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...Part ia vector calculus based on lectures by b allanach notes taken dexter chua lent these are not endorsed the lecturers and i have modied them often signicantly after they nowhere near accurate representations of what was actually lectured in particular all errors almost surely mine curves r parameterised arc length tangents normals to radius curvature integration line integrals surface volume denitions examples using cartesian cylindrical spherical coordinates change variables operators directional derivatives gradient a real valued function denition interpretation as normal level surfaces including use general orthogonal curvilinear divergence curl formulae for oper ators statement only solenoidal elds irrotational conservative scalar potentials derivative identities theorems theorem green s stokes second statements informal proofs application uid dynamics electro magnetism maxwell equations laplace equation uniqueness maximum principle solution poisson gauss method symmetry an int...