**MA 102
Mathematics-II
3-1-0-8**

**Prerequisite: **Nil

**Syllabus:**

Systems of linear equations and their solutions; vector space *R*^{n} 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.

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:**

1.D. Poole,
Linear Algebra: A Modern Introduction, 2^{nd} Edition, Brooks/Cole,
2005.

2.S. L. Ross,
Differential Equations, 3^{rd} Edition, Wiley India, 1984.

**References:**

1.G. Strang,
Linear Algebra and Its Applications, 4^{th} Edition, Brooks/Cole India,
2006.

2.K. Hoffman
and R. Kunze, Linear Algebra, 2^{nd} Edition, Prentice Hall India,
2004.

3.E. A.
Coddington, An Introduction to Ordinary Differential Equations, Prentice Hall
India, 1995.

4.E. L. Ince,
Ordinary Differential Equations, Dover Publications, 1958