Mathematics I (BES1-1)

label_important 1.1 Leibnitz's theorem

label_important1.2 Taylor & Maclaurin Series

label_important 1.3 Indeterminate Forms (L Hospital)

label_important 1.4 Maxima and Minima of functions of one variable

label_important 2.1 Partial Differentiation

label_important2.2 Euler's Theorems

label_important 2.3 Total Derivatives (Chain Rule)

label_important 2.4 Derivative of an Implicit Functions

label_important 2.5 Jacobian's

label_important 2.6 Taylors Series & Maclaurin Series

label_important 2.7 Maxima & Minima

label_important 2.8 Lagrange's Method

label_important 3.1 Matrix Introduction

label_important3.2 Rank of a matrix (Echelon form)

label_important 3.3 Rank of a matrix (Normal form or Canonical form)

label_important 3.4 Consistency of Non-Homogenous Linear Equations

label_important 3.5 Consistency of Homogenous Linear Equations

label_important 3.6 Cayley Hamilton Theorem

label_important 4.1 Linear Differential Equation

label_important4.2 Bernoullis Equation

label_important 4.3 Exact Differential Equation

label_important 4.4 Non-Linear Differential Equation

label_important 4.5 Equation Solvable for Y

label_important 4.6 Equation Solvable for X

label_important 4.7 Clairauts Equation

label_important 5.1 Linear Differential Equations of Higher Order

label_important5.2 General solution of f(D)y = e^ax

label_important 5.3 General solution of f(D)y = cos ax or sin ax

label_important 5.4 General solution of f(D)y = x^m

label_important 5.5 General solution of f(D)y = e^ax . f(x)

label_important 5.6 General solution of f(D)y = x^m . f(x)

label_important 5.7 Method of variation of parameters

label_important 5.8 Cauchy's Differential Equations

label_important 5.9 Legendre Differential Equations

label_important 5.10 Simultaneous first order linear equations with constant coefficients

label_important 5.11 Applications to Electric R-L-C circuits