The first part covers multiple integrals and vector calculus. Topics covered include: double and triple integrals, surface area, multiple integrals in polar, cylindrical and spherical coordinates, general coordinate transformations (Jacobians), Taylor series in two variables, line and surface integrals, parametric surfaces, Green's theorem, the divergence and Stokes's theorems. The second part provides a general introduction to the principles of continuum fluid mechanics. The basic conservation laws are derived in both differential and integral forms using different fluid models, and the link between the two is demonstrated. Applications covered include: dimensional analysis, hydrostatics, flow visualization, incompressible and compressible frictionless flows, the speed of sound, the momentum principle, viscous flows and selected examples of real fluid flows. The students conduct two hands-on laboratory experiments involving microfluidics and flow visualization, which complement the fluid mechanics lectures and experience technical report writing.