Humanities Course Description

Introduction to real numbers, fractions, powers, roots, exponentials, and logarithms; use of calculator. Simple polynomials, synthetic division and factorization, quadratic equation formula; simple permutations and combinations. Introduction to rectangular coordinates, distance and midpoint formulas; equation of a straight line, graph and application. Introduction to matrices and determinants; cofactors and matrix inversion; solution of system of linear equations by row operations, Cramer’s rule and matrix inversion. Introduction to finance mathematics; interest laws and application to payment computation, annuities and cost-benefits analysis.

 

Algebra:

Review: arithmetic operations and use of calculators; evaluation of powers, roots exponential and logs. Simple equations and inequalities in one and two variables; equation of a straight line, slope –intercept form and linear programming ; business applications. Introduction to matrices, determinants and basic mathematical operations; solution of system of linear equations by simple row operations, Cramer’s rule and matrix inversion; application to business problems.

Financial Mathematics:

Introduction, simple and compound interest laws; payment computation and annuity.

Calculus:

Introduction to functions , graphs , limit and continuity; average rate of change, derivative and basic laws of differentiation; instantaneous rate of change , concavity , maxima , minima , point of inflection and business applications. Integral as antidervative , basic formulas and methods of integration. Definite integral as area under the curve, area of simple figures ,mean values and numerical integration; application to business problem.

Prerequisite: QT 102

 

Introduction to statistical data, data collection and sampling techniques; frequency distribution and graphical representation, measures of central tendency, variation, skewness and kurtosis. Introduction to permutations and combinations; sets and probability, basic laws, simple, combined and conditional probabilities. Introduction to random variables and probability distributions; binomial poisson, and normal distributions and applications. Sampling distributions, estimation of parameters, testing of hypothesis and goodness of fit. Simple linear regression and correlation. Use of statistical tables. Prerequisite: QT 201

 

Algebra

Real numbers, powers, roots, basic laws of exponentials, logs and numerical computation; introduction to complex numbers and simple mathematical operations. Introduction to polynomial functions, graphs and solution of linear equations; second degree polynomials, graphs and factorization; solution of quadratic equations by factorization, basic formula, graph and nature of roots; simultaneous equations. Introduction to matrixes and determinants, simple mathematical operations, minors, cofactors and matrix inversion; system of linear equations and Cramer rule. Sequences and series; AP, GP and HP series, main properties and numerical problems. Simple permutations and combinations , binomial theorem and approximation; Simple partial fractions involving linear, repeated and quadratic factors.

Trigonometry

Introduction to angle in radians; relation and numerical problems. Trigonometric rations, mutual relations and simple identities; variation in four quadrants and graphs; application to height and distance problem. Sum, difference product, double and half angle formulas of T-ratios; area, sine and cosine formulas of a triangle.

Basic Mathematics: Complex numbers, rectangular, polar and exponential forms, simple mathematical operations, Demoivre’s theorem, powers and roots. Polynomials functions, remainder theorem, synthetic division, factorization and determinations of roots. Simple functions, standard curves, graphs and main properties.

Differential Calculus limit. continuity, derivatives and basic laws of differentiation; simple application to tangent, normal, velocity, acceleration, maxima, minima; Taylor and Maclaurin’s series and. approximation.

Integral Calculus: Integral as anti -derivative, basic formulas; Methods of integration, definite integral as limit of a sum; application to area of plane figures and volume of simple solids of revolution.

Prerequisite QT 101.

Vectors in two and three dimensions, dot and cross products, equations of line and plane. Multivariable functions, partial derivatives and differentials. Introduction to ordinary differential equations, simple first order differential equations, second order differential equations with constant coefficients and method of undetermined coefficients. Prerequisite QT 104

Nonlinear equations and solution by Iterative, Newton Raphson, Regula-Falsi and Secant Methods; systems of linear equations, row operation, solution by Gauss, Jordan, Jacobi, Seidel and Crouts methods and matrix inversion; eigen values and vectors. Introduction to finite differences, interpolation by Gregory Newton Lagrange and divided difference formulas; curve fitting by method of least square and application. Numerical differentiation; integration by Trepizidal, Sympson and Gauss rules. Solution of ordinary differential equations by Euler methods.

Prerequisite: QT105

Introduction to statistical data, data collection and sampling techniques; frequency distribution and graphical representation, measures of central tendency, variation, skewness and kurtosis. Introduction to permutations and combinations; sets and probability, basic laws, simple, combined and conditional probabilities. Introduction to random variables and probability distributions; binomial poisson, and normal distributions and applications. Sampling distributions, estimation of parameters, testing of hypothesis and goodness of fit. Simple linear regression and correlation. Use of statistical tables.

Differential Calculus

Introduction to functions, graphs, limits and continuity. Derivatives as a limit , Basic laws of differentiation, chain rule and implicit differentiation. Derivative as a slope and as a rate of change; tangent and normal, critical points, maxima, minima and point of inflection; optimization. Taylor and Maclaurin series and convergence, L’ Hopital rule and mean value theorem.

Integral Calculus

Integral as anti-derivative, basic formulas and tables, indefinite and definite integrals. Methods of integration: substitution, by parts and partial fractions. Definite integral as limit of a sum, application to area, mean values and volume of solids of revolution. Polar coordinates, simple curves, graphs and area of plane figures ; parametric curves, arc length and surface of a solid of revolution.

Introduction to multivariable functions, partial derivatives and differentials.

Pre-Requisite: Pre-Engg Maths

Introduction to complex numbers, geometrical representation and simple mathematical operations; polar and exponential forms, DeMoivre’s theorem, powers and roots.

Introduction to matrices and determinants , simple mathematical operations and special matrices. Simple row operations; Gauss elimination , echelon form , rank, linear independence and system of linear equation ; Gauss-Jordan elimination , matrix inversion and Cramer rule. Vector spaces, basis and dimensions; inner products, Gram- Schmidt process and orthogonalization; eigen values and vectors .

Vectors in space, dot and cross products; physical and geometrical application; equations of lines and planes; curves in space and length of arc; simple surfaces.

Pre-Requisite: MS 1303 Calculus

Introduction to ordinary linear differential equations: formulation, order, degree and linearity of differential equation. First order differential equations; second order homogenous and non homogenous differential equations with constant coefficients, complimentary, particular solutions and method of undetermined coefficients; variation of parameters and Cauchy-Euler differential equation; initial- and boundary-value problems; solution in series. Introduction to Laplace transformation; Laplace transform of simple functions and tables; Laplace inversion by partial fractions and convolution , application to initial value problems. Introduction to unit step and delta functions, Laplace transform of discontinuous, periodic and discrete phenomena.

Introduction; periodic functions and Fourier series; half range Fourier series, Fourier integrals and transforms of simple functions. Introduction to partial differential equations and method of separation of variables.

Pre-Requisite: MS-1303 Calculus

Complex variable

Complex variable and functions; analytic functions , Cauchy-Riemann equations, derivatives, orthogonal and harmonic properties of conjugate functions. Introduction to Complex integration: Cauchy integral theorem, Cauchy integral formula, poles , residues and residue theorem; contour integration; improper integrals.

Multivariable Calculus

Introduction to Multivariable integration; evaluation of area and volume of simple geometrical figures. Scalar and vector fields; Del operator, gradient, divergence, curl and laplacian; vector differential calculus. Line, surface and volume integrals; Green, Stokes and Gauss theorems. Simple applications.

Pre-Requisite: MS 1302 Linear Algebra

MS 2304 Differential Equations and Transforms

Introduction to statistical data, frequency distribution and graphical representation. Measures of central tendency and variation. Basic concepts of probability, simple combined and conditional probabilities, independent events, Baye’s theorem and application. Introduction to random variables; discrete and continuous probability distributions (binomial, poisson, normal, uniform and exponential); probability density function, expected values, mean, variance and standard deviation. Sampling distributions, estimation of parameters, testing of hypothesis and goodness of fit. Scatter diagram, linear regression , coefficients of correlation and determination; inferences. Use of SPSS.

Pre-Requisite: MS-1303 Calculus

Introduction to numerical methods and estimation of errors. Non linear algebric equations; Newton-Raphson , secant and Regula falsi methods; system of linear equations and LU method; Eigen values and Eigen vectors by power method. Calculus of finite differences and interpolation (equal and unequal intervals); curve fitting by least squares. Numerical differentiation; numerical integration by trapezoidal, Simpson and Gauss rules. Solution of first order ordinary differential equations by Euler and Runge – Kutta methods; system of linear differential equations. Introduction to numerical solution of partial differential equations. Use of MATLAB.

Pre-Requisite: MS 1302 Linear Algebra

MS 2304 Differential Equations and Transforms