Department of Physics

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.