# UG Courses

B. Tech. core courses New Curriculum

## MA101 Calculus, 3 (3-1-0-5-3)

Single Variable Calculus: Limits and continuity of single variable functions, differentiation and applications of derivatives, Definite integrals, fundamental theorem of calculus, Applications to length, moments and center of mass, surfaces of revolutions, improper integrals, Sequences, series and their convergence, absolute and conditional convergence, power series. Taylor’s and Maclaurin's series.

Multi-variable Calculus: Functions of several variables-limits and continuity, partial derivatives, chain rule, gradient, directional derivatives, tangent planes, normals, extreme values, saddle points, Lagrange multipliers. Taylor’s formula. Double and triple integrals with applications, Jacobians, change of variables, line integrals, divergence, curl, conservative fields, Green’s theorem, surface integrals, Stokes’s Gauss Divergence theorem.

## MA102 Linear Algebra, Integral Transforms and Special Functions, 3 (3-1-0-5-3)

Linear Algebra : Vector spaces over R and C, Subspaces, Basis and Dimension, Matrices and determinants, Rank of a matrix, System of linear equations, Gauss elimination method, Linear transformations, Rank-nullity theorem, Change of basis, Eigen values, Eigen vectors, Diagonalization of a linear operator, Inner product spaces. Spectral theorem for real symmetric matrices, application to quadratic forms.

Integral Transforms: Laplace transforms of elementary functions, Inverse Laplace transforms and applications, Fourier series, Fourier transforms, Fourier cosine and sine integrals, Dirichlet integral, Inverse Fourier transforms, Special Functions: Gamma and Beta functions, Error functions.

## MA201 Differential Equations, 3 ( 3-1-0-5-3)

Ordinary Differential Equations: First Order Equation, Exact equations, integrating factors and Bernoulli equations. Lipschitz condition, examples on non-uniqueness. Second order differential equations with constant coefficients: homogeneous and non-homogeneous differential equations. Wronskian and linear independence of solutions, method of variation of parameters. Cauchy-Euler equations, method to second order equations with variable coefficients, Some applications, Solution of IVP using Laplace Transform and Euler’s Method. Series solutions, Frobenius method, Legendere and Bessel equations, orthogonal properties of Legendre polynomials.

Partial Differential Equations: Linear second order partial differential equations and their classification, heat equation, vibrating string, Laplace equation; method of separation of variables.

## MA202 Probability and Statistics, 3 (3-1-0-5-3)

Probability: Axioms of probability, conditional probability, independence of two or more events, Bayes’ theorem. Random variable, distribution functions, standard probability distributions and their properties, Simulation. Multiple random variables, marginal and conditional probability distribution, independence of random variables, bivariate normal and multinomial distributions. Functions of random variables, covariance and correlation. Conditional expectation, sum of random number of independent random variables. Convergence in probability, laws of large numbers and central limit theorem.

Statistics: Sample, population, sampling techniques, descriptive statistics, popular sampling distributions. Point estimation, parameter estimation with MLE, interval estimation, hypothesis testing. Ordinary least Squares (OLS) regression, assumptions and limitations of OLS, inference concerning regression parameters, other regressions. Analysis of variance.

## MA203 Probability and Stochastic Processes, 3 ( 3-1-0-5-3)

Probability: Axioms of probability, conditional probability, independence of two or more events, Bayes’ theorem. Random variable, distribution functions, standard probability distributions and their properties, Simulation. Multiple random variables, marginal and conditional probability distribution, independence of random variables, bivariate normal and multinomial distributions. Functions of random variables, covariance and correlation. Conditional expectation, sum of random number of independent random variables. Convergence in probability, laws of large numbers and central limit theorem.

Stochastic Processes: Introduction and motivation, classification of stochastic processes, Bernoulli process, Poisson process, Markov chains, single/multiple server queuing models, power spectral density.