BOOK: Differential Equation, Calculus of Variations and Special Functions

UNIT – VI : Eigen values, Eigen functions and Sturm-Liouville boundary value problem

Dr. Kamlesh

Bisht

(Mathematics)

DR. KAMLESH BISHT

Academic ConsultantDepartment of Mathematics

Uttarakhand Open University, Haldwani

Content

� Objective.

� Introduction.

� Linear Homogeneous Boundary Value Problems.

Dr. Kamlesh Bisht(Mathematics)

� Linear Homogeneous Boundary Value Problems.

� Eigenvalues and eigenfunction.

� Sturm-Liouville problems.

� Orthogonality of eigenfunctions.

� References.

Objectives

After studying this unit, you should be able to-

� Get the basic knowledge of eigenvalue and eigenfunction

of the boundary value problem.

Dr. Kamlesh Bisht(Mathematics)

of the boundary value problem.

� Study special boundary value problem known as Sturm-

Louville problem and properties of eigenfunction.

� Get the knowledge about various special function that

arises in physical and engineering problems.

Introduction

Linear Homogeneous Boundary Value Problems

Eigen values and Eigen functions

Eigen value or Characteristic value

Eigen function or Characteristic function

Sturm-Liouville Problem

Orthogonality of Eigenfunctions

Theorems on Sturm-Liouville systems

References:

� Advanced Differential Equation

M.D. Raisinghania, S. Chand Publication

SLM of VMOU, Kota � SLM of VMOU, Kota

Differential Equation, Calculus of Variation and Special Functions.

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