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)
Nano Materials
Introduction, Properties of nanomaterials, Graphene, Fullerenes, Carbon nanotubes, nano wires, nano cones, Application of nano-materials.
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.