Fourier Series:  Periodic functions.  Euler formula for coefficients in Fourier sine/cosine series of a function.  Even and odd functions and their Fourier series.  Half range expansion.  Theoretical basis of Fourier series.  Application to the solution of partial differential equations.

Gamma, Beta and probability function (emphasis rather on the applications).

Differential Equation:  Equations of the form y” –f(x, y’).  Linear second order equations reducible to linear equation with constant coefficients.  Series solution of differential equation and Bessel functions of first kind; their properties and introduction to applications.

Vector Field Theory:  Scalar and Vector fields:  directional derivative; gradient of a scalar field, divergence and curl of a vector field; del operator.  Line, surface and volume integrals.  Divergence theorem of Gases and Stoke’s theorem.  Green’s theorem.  Line integrals independent of path and irrational vector fields.

Level of Study: 300 Level