MA-121 Applied Mathematics-II
Teaching Scheme			Credit	Marks Distribution			Duration of End Semester Examination
L	T	P		Internal Assessment	End Semester Examination	Total
3	1	0	4	Maximum Marks: 40	Maximum Marks: 60	100	3 Hours
				Minimum Marks: 16	Minimum Marks: 24	40

Unit - I

Ordinary Differential Equations: Review of first order linear differential equations , Exact differential equations , Second and higher order linear differential equations with constant coefficients. Cauchy's & Legendre ‘s homogeneous differential equations , method of variation of parameters , Cauchy - Euler equation.

Unit - II

Partial Differential Equations: Introduction , Homogeneous and non-homogencous linear PDE with constant coefficients.

Applications of PDE: Method of separation of variables, Solution of one-dimensional wave and heat equation and two-dimensional Laplace’s equation.

Unit - III

Laplace Transforms: Laplace transforms and its properties , Inverse Laplace transforms using partial fraction , convolution theorem (without proof) , Unit step function and Impulse function , Applications to solve initial and boundary value problems.

Fourier Series: Introduction , Fourier series on arbitrary intervals , Even Odd functions , Half range expansions , Parseval ‘s theorem.

Unit - IV

Vector calculus: Introduction to vectors , vector algebra , directional derivatives , gradient , divergence & curl , Scalar line integrals, line integrals, surface integrals , Green , Stokes and Gauss divergence theorem (without proof)