Course Descriptions

Matrices, matrix addition, matrix and scalar multiplication, algebraic properties of matrix operations, special types of matrices, solving linear systems, elementary row and column operations, echelon form of a matrix, Gauss and Gauss-Jordan method, elementary matrices and finding the inverse of a matrix by using elementary operations, real vector spaces, definition, subspaces, span and linear independence, basis and dimensions, homogeneous systems, rank of a matrix, linear spaces with inner product, definition of the inner product, Gram-Schmidt process, orthogonal complements, linear transformation and their matrix representations, kernel and range of a linear transformation, matrix of a linear transformation, determinants, definition and properties of determinants, cofactor expansion, finding inverses by using cofactors, eigenvalues and eigenvectors, characteristic polynomial and equation of a matrix, eigenvalues and eigenvectors, diagonalization of symmetric matrices.

Basic definitions, first order differential equations, second order linear differential equations with constant coefficients. Systems of first order linear differential equations with constant coefficients, Laplace transforms and its applications to linear differential systems. Linear differential equations with variable coefficients, series solutions of second-order linear differential equations.

Introduction, samples, populations, and the role of probability. Sample mean, median, range and standard deviation. Graphical plots. Probability, sample space, events, Venn diagram, multiplication rule, permutation, and combination. Probability of an event, conditional probability, Bayes’ rule. Discrete and continuous data. Random variables, discrete and continuous probability distributions, joint probability distributions. Mathematical expectations. Mean, variance, covariance and correlation of random variables. Some continuous and discrete probability distributions. Normal distribution, area under the Normal Curve and its applications. Fundamental sampling distributions, central limit theorem. Estimation. Maximum likelihood estimation. Testing a statistical hypothesis. Simple linear regression and correlation coefficient.