MG University B.Tech Syllabus S8 Civil
Module 1 Green’s Function
Heavisides, unit step function – Derivative of unit step function – Dirac delta function – properties of delta function – Derivatives of delta function – testing functions – symbolic function – symbolic derivatives – inverse of differential operator – Green’s function – initial value problems – boundary value problems – simple cases only
Heavisides, unit step function – Derivative of unit step function – Dirac delta function – properties of delta function – Derivatives of delta function – testing functions – symbolic function – symbolic derivatives – inverse of differential operator – Green’s function – initial value problems – boundary value problems – simple cases only
Module 2 Integral Equations
Definition of Volterra and Fredholm Integral equations – conversion of a linear differential equation into an integral equation – conversion of boundary value problem into an integral equation using Green’s function – solution of Fredhlom integral equation with separable Kernels – Integral equations of convolution type – Neumann series solution.
Definition of Volterra and Fredholm Integral equations – conversion of a linear differential equation into an integral equation – conversion of boundary value problem into an integral equation using Green’s function – solution of Fredhlom integral equation with separable Kernels – Integral equations of convolution type – Neumann series solution.
Module 3 Gamma, Beta functions
Gamma function, Beta function – Relation between them – their transformations – use of them in the evaluation certain integrals – Dirichlet’s integral – Liouville’s extension of Dirichlet’s theorem – Elliptic integral – Error function.
Gamma function, Beta function – Relation between them – their transformations – use of them in the evaluation certain integrals – Dirichlet’s integral – Liouville’s extension of Dirichlet’s theorem – Elliptic integral – Error function.
Module 4 Power Series solution of differential equation
The power series method – Legendre’s Equation – Legendre’s polynomial – Rodrigues formula – generating function – Bessel’s equation – Bessel’s function of the first kind – Orthogonality of Legendre’s Polynomials and Bessel’s functions.
The power series method – Legendre’s Equation – Legendre’s polynomial – Rodrigues formula – generating function – Bessel’s equation – Bessel’s function of the first kind – Orthogonality of Legendre’s Polynomials and Bessel’s functions.
Module 5 Numerical solution of partial differential equations.
Classification of second order equations- Finite difference approximations to partial derivatives – solution of Laplace and Poisson’s equations by finite difference method – solution of one dimensional heat equation by Crank – Nicolson method – solution one dimensional wave equation.
Classification of second order equations- Finite difference approximations to partial derivatives – solution of Laplace and Poisson’s equations by finite difference method – solution of one dimensional heat equation by Crank – Nicolson method – solution one dimensional wave equation.
References
1. Ram P.Kanwal, Linear Integral Equation, Academic Press, New York.
Allen C.Pipkin, Springer, A Course on Integral Equations, Verlag.
H.K.Dass, Advanced Engg. Mathematics, S.Chand.
Michael D.Greenberge, Advanced Engg. Mathematics, Pearson Edn. Asia.
B.S.Grewal, Numrical methods in Engg.&science, Khanna Publishers.
R.F. Hoskins, Generalized functions, John Wiley and Sons.
7. Bernard Friedman, Principles and Techniques of Applied Mathematics, John Wiley and sons
8. James P.Keener, Principles of Applied Mathematics, Addison Wesley.
9. P.Kandasamy, K.Thilagavathy, K.Gunavathy Numerical methods, S.Chand & co.
Allen C.Pipkin, Springer, A Course on Integral Equations, Verlag.
H.K.Dass, Advanced Engg. Mathematics, S.Chand.
Michael D.Greenberge, Advanced Engg. Mathematics, Pearson Edn. Asia.
B.S.Grewal, Numrical methods in Engg.&science, Khanna Publishers.
R.F. Hoskins, Generalized functions, John Wiley and Sons.
7. Bernard Friedman, Principles and Techniques of Applied Mathematics, John Wiley and sons
8. James P.Keener, Principles of Applied Mathematics, Addison Wesley.
9. P.Kandasamy, K.Thilagavathy, K.Gunavathy Numerical methods, S.Chand & co.