POINTS TO REMEMBER BEFORE THE EXAM FOR COMPLEX ANALYSIS
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POINTS TO REMEMBER BEFORE THE EXAM FOR LINEAR ALGEBRA
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POINTS TO REMEMBER BEFORE THE EXAM FOR VECTOR ANALYSIS
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POINTS TO REMEMBER BEFORE THE EXAM FOR LINEAR PROGRAMMING PROBLEMS
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POINTS TO REMEMBER BEFORE THE EXAM FOR NUMERICAL ANALYSIS
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POINTS TO REMEMBER BEFORE THE EXAM FOR PARTIAL DIFFERENTIAL EQUATIONS
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POINTS TO REMEMBER BEFORE THE EXAM FOR REAL ANALYSIS & CALCULUS
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POINTS TO REMEMBER BEFORE THE EXAM FOR ANALYTIC GEOMETRY
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POINTS TO REMEMBER BEFORE THE EXAM FOR MODERN ALGEBRA
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POINTS TO REMEMBER BEFORE THE EXAM FOR ORDINARY DIFFERENTIAL EQUATIONS
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MATHEMATICS OPTIONAL MAINS SYLLABUS
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IAS Mains Mathematics Syllabus Exam Paper-I Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; Linear transformations, rank and nullity, matrix of a linear transformation. Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues. Calculus: Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor's theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange's method of multipliers, Jacobian. Riemann's definition of definite in...