Knowledge in mathematical Physics
Differential equations
Differential equations is a major part of mathematics but it has a great advantage and application in physics too....order and degree of differential equation mentioned here as well as then partial differential equations are discussed and method of separation of variables to solve the equations
Ishant Goel
Homogeneous equations
Homegeneous equations have a little different method to solve and examples.... We can solve it by separating y and x variables and then put them equal to some variable
Non-homogeneous equations
Non-homogeneous equations are those equations in which x and y variables can't be separated and solve questions by putting different values for x and y in some other variables
Exact differential equations
Exact differential equations are those equations in which dM/dx =dN/dy....in questions, first of all we have to identify whether it is an exact equation or not And then we solve it by using methods and examples given for practice
Second order equations
These are the second order partial differential equations with both types of constants...some as fixed coefficients and some has variance constant and both types of questions are discussed
Method of undetermined coefficients
The method of undetermined coefficients is also a very significant method to solve differential equations... Basically in this method, we assume two or three coefficients in the differential equations and then find it's value and finally we got the answer
Wronskion
It is actually a set of functions and the set is linearly dependent if all coefficients are not zero Otherwise it is linearly independent.... In these type of questions, we have to determine that whether the given function is LI or not
Method of variation of parameters
Method of variation of parameters is another method to solve the differential equations in which the variation of parameters is required... Many examples are given for practice
Cauchy's Euler equations
Cauchy's euler equations is another important aspect for differential equations... in these equations, we find euler function to solve the problem
Simultaneous Differential equations
Simultaneous equations are those equations which involves different functions in a single function i.e. sin function, cos function and constant functions and at last, there is an assignment attached for the whole topic