Learning Outcomes
Upon successful completion of this course, the students will:
1) Understand the concept of vector / vector functions
2) Understand and apply the operations among vectors and vector functions, their derivatives and integrals
3) To know and use the applications of vectors to solve problems
Course Content (Syllabus)
Vectors in three dimensional space. Product of vectors (scalar, vector and triple) with applications to analytic geometry. Vector functions of one variable (limits, continuity, differentiation, integration). Theory of curves in the three dimensional space (tangent, perpendicular plane). Vector functions of several variables (limits, continuity, partial derivatives, total differential). Scalar and vector fields (gradient, divergence, rotation). Differentiation of scalar field along a curve and direction. Theory of surfaces (curvilinear coordinates, tangent plane and vertical vector). Line integrals of vector fields (properties, conservative fields and potential function, Green’s theorem). Line integrals of scalar fields. Area of surfaces (in Cartesian and curvilinear coordinates). Surface integrals of scalar and vector fields. Applications.
Keywords
Vectors, Scalar and vector fiends, surface, Line and surface integrals