this book as a mixture of differential equations, Fourier analysis, and applications with equal weight. Fourier analysis is construed broadly to include wavelets. The introduction to students tells them that the book’s purpose is to teach the interrelationships between these topics. The book is intended for a broad audience including mathematics, engineering...

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

This book is meant to serve as a textbook for a basic introductory course in differential equations. It has many non-standard topics, which makes it quite unique within the sea of differential equations textbooks. The classical topics are covered (e.g. first order equations, exact equations, second order equations, etc.), but they are covered with more...

Cover of the textbook "Differential Equations" by Shair Ahmad and Antonio Ambrosetti, published by De Gruyter. The subtitle reads "A First Course on ODE and a Brief Introduction to PDE." The cover features a dynamic illustration of fluid-like blue lines forming swirls and circular patterns, representing the flow of differential equations.

Extrinsic Geometric Flows

This textbook, written by four experts in the field offers an authoritative introduction and overview to the topic of extrinsic geometric flows. It will serve well as a primary text for a graduate student who already has background knowledge of differential geometry and (some) partial differential equations. It will also serve as a useful reference...