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JNTUK R19 MATHEMATICS -III  Syllabus study notes:-
UNIT–I:- Vector calculus:-
Vector Differentiation: Gradient – Directional derivative – Divergence – Curl – Scalar Potential. Vector Integration: Line integral – Work done – Area – Surface and volume integrals – Vector integral theorems: Greens, Stokes and Gauss Divergence theorems.


UNIT–II:- Laplace Transforms:-
Laplace transforms of standard functions – Shifting theorems – Transforms of derivatives and integrals – Unit step function – Dirac’s delta function – Inverse Laplace transforms – Convolution theorem (with out proof). Applications: Solving ordinary differential equations (initial value problems) using Laplace transforms.


UNIT–III:- Fourier series and Fourier Transforms:-
Fourier Series: Introduction – Periodic functions – Fourier series of periodic function – Dirichlet’s conditions – Even and odd functions – Change of interval – Half-range sine and cosine series. Fourier Transforms: Fourier integral theorem (without proof) – Fourier sine and cosine integrals – Sine and cosine transforms – Properties – inverse transforms – Finite Fourier transforms. 


UNIT–IV:-  PDE of first order:-
Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions – Solutions of first order linear (Lagrange) equation and nonlinear (standard types) equations. 


UNIT V:- Second order PDE and Applications:-
Second order PDE: Solutions of linear partial differential equations with constant coefficients – RHS term of the type ,sin( ax+by), cos(ax+by), x y  . Applications of PDE: Method of separation of Variables – Solution of One dimensional Wave, Heat and two-dimensional Laplace equation.