IIT Guwahati Syllabus
B Tech 1st Year Mathematics
MA 101.Mathematics I (3-1-0-8)
Systems of linear equations and their solutions; vector space Rn and its subspaces; spanning set and linear independence; matrices, inverse and determinant; range space and rank, null space and nullity, eigenvalues and eigenvectors; diagonalization of matrices; similarity; inner product, Gram-Schmidt process; vector spaces (over the field of real and complex numbers), linear transformations.
Convergence of sequences and series of real numbers; continuity of functions; differentiability, Rolle’s theorem, mean value theorem, Taylor’s theorem; power series; Riemann integration, fundamental theorem of calculus, improper integrals; application to length, area, volume and surface area of revolution.
 D. Poole, Linear Algebra: A Modern Introduction, 2nd Edn.,Brooks/Cole, 2005.
 G. B. Thomas, Jr. and R. L. Finney, Calculus and Analytic Geometry, 9th Edn., Pearson Education India, 1996..
 G. Strang, Linear Algebra and Its Applications, 4th Edn. Brooks/Cole India, 2006.
 K. Hoffman and R. Kunze, Linear Algebra, 2nd Edn., Prentice Hall India, 2004
 R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis, 3rd Edn., Wiley India, 2005
 S. R. Ghorpade and B. V. Limaye, An Introduction to Calculus and Real Analysis, Springer India, 2006.