School of Science
Department of Physics
ΥΚΟ12
10ΥΚΟ12 Analysis II and Applications
Course webpage: https://eclass.uoa.gr/courses/ΜΑΤΗ147
Course outline
Course content
- Vectors. Vector functions on the plane and in space. Inner and outer product. Lines. Planes. Surfaces. Arc length. Unit tangent vector. Multivariable functions. Derivatives. Limit. Continuity.
- Partial derivatives. Chain differentiation. Directional derivative. Gradient vectors. Tangent planes. Linearization. Differentials. Extrema. Saddle points.
- Lagrange multipliers. Partial derivatives of functions under constraints. Taylor’s theorem for multivariable functions.
- Curvilinear coordinate systems. Norm. Gradient. Divergence. Curl.
- Multiple (double, triple) integrals, in cartesian and other coordinates. Applications to the evaluation of areas, moments of inertia, centers of mass. Change of variables (jacobian determinant).
- Integration of vector fields. Line and surface integrals. Path independence. Potential functions and conservative fields. Green’s, Gauss’s, Stokes’ theorems and applications.