Notes in Mathematics

May 19th, 2015
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1. Linear Algebra: 1. Vector spaces over R and C, Linear dependence and independence, subspaces, bases, dimension; 2. Linear transformations, rank and nullity, matrix of a linear transformation. 2. Calculus: 1. Real numbers, 2. Functions of a real variable, Limits, continuity, differentiability,

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MATHEMATICSPAPER - I1. Linear Algebra:1. Vector spaces over R and C, Linear dependence and independence, subspaces, bases, dimension;2. Linear transformations, rank and nullity, matrix of a linear transformation. 3. Algebra of Matrices: Row and column reduction, Echelon form, congruences and similarity; 4. Rank of a matrix;5. Inverse of a matrix;6. Solution of system of linear equations;7. Eigenvalues and eigenvectors, 8. Characteristic polynomial, 9. Cayley Hamilton theorem,10. Symmetric, skew-symmetric, 11. Hermitian, skew-Hermitian, 12. Orthogonal and unitary matrices and their eigenvalues.2. Calculus:1. Real numbers, 2. Functions of a real variable, Limits, continuity, differentiability, 3. Mean value theorem, 4. Taylors theorem with remainders,5. Indeterminate forms, 6. Maxima and minima, asymptotes;7. Curve tracing; 8. Functions of two or three variables: a. Limits, b. Continuity,c. Partial derivatives, d. Maxima and minima, e. Lagranges Method of multipliers, f. Jacobian.9. Riemanns definition of a. Definite integrals; b. Indefinite integrals;c. Infinite and improper integrals;d. Double and triple integrals (evaluation t

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