Syllabus for MA-102

Linear algebra

Systems of linear equations, matrices, Gaussian elimination, echelon form, column space, null space, rank of a matrix, inverse and determinant; Vector spaces (over the field of real and complex numbers), subspaces, spanning set, linear independence, basis and dimension; Linear transformations, rank-nullity theorem, matrix of a linear transformation, change of basis and similarity; Eigenvalues and eigenvectors, algebraic and geometric multiplicity, diagonalization by similarity; Inner-product spaces, Gram-Schmidt process, orthonormal basis; Orthogonal, Hermitian and symmetric matrices, spectral theorem for real symmetric matrices

Ordinary differential equations

First order differential equations, exact differential equations, integrating factors, Bernoulli equations, existence and uniqueness theorem, applications; Higher-order linear differential equations, solutions of homogeneous and nonhomogeneous equations, method of variation of parameters, operator method; Series solutions of linear differential equations, Legendre equation and Legendre polynomials, Bessel equation and Bessel functions of first and second kinds; Systems of first-order equations, phase plane, critical points, stability.

Texts

D. Poole, Linear Algebra: A Modern Introduction, Cengage Learning India Private Limited, 4th Edition, 2015.
S. L. Ross, Differential Equations, Wiley India, 3rd Edition, 2004.

References

G. Strang, Linear Algebra and Its Applications, Cengage Learning, 4th Edition, 2006.
J. Gilbert and L. Gilbert, Linear Algebra and Matrix Theory, Academic Press, 1995.
K. Hoffman and R. Kunze, Linear Algebra, Pearson India, 2nd Edition, 2015.
E. A. Coddington, An Introduction to Ordinary Differential Equations, Dover Publications, 1989.
E. L. Ince, Ordinary Differential Equations, Dover Publications, 1958.
T. M. Apostol, Calculus, Volume-2, Wiley India, 2003.
W. E. Boyce and R. C. DiPrima, Elementary Differential Equations, Wiley India, 9th Edition, 2008.

If you need a longer list of books, talk to instructors