Details of MA1201 (Spring 2024)
| Level: 1 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA1201 | Mathematics II | Anirban Banerjee |
| Syllabus |
|---|
| Part I: Matrix Theory
Linear System: System of linear equations and its solvability, Gauss elimination and Gauss-Jordan elimination methods. 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. Eigenvalues: Eigenvalues and eigenvectors; Calculation of eigenvalues, Cayley-Hamilton theorem. Part II: Ordinary Differential Equations First Order Equations: Linear equations, integrating factor, Bernoullis Equation; Clairauts Equation. Second Order Equations: Linear equations with constant coefficients, general solutions, non-homogenous equations, complementary function and particular integral; Linear equations with variable coefficients -Power series solutions. Part III: Set Theory Finite & infinite sets: countable and uncountable sets, Hilbert's infinite hotel, Russell's barber paradox, power set, sets indexed by another set. Fundamental arguments: Cantor's Theorem, Cantor's diagonalization argument, Schroder-Bernstein Theorem Part IV: Calculus Partial derivatives, Mixed derivatives, Chain rule, Line integral, Greens theorem; (If time permits: 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 |
|---|
| 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. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Not Allowed |
| 5 | MP | 4 | Not Allowed |
| 6 | MR | 2 | Not Allowed |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 2 | Core |
| 9 | RS | 1 | Not Allowed |
| 10 | RS | 2 | Not Allowed |