University of Iceland

This course is a continuation of Ritmál II. Students gain greater proficiency in Kanji and Katakana, as well as improving reading and writing skills in Japanese.

This course is a continuation of Málnotkun (Language Use) II. Students who took Málnotkun I and II can take Málnotkun III to continue their study. The main focus in Japanese Language III is going over the beginners level grammar not covered in previous courses, as well as increasing the students' vocabulary. There are regular quizzes, and students are expected to do considerable amount of preparation and homework. Regular attendance is crucial to follow the course.

The course is an introduction to three important tools of applied mathematics, namely ordinary differential equations, Fourier-series, and partial differential equations. Some basic theoretical properties are proved and solution methods presented. Ordinary differential equations: linear differential equations of order n, the Cauchy problem, Picard's existence theorem, solution by power series and equations with singular points.  Fourier series: convergence point-wise, uniformly and in the mean-square, Parseval's equation. Partial differential equations: the heat equation and the wave equation solved on a finite interval by separation of variables and Fourier series and their solutions compared, the Dirichlet problem for the Laplace equation on the rectangle and the disc, the Poisson integral formula.

The course covers cities, towns, villages, and farming communities in a world of globalization. It will emphasize the mobility of people, money, products, and information which has transformed the logic, delimitation, and relations between urban and rural communities in different countries. Major theories on the interplay between culture and structure are covered as well as the societal and technological changes which have reconstructed urban-rural distinctions and interconnections. Special attention is given to patterns of migration within and between countries and their effects on the development of different settlements.

The course is an introduction to three important tools of applied mathematics, namely ordinary differential equations, Fourier-series, and partial differential equations.  Some basic theoretical properties are proved and solution methods presented. Ordinary differential equations: linear differential equations of order n, the Cauchy problem, Picard's existence theorem, solution by power series and equations with singular points.  Fourier series: convergence point-wise, uniformly and in the mean-square, Parseval's equation. Partial differential equations: the heat equation and the wave equation solved on a finite interval by separation of variables and Fourier series and their solutions compared, the Dirichlet problem for the Laplace equation on the rectangle and the disc, the Poisson integral formula.

The course covers the following topics. Newtonian dynamics of a particle in various coordinate systems. Harmonic, damped, and forced oscillations of a pendulum. Nonlinear oscillations and chaos. Gravitation and tidal forces. Calculus of variations. Lagrangian and Hamiltonian dynamics, generalized coordinates and constraints. Central force motion and planetary orbits. Dynamics of a system of particles, collisions in a center-of-mass coordinate system and in a lab system. Motion in a non-inertial reference frame, Coriolis and centrifugal forces. Motion relative to the Earth. Mechanics of rigid bodies, inertia tensors and principal axes of inertia. Eulerian angles, and Euler's equations for a rigid body. Precession, motion of a symmetric top and stability of rigid body rotations. Coupled oscillations, eigenfrequencies and normal modes.

This is a beginners’ course in Icelandic. The focus is on the basic features of language use and grammar. Students also gain some insight into Icelandic culture and society. Students gain practice through language tasks relating to daily life. The course is a combination of classroom study (lectures and assignments) and self study. Active participation is required.