## Details of MA1202 (Spring 2019)

 Level: 1 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA1202 Mathematical Methods I Ananda Dasgupta,
Ratikanta Behera

Syllabus
Part I: Matrix Theory
1.Linear System: System of linear equations and its solvability, Gauss elimination and Gauss-Jordan elimination methods.
2.Matrices & Determinants: Rank and inverse of a matrix. Some important classes of matrices: Symmetric, anti-symmetric, orthogonal, Hermitian and unitary matrices.
Determinant of a matrix. Similarity transformation.
3.Eigenvalues: Eigenvalues and eigenvectors. Calculation of eigenvalues, Cayley-Hamilton theorem.
Part II: Ordinary Differential Equations
1.First Order Equations: Linear equations, integrating factor, Bernoullis Equation. Clairauts Equation.
2.Second Order Equations: Linear equations with constant coefficients, general solutions, non-homogenous equations, c
omplementary function and particular integral. Linear equations with variable coefficients -Power series solutions.
Part III: Calculus II
1.Calculus with complex numbers. Differentiability -Cauchy Riemann conditions. Analytic functions. Singularities. Cauchy's theorem. Residue theorem. Applications to the calculation of sums and integrals.

References
1.Apostol, T. M., Calculus I (2nd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2011.
2.Apostol, T. M., Calculus II (2nd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2007.
3.Arfken, G. B., Weber, H. & Harris, F., Essential Mathematical Methods for Physicists and Engineers, Academic Press, 2003.
4.Boas, M. L., Mathematical Methods In The Physical Sciences (3rd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2006.
5.Kreyszig, E., Advanced Engineering Mathematics (8th Edition), Wiley India Pvt Ltd, 2010.

#### Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Not Allowed
2 IP 4 Not Allowed
3 IP 6 Not Allowed
4 MR 2 Not Allowed
5 MR 4 Not Allowed
6 MS 2 Core
7 RS 1 Not Allowed
8 RS 2 Not Allowed