Notes for Applied Mathematics-1 - M-1 by Aditya Ravi

First order differential equations, arithmetic problems

Equation reduceable to separable form, homogeneous function, homogeneous differential equation, non-homogeneous equation reducable to separable equation

condition of exactness, Defination of integrating factor, Rules for finding Integrating factor

Linear differential equation, Equation reducable to linear form

Bernoulli's equation and application to Electrical circuits

Modeling of electric circuits

Linear differential equation of second order

Homogeneous equation with constant co-efficient, Euler-Cauchy equations, non-homogeneous equations

Solution by undetermined co-effficient

Solutions by variation of parameters

Power series method

Legendre equation and Legendre polynomials

Matrices

Newton law of cooling, Salt mixing problem

Radius of convergence, Shifting of index