**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.

**➥DOWNLOAD UNIT-1**

**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.

**➥DOWNLOAD UNIT-2**

**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.

**➥**

**DOWNLOAD UNIT-3**

**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.

**➥DOWNLOAD UNIT-4**

**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.

➥DOWNLOAD UNIT-5

➥DOWNLOAD UNIT-5