Matrices and Calculus (MA101BS)

label_important 1.1 Matrix Introduction

label_important1.2 Real matrices: Symmetric, skew – symmetric, orthogonals

label_important 1.3 Complex matrices: Hermitian, Skew - Hermitian, Unitary Matrices

label_important 1.4 Rank of a matrix (Echelon form)

label_important 1.5 Rank of a matrix (Normal form or Canonical form)

label_important 1.6 Inverse of a matrix by Gauss – Jordan method

label_important 1.7 Consistency of Non-Homogenous Linear Equations

label_important 1.8 Gauss – Elimination method

label_important 1.9 Consistency of Homogenous Linear Equations

label_important 1.10 Gauss - Seidal Method

label_important 2.1 Characteristic Equation

label_important2.2 Eigen values and Eigen vectors

label_important 2.3 Properties of Eigen values and Eigen vectors

label_important 2.4 Cayley Hamilton Theorem

label_important 2.5 Diagonalisation of matrix (Similarity Transformation)

label_important 2.6 Diagonalisation of matrix (Orthogonal Transformation)

label_important 3.1 Sequences

label_important3.2 Infinite series

label_important 3.3 Comparison test

label_important 3.4 Integral test

label_important 3.5 D'Alembert's ratio test

label_important 3.6 Raabe's test

label_important 3.7 Cauchy's root test

label_important 3.8 Logarithmic test

label_important 3.9 Gauss's test

label_important 3.10 Alternating series

label_important 3.11 Absolute and and conditional convergence

label_important 4.1 Rolle’s Mean value Theorem

label_important4.2 Lagrange’s Mean Value Theorem

label_important 4.3 Cauchy’s and Generalized mean value Theorem

label_important 4.4 Taylor & Maclaurin Series

label_important 4.5 Beta Function

label_important 4.6 Gamma Function

label_important 4.7 Relation Between Gamma and Beta Function

label_important 5.1 Function of two or more variables (Limit & Continuity)

label_important5.2 Partial Differentiation

label_important 5.3 Euler's Theorems

label_important 5.4 Total Derivatives

label_important 5.5 Maxima & Minima

label_important 5.6 Lagrange's Method