The purpose of this course is to provide an introductory treatment of some mathematical concepts and techniques. It provides an introduction to the basic variety of numerical processes that enable them to obtain approximate but useful solutions to mathematical models relevant to real estate valuation and management. It will include Calculus: curve sketching in Cartesian and polar co ordinates. Fundamental Theorem.Integration by parts, partial fractions, reduction formulae.Improper integrals.Arc length, surface area, volume.Theorems of Pappus.Sequences and series.McLaurine series. Algebra: determinants. Solutions of systems of equations by reduction to echelon form.Linear transformations in two and three dimensions.Eigensystems.Reduction of the general conic equation to standard form. Multivariate Calculus: functions of several variables, surfaces in three dimensions, partial differentiation, Differentials, applications to small errors, implicit functions, chain rules. Taylor expansions, application to maxima and minima with and without constraints. Double and triple integrals, inversion of order, determination of limits of integration. Geometry: three dimensional coordinates geometry. Cartesian, cylindrical and spherical polar co ordinates.Vector geometry.Scalar and vector products, direction cosines.Geometry of lines and planes.Tangent and normal vectors.SerretFrenet formulae.The evolute.Projective transformations.
