|Department of Mathematics
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MA 100 Foundational Mathematics Limits, Continuity, Differentiation, Extreme Values, Curve Sketching, Integration, Transcendental Functions, Infinite Series, Complex Numbers
MA 101 Calculus I Limits, Continuity, Derivatives, The chain Rule, Applications of derivatives, mean value theorem, Extreme Values, Curve Sketching, Integration, Integration by substitution ¿ running the chain rule backwards, Applications of integrals, Techniques of integration, Transcendental Functions-Natural Log and Exponential functions, L¿Hôpital¿s Rule, inverse trigonometric function, hyperbolic functions Infinite Series, Complex Numbers
MA 102 Calculus II Conic Sections (hyperbola, parabola, ellipse circles), Vectors in IR¿ (dot product, vector product) lines and planes, geometry of space curves, Multivariable Calculus (double integral, area volume, surface area, Jacobian, parametric equation and polar coordinates, multiple Integrals, Calculus of Vector Fields (line integral, surface integral independence of path, Green¿s theorem, divergence theorem, Stokes¿ theorem).
MA 104 Business Mathematics This is a basic quantitative course at the undergraduate level. It covers preliminaries, linear equations, mathematical functions, linear functions and their applications. Other topics include quadratic equations, exponential and logarithmic functions and their applications in business.
MA 105 Multi-Variable Calculus Conic Sections (hyperbola, parabola, ellipse circles), Vectors in IR¿ (dot product, vector product) lines and planes, geometry of space curves, (double integral, area volume, surface area, Jacobian, parametric equation and polar coordinates, multiple Integrals
MA 106 Differential Equations First-order differential equations and their applications, linear differential equations with constant coefficients and their applications, Euler- Cauchy equations, method of variation of parameters, theory of power series method, Legendre¿s equations, Bessel¿s Equation. Introduction to system of differential equations. Laplace transform and its applications. Introduction to partial differential equations
MA 107 Matrix Algebra and Differential Equations Matrix Operations, System of Linear Equations, Introduction to Linear Transformations Matrix Factorization, Introduction to Determinants, Cramer's Rule, First-order differential equations and their applications, linear differential equations with constant coefficients and their applications, Euler- Cauchy equations, method of variation of parameters, Introduction to system of differential equations,
Introduction to partial differential equations.
MA 201 Linear Algebra Basic Concepts, Matrix Operations, System of Linear Equations, Linear Independence, Iterative Solutions of Linear System, Introduction to Linear Transformations, Inverse of a Matrix, Matrix Factorization, Introduction to Determinants, Cramer's Rule, Vector Spaces, Eigenvalues and its Applications, Inner Product Spaces, Orthogonality, The Gram- Schmidt Process.
MA 202 Numerical Analysis and Computation Solution of non-linear equations (bisection method, secant method and Newton¿s method), solution of linear algebraic equations, interpolation, numerical integration, finite difference, numerical solutions of ordinary differential equations (Euler¿s method, Runge-Kutta, boundary value problems). Computer implementation (Matlab(Retd) and C) .
MA 205 Business Statistics An introductory statistics course covering areas of data analysis, frequency distributions, measurement of central tendency, dispersion, variability, simple linear regression, correlation, index number, probability, discrete probability distribution, normal distribution and other continuous probability distribution. Fundamental concepts learnt in this course will help students to relate statistics with vital business decisions.
MA 206 Statistical Inference The course covers more advanced topics in statistics and their application to business decisions. Topics include sampling and sampling distributions, estimation, testing of hypothesis, chi-square, analysis of variance, time series analysis, quality and quality control.
MA 207 Calculus A comprehensive course spanning diverse areas such as limits and continuity, concavity and inflection points, maxima and minima of functions, the chain rule, implicit differentiation, introduction to higher derivatives, the first and second derivative tests and points of inflection. Other key topics cover logarithmic and exponential functions including simple graphs,differentiation and integration of log and exp, anti- derivatives, integral as anti-derivatives, indefinite integrals, integration by substitution, and the fundamental theorem of calculus and application of definite integral to area concept of triple integrals.
MA 208 Engineering Probability and Statistics This course provides introduction to probability and Statistics with applications in mechanical engineering. Topics include: Sample spaces, counting techniques, axiomatic approach, conditional probability, Bayes¿ rule, random variables, probability density and cumulative distribution functions, Probability distributions, Binomial, Poisson, Normal and Exponentials, statistical analysis, measure of location, dispersion, skewness, kurtosis, Sampling procedure, Markov chain, random walk model, stationary and non-stationary phenomenon
MA 209 Complex Analyses A quick review of Complex numbers, Analytic function and their properties, elementary functions of Complex variable, Integration of complex functions, Cauchy-Gaursat theorem, Cauchy integral formula, Fundamental theorem of algebra. Series representation of analytic function, Residues and poles, evaluation of improper real integrals, Mappings by Elementary functions, Conformal mappings and their properties, some simple applications of conformal mappings.
MA 211 Probability Methods in Engineering Introduction to probability theory & distribution functions, Modeling of uncertainty & decision analysis, Weak law of large numbers & central limits theorem, Determination of distribution & parameters from observed data, Moments, Statistical dependence, Game theory & randomized strategies, Analysis of engineering dataset and an introduction to statistical methods. Course emphasizes application to physical problems.
MA 303 Probability and Random Variables Basic concepts of probability, conditional probability, independent events, Bayes¿ formula, discrete and continuous one and two dimensional random variables, marginal and joint distributions and density functions, probability distributions (Binomial, Poisson, Hyper geometric, Normal, Uniform and Exponential), Mean, variance, standard deviations, moments and moment generating functions, linear regression and curve fitting, central limits theorems, stochastic processes, first and second order characteristics, applications to real life.
MA 304 Probability and Statistics This course provides an elementary introduction to probability and statistics with applications. Topics include: basic probability models; combinatorics; random variables; discrete and continuous probability distributions; statistical estimation and testing; confidence intervals; and an introduction to linear regression.
MA 404 Discrete Mathematics Proportional and first-order logic, Equivalence, inference and method of proof, Mathematical induction, diagonalization principle, Basic counting, Set operations, relations, functions, Boolean algebra, Truth tables and minimization of Boolean expressions, Applications to computer science and engineering
MA 501 Quantitative Analyses and Techniques It covers a vast variety of mathematical concepts including linear equations and functions, quadratic and polynomial functions, exponential and logarithmic functions, matrix algebra, set theory, permutations and combinations, probability, random variables, frequency distribution time series, measures of central tendency, measures of dispersion, estimation, forecasting and index numbers.
MA 502 Numerical Methods Pre-requisite: Differential Equations
This course is an advanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, well-posedness and stability, boundary and nonlinear instabilities. The course assumes familiarity with basic (numerical) linear algebra and will involve a certain amount of programming in MATLAB (Retd) or another programming language of your choice.
MA 630 Partial Differential Equations 1 No course outline is available.
MA 630 Partial Differential Equations-I Introduction to partial differential equations; classification of PDEs (Parabolic, Hyperbolic, Elliptic); Origin (derivation of the heat equation, wave equation, Poison¿s Equation); Separation of variables; Eigenfunction method; Integral Transforms (Fourier Laplace etc.)Method of Characteristics; D¿ALembert solution of the wave equation; Nondimensionalisation; System of PDEs; Green¿s Function for Time Independent and Dependent Problems.
MA 644 Advance Engineering Mathematics No course outline is available.
MA 644 Advanced Engineering Mathematics Pre requisite: Undergraduate Engineering Mathematics Applied calculus, application of numerical linear algebra, vector calculus, Ordinary and Partial Differential Equations; solution techniques with exact and approximate methods. Coupled equations. Difference equations. Integro-differential equations and solution techniques. Integral equations (Volterra and Fredholm type). Exact solutions for infinite and semi- infinite systems, Optimization of multivariable calculus, quadratures, Laplace and Fourier transformations.
MA 645 Advanced Numerical Techniques Numerical Technique to solve Linear and Non-Linear systems, Generalized Newton¿s Method. Finite difference Method, Finite Volume Method for PDEs. Upwind Schemes, TVD Schemes, Marker and Cell Method, Multi grid Method, Pseudo-spectral Method. Matlab applications for solving PDEs.
MA 646 Introduction to Modeling and Simulation Pre-requisite: MA 502
This course surveys the basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. It covers techniques and software for statistical sampling, simulation, data analysis and visualization, and uses statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications are drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal footing with theory and experiment. A term project allows development of individual interests. Students are mentored by a coordinated team of participating faculty from across the Institute.
MA 650 FEM for Partial Differential Equations Pre-requisite: Differential Equations and Complex Variables A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.
MA 662 Linear Partial Differential Equations Pre-requisite: Differential equations
This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems, and Green's functions.
MA 670 Approximation Theory Normed Spaces, Approximation by Algebraic Polynomials ,Exercises on Approximation by Polynomials, Approximation by Trigonometric Polynomials, Exercises on Trigonometric Polynomials, Characterization of Best Approximation, Exercises on Chebyshev Polynomials, Simple Application of Chebyshev Polynomials, Lagrange Interpolation, Orthogonal Polynomials, Gaussian Quadrature
MA 680 Applied Partial Differential Equations Pre-requisite: MA 662
Systems of partial differential equations, characteristics, Weak solutions, Riemann¿s function, Maximum principles, comparison methods, well- posed problems, and Green¿s functions for the heat equation and for Laplace¿s equation, Fredholm alternative and Green's functions for non-self-adjoint problems, application of delta functions, Further development of hyperbolic equations, Cauchy-Kovalevskaya theorem, Riemann invariants, shocks and weak solutions, causality.
MA 684 Mathematical Methods Pre-requisite: MA502
Modeling and conservation laws, Scaling and non-dimensionalisation, Simple boundary layer theory, Nonlinear oscillations, Multiple scale methods, Ordinary differential equations: hysteresis and stability, Sturm¿Liouville systems, Integral equations and eigenfunctions, Partial differential equations: shocks, similarity solutions, Calculus of Variations; optimal control.
MA 686 Stochastic Differential Equations Pre-requisite: Differential Equations
Strong solutions, questions of existence and uniqueness, diffusion processes, Cameron¿Martin formula, weak solution and martingale problem. Some selected applications chosen from topics including option pricing and stochastic filtering.
MA 688 Applied Linear Algebra Pre-requisit: Linear Algebra
Linear Algebra is a central and widely applicable part of Mathematics. It is estimated that many (if not most) computers in the world are computing with matrix algorithms at any moment in time whether these be embedded in visualization software in a computer game or calculating prices for some financial option. This course builds on elementary linear algebra and in it we derive, describe and analyse a number of widely used constructive methods (algorithms) for various problems involving matrices.
MA 700 Computational Fluid Dynamics Pre-requisite: Undergraduate course on Fluid Mechanics/Dynamics Numerical solution of 1D, 2D and 3D Transport equations, Euler¿s equations, Burger¿s equations, Incompressible Navier-Stokes equations, compressible Navier-Stokes equations, advanced numerical techniques, multi-grid methods, spectral methods.
MA 741 Advanced Statistical Inference This is an advanced course in statistical analysis which highlights the significance of planning, collection, analysis and interpretation of complex data. Students are taught to devise research problems and hypothesis and prepare the necessary tests to avoid Type I or Type II errors. The course also utilizes extensive use of univariate, bivariate and discriminant analysis. The last few units stress on deriving useful information from the tests in order to help students make smart decision
MA 741Advanced Statistical Techniques This is an advanced course in statistical analysis which highlights the significance of planning, collection, analysis and interpretation of complex data. Students are taught to devise research problems and hypothesis and prepare the necessary tests to avoid Type I or Type II errors. The course also utilizes extensive use of univariate, bivariate and discriminant analysis. The last few units stress on deriving useful information from the tests in order to help students make smart decisions.
MA 750 Computational Fluid Dynamics Pre-requisite: Undergraduate course on Fluid Mechanics/Dynamics Numerical solution of 1D, 2D and 3D Transport equations, Euler¿s equations, Burger¿s equations, Incompressible Navier-Stokes equations, compressible Navier-Stokes equations, advanced numerical techniques, multi-grid methods, spectral methods.
MA 770 Modeling and Simulation of Dynamical Systems Pre-requisite: MA 645
This course is about modeling multi-domain engineering systems at a level of detail suitable for design and control system implementation. It also describes Network representation, state-space models, Multiport energy storage and dissipation, Legendre transforms, Nonlinear mechanics, transformation theory, Lagrangian and Hamiltonian forms, Control- relevant properties. The application examples may include electro- mechanical transducers, mechanisms, electronics, fluid and thermal systems, compressible flow, chemical processes, diffusion, and wave transmission.
MA 772 Mathematics for Geo-Sciences Pre-requisite: MA502
The course starts with some background to the geology, geophysics and engineering involved in the recovery of oil from deep inside the Earth. Flow through porous media - balance laws, Darcy's law, analytical and numerical methods, Grid generation and geometric modeling - surface modeling, structured and unstructured grids, stochastic sampling, groundwater modeling, the study of subsurface pollution and remediation, and even to problems outside the geosciences.
MA 780 Solid Mechanics Pre-requisite: Fluid Mechanics
Lagrangian and Eulerian descriptions of motion, analysis of strain, Balance laws of continuum mechanics, Frame-indifference, Constitutive equations for a nonlinear elastic material. Linear elasticity as a linearization of nonlinear elasticity. Incompressibility and models of rubber. Exact solutions for incompressible materials, phase transformations, shape-memory effect.
MA 782 Topics in Fluid Mechanics Pre-requisite: Applied Differential Equations
Convection, stability, boundary layers, parameterized convection, Rotating flows, atmosphere and oceans, Waves, geostrophy, boilers, condensers, fluidised beds. Flow régimes. Homogeneous, drift-flux, two-fluid models. Ill-posedness, waves, density wave oscillations. coatings and foams. gravity flows, Droplet dynamics, contact lines, Drying and wetting, Foam drainage.
MA 784 Mathematical Methods for Signal Processing Pre-requisite: Applied Differential Equations
Introduction to signal processing, Signal formation and sampling in MRI and FMRI, Representation of a signal in the frequency domain (Fourier methods), Compression (wavelets), Filter operations for attenuation of a signal, Extracting information from a signal without a model (PCA,ICA), De-noising, Applications in speech and biomedical signal processing, Applications in learning how the brain functions (FMRI).
MA 786 Waves and Compressible Flow Pre-requisite: Fluid Mechanics
Equations of inviscid compressible flow including flow relative to rotating axes, Models for linear wave propagation including Stokes¿ waves, Inertial waves, Rossby waves and simple solutions, Theories for Linear waves: Fourier Series, Fourier integrals, method of stationary phase, dispersion and group velocity. Flow past thin wings, simple wave flows applied to one-dimensional unsteady gas flow and shallow water theory, Shock Waves: weak solutions, Rankine¿Hugoniot relations, oblique shocks, bores and hydraulic jumps.
MA 800 Advance Computational Fluid Dynamics No course outline is available.
MA 801 Applied Cryptography No course outline is available.
MA 802 Optimization Prerequisite: Multivariable calculus and Numerical linear algebra.
Introduction to optimization. Relative and absolute extrema. Convex, concave and unimodal functions. Constraints. Mathematical programming problems. Optimization of one, two and several variables functions and necessary and sufficient conditions for their optima. Optimization by equality constraints, Direct substitution method and Lagrange multiplier method, necessary and sufficient conditions for an equality constrained optimum with bounded independent variables. Inequality constraints and Lagrange multipliers. Kuhn-Tucker Theorem. Multidimensional optimization by Gradient method. Convex and concave programming. Calculus of variation and Euler Lagrange equations. Functionals depending on several independent variables. Variational problems in parametric form. Generalized mathematical formulation of dynamics programming. Non-linear continuous models. Dynamics programming and variational calculus. Control theory.
MA 805 Advance Numerical Techniques No course outline is available.
MA 806 Formal Languages No course outline is available.
MA 807 Stochastic Operations Research Stochastic models of inventory, reliability, queuing, sequencing, and transportation. Applications of these models to problems arising in industry, government, and business.
MA 810 Aerodynamics No course outline is available.
MA 811 Theoretical Computer Sciences No course outline is available.
MA 812 Deterministic Operations Research Prerequisite: Multivariable calculus and linear algebra
Linear, integer, nonlinear and dynamic programming, classical optimization problems, network theory. CGU.
MA-817 Monte Carlo & Quasi-Monte Carlo Methods
Prerequisites: A graduate course in probability theory, a basic course in numerical methods, and facility in programming a computer using a language such as FORTRAN, C, or Basic
This is an advanced course in which stochastically- motivated mathematical methods are applied to problems of various kinds (e.g. radiation transport, semiconductor, geological and financial modeling, or statistical mechanics) that can be solved by simulations carried out on a computer. Problems studied in this way include the most naturally formulated as integral equations over relatively high dimensional phase spaces, as well as those in which estimates of integrals of functions of a large number of variables are sought. This should be regarded as an advanced course in the applications of probability theory to numerical analysis.
MA 815 Magnetohydrodynamics Equations of electrodynamics, Equations of Fluid Dynamics, Ohm¿s law equations of magnetohydrodynamics. Motion of a viscous electrically conducting fluid with linear current flow, steady state motion along a magnetic field, wave motion of an ideal fluid.
Magneto-sonic waves. Alfve¿s waves, damping and excitation of MHD waves, characteristics lines and surfaces. Kinds of simple waves, distortion of the profile of a simple wave, discontinuities, simple and shock waves in relativistic magnetohydrodynamics, stability and structure of shock waves, discontinuities in various quantities, piston problem, oblique shock waves.
MA 816 Advance Analysis Algorithm No course outline is available.
MA 820 Advance Dynamics Equations of dynamic and its various forms. Equations of Langrange and Euler. Jacobi¿s elliptic functions and the qualitative and quantitative solutions of the problem of Euler and Poisson. The Problems of Langrange and Poisson. Dynamical system. Equations of Hamilton and Appell. Hamilton-Jacobi theorem. Separable systems. Holder¿s variational principle and its consequences.
MA 821 Number Theory Number Theory is often considered one of the most beautiful and elegant topics in mathematics. We will study properties concerning the integers, such as divisibility, congruences, and prime numbers. More advanced topics include encryption, quadratic reciprocity, and Diophantine approximation. Finally we will introduce elliptic curves and see how these curves relate to the proof of Fermat's last theorem.
MA 822 Nonlinear Optimization Prerequisites: linear algebra, multivariate calculus, and (preferably) experience in programming in Matlab.
This course will survey widely used methods for continuous optimization, focusing on both theoretical foundations and implementation as numerical software. Topics include linear programming (optimization of a linear function subject to linear constraints), line search and trust region methods for unconstrained optimization, and a selection of approaches (including active-set, sequential quadratic programming, and interior methods) for constrained optimization.
MA 826 Coding Theory No course outline is available.
MA 827 Advance Integral Equations Transforms covered will include: Fourier, Laplace, Hilbert, Hankel, Mellin, Radon, and Z. The course will be relevant to mathematicians and enginners working in communications, signal and image processing, continuous and digital filters, wave propagation in fluids and solids, etc.
MA 831 Advance Statistical Analysis No course outline is available.