Syllabus
|
Course Code: OEM20- 207 Course Name: Basic Mathematics-I |
||
| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
|---|---|---|
| 1 | Sequences and series: sequences, bounded, convergent and monotonic sequences, infinite series, convergence and divergence of an infinite series, positive term series, geometric series, comparison test for positive term series, Cauchy's root test, D'Alembert's ratio test. Raabe's test, logarithmic test, integral test, Gauss's test. (Scope as in relevant portions of chapters 3 and 4 of the book recommended at Sr. No. 1) | |
| 2 | Fourier Series : Periodic function, Euler's formulae, conditions for Fourier expansion, functions having points of discontinuity, even and odd functions, Fourier series for even and odd functions, half range Fourier series. (Scope as in relevant portions of chapter 1 of the recommended at Sr. No. 2) | |
| 3 | Algebra of matrices: Basic operations on matrices, special type of square matrices: idempotent matrix, nilpotent matrix, involutary matrix, orthogonal matrix, unitary matrix; rank of a matrix (Scope as in relevant portions of chapters 2 and 4 of the book recommended at Sr. No. 3) | |
| 4 | Systems of linear equations:, system of linear homogeneous equations, systems of linear nonhomogeneous equations, matrices of reflection and rotation. Characteristic roots and characteristic vectors of a square matrix. Characteristic matrix and characteristic equation of a matrix, Cayley-Hamilton theorem (without proof). (Scope as in relevant portions of chapters 6 and 11 of the book recommended at Sr. No. 3) |
|
