Vector Valued Function Of Single Variable, Derivative Of Vector Function And Geometrical Interpretation, Motion Along A Curve-velocity, Speed And Acceleration. Concept Of Scalar And Vector Fields, Gradient And Its Properties, Directional Derivative, Divergence And Curl, Line Integrals Of Vector Fields, Work As Line Integral, Conservative Vector Fields, Independence Of Path And Potential Function (results Without Proof).

Green’s Theorem (For Simply Connected Domains, Without Proof) And Applications To Evaluating Line Integrals And Finding Areas. Surface Integrals Over Surfaces Of The Form Z = G(x, Y), Y = G(x, Z) Or X = G(y, Z), Flux Integrals Over Surfaces Of The Form Z = G(x, Y), Y = G(x, Z) Or X = G(y, Z), Divergence Theorem (Without Proof) And Its Applications To Finding Flux Integrals, Stokes’ Theorem (Without Proof) And Its Applications To Finding Line Integrals Of Vector Fields And Work Done.

Homogenous linear differential equation of second order, superposition principle, general solution, homogenous linear ODEs with constant coefficients-general solution. Solution of Euler-Cauchy equations (second order only). Existence and uniqueness (without proof). Non-homogenous linear ODEs-general solution, solution by the method of undetermined coefficients (for the right-hand side of the form $x^{n}, e^{k x}, \sin(ax), \cos(ax), e^{k x} \sin(ax) e^{k x} \cos(ax)$ and their linear combinations), methods of variation of parameters. Solution of higher-order equations-homogeneous and non-homogeneous with constant coefficient using the method of undetermined coefficient.

Laplace Transform And Its Inverse, Existence Theorem (Without Proof), Linearity, Laplace Transform Of Basic Functions, First Shifting Theorem, Laplace Transform Of Derivatives And Integrals, Solution Of Differential Equations Using Laplace Transform, Unit Step Function, Second Shifting Theorems. Dirac Delta Function And Its Laplace Transform, Solution Of Ordinary Differential Equation Involving Unit Step Function And Dirac Delta Functions. Convolution Theorem (without Proof) And Its Application To Finding Inverse Laplace Transform Of Products Of Functions.

Fourier Integral Representation, Fourier Sine And Cosine Integrals. Fourier Sine And Cosine Transforms, Inverse Sine And Cosine Transform. Fourier Transform And Inverse Fourier Transform, Basic Properties. The Fourier Transform Of Derivatives. Convolution Theorem (Without Proof).