Differential Equations

1.    The Ordinary Differential Equations of second order with constant coefficients.

2.     Determination of complimentary functions and particular integrals

Numerical Analysis:

1.    Estimation of errors, Solution of polynomials and interpolation.

2.    Computer Application of Numerical Techniques.

Vector Analysis

Scalar and vector quantities, algebra of vectors. Dot and cross product of vectors. Differentiation and integration of vector function. Multiple integrals. Gradient of  a scalar point functions. Divergence and curl of a vector field, Equations of the straight line, the plane and the sphere. Complex variables: function of a complex variables, Derivative of function of a complex variables, analytic function and Cauchy Reimann Equations, Cauchy’s Theorem .Laurent’s expansion and theory of Residues.

Fourier Series and Laplace Transform

Introduction to Periodic functions,  Fourier Series, convergence of  Fourier Series, , Fourier Series of functions with arbitrary periods, , Fourier Series for even and odd foundations, Laplace Transform, derivatives and integrals, Transformation of ordinary differential equations and their solutions. Differentiation and integration of Transforms.

Potential Theory

Laplace Equations in Polar and Cylindrical Coordinate

Power functions through seismic velocities, trigonometry through cliff erosion, and integration through sediment accumulation