Syllabus
Integration of functions of several variables
Double and triple integral (definition, evaluation using Fubini´s theorem in various coordinates, applications). Integration of the first kind along curves and surfaces. Integration of the second kind along curves and surfaces (conservative fields, circulation of the vector field along the curve, the flow of a vector, conservation laws).
Operators
Physical meaning and definition of grad, div, rot and Laplace operator. Gauss´s and Stokes´s theorem including thein main applications. The explicit form of the operators in curvilinear coordinates (Lamé coefficients). Several illustrations taken from the electromagnetic theory.
Tensors
The transformation matrix for a rotation, relations of orthogonality and transforming a vector. Definitions of a scalar, vector and tensor using transformation properties of their components. Physical applications (the tensor of inertia).
Annotation
The subject focuses on the explanation and exercising of various mathematical methods used in the introductory physics course. Practical applications and strategies needed to solve particular physical problems are emphasized.