This course introduces the student to complex and the manipulation of complex numbers.
Introduction to Algebra: Brief history of numbers; Natural numbers and real numbers: Principle of mathematical induction.
Complex Numbers: Definitions; Addition, multiplication , division; plane geometry of complex numbers; polar forms; de Moivre’s theorem extraction of roots; Elementary functions of complex variable; Application to trigonometry.
Vector Algebra and Application: Vector space; Linear independence; Basis and dimension. Geometrical vectors; Cartesian basis; Scalar product and its properties; vector triple product and its properties.
Applications: Equation of a straight line in various forms; Equation of a plane in various forms; intersection of lines in space and related kinematic problems; skewed lines. Matrix Algebra: Definition; Matrix operations and properties.
Definition of determinant and properties; inverse and methods of computation; Application to the solution of system of linear equations. Gaussian elimination, consistency. Eigen value problem; Diagonilization of symmetric matrix.