Syllabus OF M-III
Differentiation of vector Radial,Transverse, Normal and Tangential components of velocity and acceleration, Scalar and vector point fuctions, Gradient of scalar point fuction, Divergence and curl of a vector point fuction, Solenidal and irrotational fields, Line integral, Surface integral, Gauss's divergence theorem, Green's therom, Cylindrical, Spherical, polar and Curvilinear conditions.
Fourier integral, Fourier sine and cosine integral, Complex form of Fourier integral, Fourier transform, Fourier sine and cosine transform and inverse transform.
3.Linear Differential Equation
Solution of Linear differential equation and of nth order with constant coefficients, General method, shorter method to find particular integral method of varitions of parameters, Equation reducible to linear form i.e. Cauchy's and Legendre's form Solution of simultaneous linear differential equation. Apllication to Civil, Mechanical, Electrical and Electronics Engineering.
Introdution to Laplace transform, Properties and theorms of Laplace transform, Laplace transform of special fuctions, Bessel's Periodic, Error fuction. Heaviside Unit Step Fuction, Dirac-Delta fuction (impluse fuction), Inverse Laplace Transform, Methods to find inverse Laplace transform by
(i)use of Laplace transform table
(ii)use of theorems
(iii)use of partial equations of nth
solution of linear differencal equations of nth order with constant coefficients and simultaneous linear differentil equations by Laplace Transform.
Section A Chapter 1 and Chapter 2
Section B Chapter 3 and Chapter 4
1.A text book of Applied Mathematics Volume II and III
Author:P.N.Wartikar and J.N.Wartikar
2.Advanced Engineering Mathematics
3.Engineering Mathematics III
4.Higher Engineering Mathematics