The word dimension means the number of pieces of information required to identify a point in the space under consideration. For example, your eyes have three types of cones, sensitive to red, green and blue lights, and these three combine in various intensities to make the colors that we see. Thus the world of colors is three-dimensional. In the first course on Calculus, we consider one or two dimensional objects, with functions of one variable that can be visualized as graphs in the plane. We continue the study of Calculus by considering functions that are defined parametrically and then functions of 2 or more variables and vector valued functions. The themes remain the same (quadrature, optimisation, linearization), but visualising what is going on is more complicated. We will make use of the computer algebra system Sage to assist us in gaining intuition and for mechanical computations. This will get you started on a handy tool to use in understanding the new mathematics that you learn in the future. The course is expected to be extremely useful if you study Physics, Chemistry, Computer Science, and of course, Mathematics.
Syllabus: Review of vectors and matrices. Curves and surfaces. Partial derivatives. Maximum and minimum values. Double integrals. Line integrals in the plane. Green’s theorem. Triple integrals and surface integrals in 3-space. Stoke’s theorem. Applications of multivariable calculus.