In this course we will cover 

Vector Algebra: Scalars and vectors; types of vectors; addition and subtraction; multiplication and division by a scalar; position vector of point of division, scalar (or dot) product; vector (or cross) product scalar triple product; vector triple product; vector product of vectors; reciprocal vector triads; applications of vector algebra.              

Vector Calculus: Differential vector calculus; applications of differential geometry and mechanics; Integral calculus; Riemann, line, vector line, double, surface and volume.  Gradient of a scalar function;Divergence of a vector; curl of a vector. Stoke’s and Green’s theorems:  orthogonal curvilinear coordinates.