A diagrammatic view of differential equations in physics

<abstract><p>Presenting systems of differential equations in the form diagrams has become common certain parts physics, especially electromagnetism and computational physics. In this work, we aim to put such use on a firm mathematical footing, while also systematizing broadly applicable framework reason formally about their solutions. Our main tools are category-theoretic diagrams, which well known, morphisms between have been less appreciated. As an application diagrammatic framework, show how complex, multiphysical can be modularly constructed from basic physical principles. A wealth examples, drawn electromagnetism, transport phenomena, fluid mechanics, other fields, is included.</p></abstract>