Infinite Fourier transform- sine and cosine transforms –Theorems-Related problems-Application of Fourier transforms to boundary value problems: Applications of infinite Fourier transform-Examples Theorems
Infinite Hankel transforms-Theorems-Applications-Examples-Finite Hankel transforms-Theorems-Examples
Preliminary concepts-Introduction-Definition-Fredholn, Voltera Integral equations-First, second kinds. Special kinds ok kernals-Integral equation of convolution type- Resolvent kernals-Eigen values-Eigen functions-Regularity conditions-Inner or scalar product of two functions-Solution of an integral equations-Solved problems-Homogeneous and non homogeneous- Fredholn integral equations of second kind with separable kernals-Solution of Fredholn integral equations of second kind successive approximation method(Problems only).
Solution of Voltera integral equations of second kind of successive approximation method-Solved problems. Solution of Voltera integral equation of first kind. Singular Integral Equation: Definition-solution of Abel integral equation-General form of Abel singular equation
Variation and its properties – Euler’s equation (Statement only) – Alternative forms- Variational problems for functional involving several dependent variables (Statement only) –Functional dependent on higher order derivative
Reference Book:
Differential equations and Calculus of variations by Rakesh Kumar, Nagendra Kumar, CBS Publications, First Edition, 2013
Text Book:
1. Integral Transform By, Goyal Gupta, A Pragati Prakashan, Fifteenth Revisited edition 2012. (For Units I and II) Unit I: Chapter 2: Sections: 2.0 -2.3. Examples (1-8, 16-22, 25-28) Theorems (1- 7, 9), Chapter 6: Examples 1, 10-12, 14, 15 Unit II: Examples: 1-19, Examples: 1-5 2. “Integral Equations and Boundary value Problems” by M.D.Raisinghania, Fourth revised Edition 2011. S.Chand Publications. (For Units III and IV) Unit III: Chapter 1: Sections: 1.1, 1.3, 1.5,1.6, 1.8,1.9,1.11,1.12,1.15-1.18 Chapter 3: Sections: 3.2 Examples (1-5) Chapter 4: Sections: 4.2 Examples (1-9) Chapter 5: Section: 5.9 Unit IV: Chapter 5: Section: 5.13, 5.17. Chapter 8: Section: 8.1-8.3. 3. “Advanced Differential Equations” by Dr.M.D. RaisingHania, Fifteenth revised edition 2012. S.Chand Publications. (For Unit V) Unit V: Chapter 1: Sections: 1.2, 1.2A, 1.4, 1.5, 1.5A, 1.5B, 1.5D, 1.5E, 1.5F, 1.8, 1.8B, 1.9, 1.9A, 1.9B.
