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Teaching Scheme Examination Scheme Lectures : 2 hrs / week Internal Test 1 : 20 marks Tutorials: 1 hr / week Internal Test 2: 20 marks Self-study: 1 hr/week End Sem. Exam: 60 marks Unit I: Matrices and Linear Equations: Basic properties of matrices, row operations and Gauss elimination, Determinants, and their basic properties, Basic concepts in linear algebra: vector spaces, subspaces, linear independence, and dependence of vectors. Row and Column rank. Solutions of Systems of linear equations using Gauss Elimination method, Rank and Nullity, Eigen Values and Eigen Vectors. S: basic properties of matrices, row operations, Determinants, and their basic properties. [ 8 L+4T+4S] Unit II: Integral Calculus: Double integrals in Cartesian and polar co-ordinates, iterated integrals, change of variables, triple integrals in Cartesian, spherical and cylindrical co-ordinates, substitutions in multiple integrals, Applications to Area, Volume, Moments, and Center of Mass. Vector differentiation, gradient, divergence and curl, line integral and arc length parameterization, surface integrals, path independence, statements, and illustrations of theorems of Green, Stokes and Gauss, applications. S: Area, Volume, Moments, and Center of Mass. [ 12 L+6T+6S] Unit III: Probability: Mean, median, mode, standard deviation, combinatorial probability, joint and conditional probability. Probability distributions, Binomial distribution, Poisson distribution, Normal distribution, exponential distribution. S: Joint and conditional probability, exponential distribution. [8L+4T+4S] Text Book:
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