Calculus in several variables

Main course components: <br> \- Basic topological concepts: open, closed and compact sets<br> \- Functions of several variables with limits and continuity, partial derivatives, the chain rule, directional derivatives and gradients, tangent planes, Jacobian matrices and Jacobian determinants. <br> \- Coordinate transformations, simple partial differential equations. <br> \- Taylor polynomials in several variables. <br> \- Extreme values: classifying critical points, local and global extreme values, the method of Lagrange multipliers. <br> \- Double and triple integrals: iterated integration, change of variables with polar, cylindrical and spherical coordinates, generalized integrals <br> \- Geometrical and physical applications: area of curved surface, volume, mass and centre of mass <br> \- Vector fields, conservative vector fields, potentials <br> \- Divergence and rotation operators, nabla operator <br> \- Line integrals, surface integrals, flux integrals <br> \- Green's formula, Gauss' divergence theorem, Stokes' theorem.