Linear Algebra and Calculus (20A54101)

label_important 1.1 Matrix Introduction

label_important1.2 Rank of a matrix (Echelon form)

label_important 1.3 Rank of a matrix (Normal form or Canonical form)

label_important 1.4 Inverse of a matrix by Gauss – Jordan method

label_important 1.5 Consistency of Non-Homogenous Linear Equations

label_important 1.6 Consistency of Homogenous Linear Equations

label_important 1.7 Characteristic Equation

label_important 1.8 Eigen values and Eigen vectors

label_important 1.9 Properties of Eigen values and Eigen vectors

label_important 1.10 Cayley Hamilton Theorem

label_important 1.11 Diagonalisation of matrix (Similarity Transformation)

label_important 1.12 Diagonalisation of matrix (Orthogonal Transformation)

label_important 2.1 Rolle’s Mean value Theorem

label_important2.2 Lagrange’s Mean Value Theorem

label_important 2.3 Cauchy’s and Generalized mean value Theorem

label_important 2.4 Taylor & Maclaurin Series

label_important 3.1 Partial Differentiation

label_important3.2 Total Derivatives (Chain Rule)

label_important 3.3 Change of variable

label_important 3.4 Jacobian's

label_important 3.5 Maxima & Minima

label_important 3.6 Lagrange's Method

label_important 4.1 Double Integral

label_important4.2 Change of Order of Integration

label_important 4.3 Change of Variables (Double Integral)

label_important 4.4 Application of Double Integral (Area)

label_important 4.5 Triple Integral

label_important 4.6 Change of Variables (Triple Integral)

label_important 4.7 Application of Triple Integral (Volume)

label_important 5.1 Beta Function

label_important5.2 Gamma Function

label_important 5.3 Relation Between Gamma and Beta Function