Course Details:

Systems of linear equations and their solutions. Rn and Cn as vector spaces and their linear subspaces; spanning set and linear independence; basis and dimension of a subspace of Rn. Matrices and their associated four fundamental subspaces: null space, column space, row space of a matrix and null space of its transpose. Row rank and column rank.

Elementary row operations on matrices and elementary matrices; Reduced row echelon form. Gaussian elimination method for solving systems of linear equations. Determination of row rank, column rank using elementary row operations; row rank equals column rank. Inverse and determinant of a square matrix. The Gauss-Jordan method of computing the inverse of an (invertible) matrix.

Linear transformations and their matrix representations. Effect of a change of basis on their matrix representations. Null space and range of a linear transformation. Rank-nullity theorem.

Eigenvectors and eigenvalues. Characteristic polynomials, Cayley-Hamilton theorem, eigenvalues of special matrices, algebraic and geometric multiplicity, diagonalization.

Sequences and series of real numbers: tests for convergence.

Power series, Taylor series and Fourier series.

Text Books:

  1. Gilbert Strang, Linear Algebra and Its Applications, Thomson, Brooks/Cole (2006),
  2. E. Kreyszig, Advanced engineering mathematics, 10th Edition, John Wiley & sons (2011)
  3. G. B. Thomas Jr., M.D. Weir and J.R. Hass, Thomas Calculus, Pearson Education, (2009)

Reference Books:

  1.  S. Lang, Introduction to Linear Algebra, 2nd Ed., Springer 2012
  2. D. W. Lewis, Matrix Theory, World Scientific, 1991
  3. K. D. Joshi, Calculus for Scientists and Engineers: An Analytical Approach, Alpha Science International Limited 2007
  4. S. R. Ghorpade, B. V. Limaye, A Course in Calculus and Real Analysis, Springer 2018
  5.  Thamban Nair, Calculus of One Variable: For Science and Engineering Students, Ane Books, 2015
  6.  Tom M. Apostol, Calculus - Volume I: One-variable Calculus, with an Introduction to Linear Algebra, 2nd Ed, 2007
  7.  Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, (2nd Edition) Springer 2013