1. Vector Calculus : Parametrization of curves, Arc leωJth of curve in space, Line Intes;irals, \?ector fields and applications as Wori<, Circulation and Flux, Path independence, potential function, piecewise smooth, connected domain, simply connected domain, fundamental theorem of line intes;irals, Conservative fields, component test for conservative fields, exact differential forms, Div, Curl, Green's theorem ίη the plane (without proof). (Chapter - ι) 2. Laplace Transform and inverse Laplace transform. Linearity. First ShiftinSJ Theorem (s-Shiftins;i). Transforms of Derivatives and Intes;irals. ODEs. Unit Step Function (Heaviside Function). Second ShiftinSJ Theorem (t-Shiftins;i). Laplace transform of periodic functions. Short Impulses. Dirac's Delta Function. Convolution. Intes;iral Equations. Differentiation and Intes;iration of Transforms. ODEs with \?ariable Coefficients. Systems of ODEs.(Chapter - 2) 3. Fourier Intes;iral, Fourier Cosine Intes;iral and Fourier Sine Intes;iral. (Chapter - 3) 4. First order ordinary differential equations, Exact, linear and Bernoulli's equations, Equations not of first des;iree: equations solvable for p, equations solvable for y, equations solvable for χ and Clairaut's type.. (Chapter - 4) 5. Ordinary differential equations of his;iher orders, Homos;ieneous Linear ODEs of His;iher Order, Homos;ieneous Linear ODEs with Constant Coefficients, Euler-Cauchy Equations, Existence and Uniqueness of Solutions, Linear Dependence and Independence of Solutions, Wronsi