Differentiation of vectors, curves in space, Velocity and acceleration, Relative velocity and
acceleration, Scalar and Vector point functions, Vector operator ", " applied to scalar point
functions, Gradient, " applied to vector point functions, Divergence and curl, Physical
interpretations of ", F and " × F, " applied twice to point functions, " applied to products of
point functions, integration of vectors, Line integral, Circulation, Work, Surface integral-flux,
Green s theorem in the plane, Stoke s theorem, Volume integral, Divergence theorem, Irrotational and solenoidal fields, Green s theorem, Introduction of orthogonal curvilinear coordinates : Cylindrical, Spherical and polar coordinates

Formation of partial differential equations, Solutions of PDEs, Equations solvable by direct
integration, Linear equations of first order, Homogeneous linear equations with constant
coefficients, Rules for finding the complimentary function, Rules of finding the particular
integral, Working procedure top solve homogeneous linear equations of any order, Nonhomogeneous linear equations

Method of separation of variables, Vibrations of a stretched string-wave equations, Onedimensional and two-dimensional heat flow equations, Solution of Laplace s equation, Laplace s equation in polar coordinates

Introduction, Definition, Fourier Integral, Sine and Cosine Integrals, Complex Forms of Fourier
Integral, Fourier Transform, Fourier and Cosine Transforms, Finite Fourier Sine and Cosine
Transforms, Properties of F - Transforms, Convolution Theorem for F - Transforms, Parseval s
Identity for Fourier Transforms, Fourier Transforms of the Derivatives of a Function,
Applications to Boundary Value Problems, Using Inverse Fourier Transforms only