: Mapping and transformations in 3D space.

Stress and strain are rank-2 tensors. The equilibrium equations (( \nabla \cdot \boldsymbol{\sigma} = \mathbf{0} )) are vector-tensor equations. Differential geometry appears when modeling shells (thin curved surfaces).

"Tensor and Vector Analysis: With Applications to Differential Geometry" by C.E. Springer It is highly regarded because: Bridge to Modern Math

: Differential Geometry and Tensor Calculus by Naveen Durvasula.

Path planning on curved surfaces (e.g., a robot moving on a sphere or a car driving on hilly terrain) requires geodesic equations—a direct application of tensor calculus and differential geometry.