To equip students with series representation of functions of a real variable, and methods of matrix theory.These topics have applications in all branches of engineering and sciences.
Course Content: Series: Sequences of real numbers, Series, ratio and root test, improper integral, integral test, alternating series,absolute and conditional convergence, power series, radius and interval of convergence of power series, term by termdifferentiation and integration of power series, Taylor’s formulas, Taylor series, periodic functions and Fourier series,convergence of Fourier series, functions of any period, even and odd functions, half-range expansions.Matrices: Matrix operations, special types of matrices, matrices as linear transformations, linear independence,basisand dimension, rank of a matrix, nullity of a matrix, elementary operations, inverse of a matrix, orthogonalization,determinant, existence- uniqueness of solutions of a linear system, Gaussian elimination, Gauss-Jordan elimination,Eigenvalues, eigenvectors, eigenvalues of special types of matrices, similarity of matrices, basis of eigenvectors,diagonalization.
1. G.B. Thomas Jr., M.D. Weir and J.R. Hass, Thomas Calculus, Pearson Education, 2009.2. E. Kreyszig, Advanced Engineering Mathematics, 10th Ed., John Willey & Sons, 2010.
Reference Books: 1. J. Hefferon, Linear Algebra, http://joshua.smcvt.edu/linearalgebra, 2014.
2. S. Lang, Introduction to Linear Algebra, 2nd Ed., Springer-Verlag, 1986.
3. M.T. Nair, Calculus of One Variable, Ane Books, 2014.
4. N. Piskunov, Differential and Integral Calculus Vol. 1-2, Mir Publishers, 1974.
5. G. Strang, Linear Algebra and its Applications, Cengage Learning, 4th Ed., 2006.