Direction of steepest ascent, perpendicularity to level curves, magnitude as rate of change.
Analysis IISources and sinks, infinitesimal flux, and the connection to the divergence theorem.
Analysis IIRotation and circulation, the paddle wheel test, and Stokes' theorem connection.
Analysis IILine integrals equal area integrals — verify numerically with interactive closed curves.
Analysis IISurface integrals of curl equal line integrals around the boundary.
Analysis IIVolume integrals of divergence equal surface flux — Gauss's theorem in action.
Analysis IIDeformable bodies, normal & shear strains, principal strains, Mohr's circle, volumetric/deviatoric decomposition.
MechanicsCauchy stress, traction vectors, normal & shear stresses, principal stresses, Mohr's circle, hydrostatic/deviatoric decomposition, von Mises.
MechanicsHooke's law: stress ↔ strain via compliance & stiffness matrices. Young's modulus, Poisson's ratio, plane stress/strain.
MechanicsCurrent & charge, circuits, Ohm's law, Kirchhoff's laws, power, resistivity, exercises with solutions.
PhysicsE-Felder, Gauss, Potential, Coulomb, Kondensatoren, Ladevorgang, Dielektrikum, Kraft & Energie, Fluss.
PhysicsMagnetismus, Induktion, Wechselstrom
Physics