**Introduction to Some Special Functions:**Gamma function, Beta function, Bessel function, Error function and complementary Error function, Heaviside’s function, pulse unit height and duration function, Sinusoidal Pulse function, Rectangle function, Gate function, Dirac’s Delta function, Signum function, Saw tooth wave function, Triangular wave function, Half wave rectified sinusoidal function, Full rectified sine wave, Square wave function.**Fourier Series and Fourier integral:**Periodic function, Trigonometric series, Fourier series, Functions of any period, Even and odd functions, Half-range Expansion, Forced oscillations, Fourier integral.**Ordinary Differential Equations and Applications:**First order differential equations: basic concepts, Geometric meaning of y’ = f(x,y) Direction fields, Exact differential equations, Integrating factor, Linear differential equations, Bernoulli equations, Modeling , Orthogonal trajectories of curves. Linear differential equations of second and higher order: Homogeneous linear differential equations of second order, Modeling: Free Oscillations, Euler- Cauchy Equations, Wronskian, Non homogeneous equations, Solution by undetermined coefficients, Solution by variation of parameters, Modeling: free Oscillations resonance and Electric circuits, Higher order linear differential equations, Higher order homogeneous with constant coefficient, Higher order non homogeneous equations. Solution by [1/f(D)] r(x) method for finding particular integral.**Series Solution of Differential Equations**: Power series method, Theory of power series methods, Frobenius method.**Laplace Transforms and Applications**: Definition of the Laplace transform, Inverse Laplace transform, Linearity, Shifting theorem, Transforms of derivatives and integrals Differential equations, Unit step function Second shifting theorem, Dirac’s delta function, Differentiation and integration of transforms, Convolution and integral equations, Partial fraction differential equations, Systems of differential equations.**Partial Differential Equations and Applications:**Formation PDEs, Solution of Partial Differential equations f(x,y,z,p,q) = 0, Nonlinear PDEs first order, Some standard forms of nonlinear PDE, Linear PDEs with constant coefficients, Equations reducible to Homogeneous linear form, Classification of second order linear PDEs. Separation of variables use of Fourier series, D’Alembert’s solution of the wave equation, Heat equation: Solution by Fourier series and Fourier integral

**Text Books:**

1. Advanced Engineering Mathematics (8th Edition), by E. Kreyszig, Wiley-India (2007). (1.1,

1.2, 1.5, 1.6, 1.7, 1.8, 2.1 to 2.15, 4.1, 4.2, 4.4, 5.1 to 5.9, 10.1 to 10.4, 10.6, 10.8, 11.3, 11.4,

11.5, 11.6)

2. Engineering Mathematics Vol 2, by Baburam, Pearson( 1.12, 4.20,5.1 to 5.8)

**Reference Books:**

1. W. E. Boyce and R. DiPrima, Elementary Differential Equations (8th Edition), John Wiley (2005).

2. R. V. Churchill and J. W. Brown, Fourier series and boundary value problems (7th Edition),

McGraw-Hill (2006).

3. T.M.Apostol, Calculus , Volume-2 ( 2nd Edition ), Wiley Eastern , 1980 Projects

The following projects are recommended for the students to perform during semester.