label_important1. MATRICES
10 Chapters | 59 Solved Problems
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_important2. EIGEN VALUES AND EIGEN VECTORS
6 Chapters | 47 Solved Problems
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_important3. SEQUENCES AND SERIES
11 Chapters | 54 Solved Problems
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_important4. CALCULUS
7 Chapters | 62 Solved Problems
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_important5. MULTIVARIABLE CALCULUS (PARTIAL DIFFERENTIATION AND APPLICATIONS)
6 Chapters | 42 Solved Problems
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
