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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:

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