Rectangular (Cartesian) coordinates in a three-dimensional system. Distance, midpoint, spheres and cylindrical surfaces. Factors in two- and three-dimensional spaces. Do product, projections, cross product. Parametric equation of lines in two- and three- dimensional spaces. Planes in a three-dimensional space. Quadric surfaces. Cylindrical and spherical coordinate systems. Graphs. Conversion between rectangular, cylindrical and spherical coordinates. Vector values functions. Graphs, limits, derivatives, integrals. Change of parameter. Arc length. Unit tangent and unit normal vectors. Curvature. Motion along a curve. Divergence and curl. Functions of two or more variables, limits and continuity, partial derivatives, differentiability and chain rule, tangent plane, total differential, directional derivatives and gradients of functions of two variables and three variables, maxima and minima, Lagrange multipliers. Double integrals including over non rectangular regions and polar coordinates, parametric surfaces, surface area.
Contact hours:
5 lectures/tutorials per week.Assessment:
2 tests (25%), 3 or 4 assignments (15%) and final exam (60%).Prerequisite: 1.20802
Text:
Anton, H., Bivens, I. & Davis, S., 2002, Calculus, 7th Edition, John Wiley, New York