Read the linear algebra chapters until you understand change of basis and eigenvectors. Then, read the vector analysis chapter on directional derivatives. Notice: the gradient is a linear combination of basis vectors.
A solid resource starts with the definition of vector spaces, subspaces, and basis. Understanding —how one vector is mapped to another—is the "engine" of linear algebra. 2. Matrices and Determinants linear algebra and vector analysis pdf
Re-prove Green’s theorem using matrix determinants. Show that Stokes’ theorem is a coordinate-invariant statement, relying on the fact that the curl transforms as a pseudovector under orthogonal transformations (a linear algebra concept). Read the linear algebra chapters until you understand
For scalar field $f(x,y,z)$: $$\nabla f = \left( \frac\partial f\partial x, \frac\partial f\partial y, \frac\partial f\partial z \right)$$ Points in direction of greatest increase of $f$. A solid resource starts with the definition of
Take a PDF that includes code (like Robinson’s). Write a Python script to: