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...B tech mathematics iii lecture note partial differential equation a containing terms as derivatives is called pde the order of highest derivative dependent variable z depends on independent variables x and y p q r s t for example px formation by eliminating arbitrary constant f differentiating w to partially constants we get from form solution respectively qx py required function let u v g shall eliminate above equations which an involving atleast one or more linear if it first degree in its each term such contains either homogeneous important second c dimensional wave tt xx heat two laplace yy three zz poisson problems verify that e sin putting deivativers hence satisfied solve uxy uy put then integrating ln d where modeling derive small transverse vibration elastic string stretch length l fixed at both ends assumptions does not have resistance bending mass per unit tension caused stretching before fixing too large so can neglect action gravitational force performs motion vertical pla...