MATHEMATICS-I (CALCULUS, LINEAR ALGEBRA)

label_important 1.1 Rolle’s Mean value Theorem

label_important1.2 Lagrange’s Mean Value Theorem

label_important 1.3 Cauchy’s and Generalized mean value Theorem

label_important 1.4 Taylor & Maclaurin Series

label_important 1.5 Indeterminate Forms (L Hospital)

label_important 1.6 Maxima and Minima of functions of one variable

label_important 1.7 Definite Integral

label_important 1.8 Improper Integrals

label_important 1.9 Beta Function

label_important 1.10 Gamma Function

label_important 1.11 Relation Between Gamma and Beta Function

label_important 1.12 Sequences

label_important 1.13 Infinite series

label_important1.14 Comparison test

label_important 1.15 Integral test

label_important 1.16 D'Alembert's ratio test

label_important 1.17 Raabe's test

label_important 1.18 Logarithmic test

label_important1.19 Cauchy's root test

label_important 1.20 Alternating series

label_important 2.1 Function of two or more variables (Limit & Continuity)

label_important2.2 Partial Differentiation

label_important 2.3 Tangent and normal to a surface

label_important 2.4 Maxima & Minima

label_important 2.5 Lagrange's Method

label_important 2.6 Gradient

label_important 2.7 Directional derivatives

label_important 2.8 Curl & Divergence

label_important 2.9 Solenoidal & Irrotational

label_important 3.1 Double Integral

label_important3.2 Change of Order of Integration

label_important 3.3 Change of Variables (Double Integral)

label_important3.4 Application of Double Integral (Area)

label_important 3.5 Triple Integral

label_important3.6 Change of Variables (Triple Integral)

label_important3.7 Application of Triple Integral (Volume)

label_important3.8 Mass, Center of Mass and Gravity

label_important3.9 Greens Theorem

label_important3.10 Gauss divergence Theorem

label_important3.11 Stokes Theorem

label_important 4.1 Matrix Introduction

label_important 4.2 Real matrices: Symmetric, skew – symmetric, Orthogonals

label_important 4.3 Rank of a matrix (Echelon form)

label_important 4.4 Rank of a matrix (Normal form or Canonical form)

label_important 4.5 Consistency of Non-Homogenous Linear Equations

label_important 4.6 Characteristic Equation

label_important 4.7 Eigen values and Eigen vectors

label_important 4.8 Properties of Eigen values and Eigen vectors

label_important 4.9 Cayley Hamilton Theorem

label_important4.10 Diagonalisation of matrix (Similarity Transformation)

label_important4.11 Diagonalisation of matrix (Orthogonal Transformation)