#### Methods of Applied Mathematics (Code-09050505)

S.No. |
Topic |
Domain |
Hours as per UGC |

1 | · Solution of 3D Laplace | Must know | 10 |

· Wave and heat equations in spherical polar co-ordinates by the method of separation of variables | |||

· Fourier series solution of the wave equation | |||

· Transformation of boundary value problems | |||

2 | · Fourier series solution of the heat equation | Must know | 15 |

· Steady-state temperature in plates | |||

· The heat and wave equations in unbounded domains | |||

· Fourier transform solution of BVPs | |||

· The heat equation in an infinite cylinder and in a solid sphere | |||

3 | · Hankel transform of elementary functions | Must know | 15 |

· Operational properties of the Hankel transform | |||

· Applications of Hankel transforms to PDE | |||

· Definitions and basic properties of finite Fourier sine and cosine transforms | |||

· Its application to the solutions of BVP’s and IVP’s | |||

4 | · Moments and products of inertia | Must know | 12 |

· Angular momentum of a rigid body | |||

· Principal axes and principal moment of inertia of a rigid body | |||

· Kinetic energy of a rigid body rotating about a fixed point | |||

· Momental ellipsoid and equimomental systems | |||

· Coplanar mass distributions | |||

· General motion of a rigid body |

Books Recommended:

- Jerri, A.J. ,Introduction to Integral Equations with applications.
- Lokenath Debnath, Integral Transforms and their Applications, CRC Press, Inc., 1995.
- Peter V. O”Neil, Advanced Engineering Mathematics, 4
^{th}, An International Thomson Publishing Company, - Sneddon, I.N., Special Function of Mathematical Physics and Chemistry
- Sneddon, I.N., Elements of Partial Differential equation, Printice Hall, McGraw Hill.
- Chorlton, F., Dynamics, CBS Publishers Ans Distributers.