Fundamentals of Mathematics

Course Code:6373, Course Title: Fundamentals of Mathematics Marks 100, 4 Credits, 60 Lectures Real Number System: Field and order properties, Natural numbers, Integers and rational numbers, Absolute value and their properties, Basic inequalities. Complex Number System: Field of Complex numbers, De Moivre's theorem and its applications. Theory of equations: Relations between roots and coefficients, Symmetric functions of roots, Sum of the powers of roots, Synthetic division, Des Cartes’ rule of signs, Multiplicity of roots, Transformation of equations. Matrices and Determinants:, Notion of matrix. Types of matrices. Algebra of matrices. Determinant function and its properties. Minors, Cofactors, expansion and evaluation of determinants. Elementary row and column operations and row-reduced echelon matrices. Invertible matrices. Diagonal, triangular and symmetric matrices. System of Linear Equations: System of linear equations (homogeneous and non-homogeneous ) and their solutions. Gaussian elimination, Application of matrices and determinants for solving system of linear equations. Applications of system of equations in real life problems. Vector Spaces: : Euclidean n-space. Real vector spaces. Subspaces. Linear combination of vectors. Linear dependence of vectors. Basis and dimension. Linear transformations. Matrix representation of linear transformation. Kernel and image. Eigenvalues and eigenvectors. Two-dimensional Geometry: Transformation of coordinates, Pair of straight lines (homogeneous second degree equations, general second degree equations representing pair of straight lines, angle between pair of straight lines, bisectors of angle between pair of straight lines), General equations of second degree (reduction to standard forms, identifications, properties and tracing of conics).
 Three-dimensional Geometry: Three-dimensional coordinates, Distance, Direction cosines and direction ratios. Planes and straight lines. Vectors in plane and space. Algebra of vectors. Scalar and vector product. Vector equations of straight lines and planes.Evaluation: Final examination (Theory, 4 hours): 100 marks. Ten questions will be set, of which any six are to be answered. Books Recommended : 1.S. Bernard & J M Child- Higher algebra. 2.Howard Anton & Chris Rorres – Elementary Linear Algebra with Application. 3.Khosh Mohammad- Analytic Geometry and Vector Analysis. 4.Md. Abdur Rahman – Linear Algebra.