Multiple integration 1

Evaluate double and triple integrals and apply them to the determination of the areas of plane figures and the volumes of solids Understand the role of the differential of a function of two or more real variables Determine exact differentials in two real variables and their integrals Evaluate the area enclosed by a closed curve by contour integration Evaluate line integrals and appreciate their properties Evaluate line integrals around closed curves within a simply connected region Link line integrals to integrals along the x-axis Link line integrals to integrals along a contour given in parametric form Discuss the dependence of a line integral between two points on the path of integration Determine exact differentials in three real variables and their integrals Demonstrate the validity and use of Green’s theorem