  One of the hurdles in teaching undergraduate thermodynamics is a plethora of
complicated partial derivative identities. Students suffer from difficulties in
deriving, justifying, or interpreting the identities, misconceptions about
partial derivatives, and a lack of in-depth understanding of the meanings of
identities. We propose a novel diagrammatic method for the calculus of
differentials and partial derivatives called the "sunray diagram" that resolves
the difficulties above. The sunray diagram technique relates a partial
derivative with "arrow sliding," which enables an aesthetic and intuitive
manipulation of partial derivative expressions in the form of successive arrow
slidings. Furthermore, the sunray diagram is more than an ad hoc or abstract
machinery but is based on the symplectic structure of thermodynamics; the
sunray diagram admits a direct physical interpretation on the P-V (or T-S)
plane. We elaborate on such physical semantics of the sunray diagram by taking
Maxwell's approach to the geometry of thermodynamic structures--reinterpreted
in terms of differential geometry--as a reference point. We anticipate that our
discussion introduces the geometry of thermodynamics to learners and enriches
the graphical pedagogy in physics education.
