MA-154 Mathematics 1, Mathematics 2 or equivalent.
Conic section and quadratic curves, polar coordinates. Vectors, lines and planes in three dimensions, cylinders and quadratic surfaces. Two and three dimensional position vectors, tangent and normal vectors. Newton's laws, particle motion in the gravitational field, planet and satellite motion. Double and triple integrals. Area, substance, momentum and radius of inertia. Cylindrical and spherical coordinates. Curve, surface and volume integrals of scalar and vector functions. Work, circulation and flux. Divergence and curl. The theorems of Green, Stokes and Gauss. Fourier series: sine series and cosine series. Solving partial differential equation by means of power series and Fourier series.
After completing the course, the student is expected to be able to:
characterise the properties with quadratic curves and surfaces
master vector multiplications and applications associated with lines and planes
put up and solve equations for motion of particles and bodies in the gravitational field
master curve, surface and volume integrals in different systems of coordinates
calculate work, circulation and flux
apply the theorems of Green, Stokes and Gauss
solve differential equations by means of power series and Fourier series
Teaching methods and workload
Lectures and exercises, and group work.
The study programme manager, in consultation with the student representative, decides the method of evaluation and whether the courses will have a midterm- or end of term evaluation, see also the Quality System, section 4.1. Information about evaluation method for the course will be posted on Canvas.