# InfoCoBuild

### Ordinary and Partial Differential Equations and Applications

Ordinary and Partial Differential Equations and Applications. Instructors: Dr. P. N. Agrawal and Dr. D. N. Pandey, Department of Mathematics, IIT Roorkee. Differential equation are used to express many general laws of nature and have many applications in physical, biological, social, economical and other dynamical systems. This course contains existence and uniqueness of solutions of an ODE, homogeneous and non-homogeneous linear systems of differential equations, power series solution of second order homogeneous differential equations. Frobenius method, boundary value problems for second order ODE, Green's function, autonomous systems, phase plane, critical points and stability for linear and non-linear systems, eigenvalue problems, Sturm-Liouville problem. Classification of first order PDE, existence and uniqueness of solutions, Nonlinear PDE of first order, Cauchy method of characteristics, Charpit's method, PDE with variable coefficients, canonical forms, characteristic curves, Laplace equation, Poisson equation, wave equation, homogeneous and nonhomogeneous diffusion equation, Duhamel's principle. This course has tremendous applications in diverse fields of Engineering and Sciences such as control theory, numerical analysis and dynamical systems etc. (from nptel.ac.in)

 Introduction to Differential Equations

 Lecture 01 - Introduction to Differential Equations Lecture 02 - Initial and Boundary Value Problems with Some Examples Lecture 03 - Existence and Uniqueness of Solutions of Differential Equations Lecture 04 - Existence and Uniqueness of Solutions of Differential Equations (cont.) Lecture 05 - Existence and Uniqueness of Solutions of Differential Equations (cont.) Lecture 06 - Existence and Uniqueness of Solutions of a System of Differential Equations Lecture 07 - Linear System Lecture 08 - Properties of Homogeneous Systems Lecture 09 - Solution of Homogeneous Linear System with Constant Coefficients Lecture 10 - Solution of Homogeneous Linear System with Constant Coefficients (cont.) Lecture 11 - Solution of Homogeneous Linear System with Constant Coefficients (cont.) Lecture 12 - Solution of Nonhomogeneous Linear System with Constant Coefficients Lecture 13 - Power Series Lecture 14 - Uniform Convergence of Power Series Lecture 15 - Power Series Solution of Second Order Homogeneous Equations Lecture 16 - Regular Singular Points I Lecture 17 - Regular Singular Points II Lecture 18 - Regular Singular Points III Lecture 19 - Regular Singular Points IV Lecture 20 - Regular Singular Points V Lecture 21 - Critical Points Lecture 22 - Stability of Linear Systems I Lecture 23 - Stability of Linear Systems II Lecture 24 - Stability of Linear Systems III Lecture 25 - Critical Points and Paths of Nonlinear Systems Lecture 26 - Boundary Value Problems for Second Order Differential Equations Lecture 27 - Self Adjoint Form Lecture 28 - Sturm-Liouville Problem and its Properties Lecture 29 - Sturm-Liouville Problem and its Applications Lecture 30 - Green's Function and its Application Lecture 31 - Green's Function and its Application (cont.) Lecture 32 - Origins and Classification of First Order PDEs Lecture 33 - Initial Value Problem for Quasi-Linear First Order Equations Lecture 34 - Existence and Uniqueness of Solutions Lecture 35 - Surfaces Orthogonal to a Given System of Surfaces Lecture 36 - Nonlinear PDE of First Order Lecture 37 - Cauchy Method of Characteristics Lecture 38 - Cauchy Method of Characteristics: Examples Lecture 39 - Compatible System of First Order Equations Lecture 40 - Charpit's Method Lecture 41 - Charpit's Method (cont.) Lecture 42 - Second Order PDE with Variable Coefficients Lecture 43 - Classification and Canonical Form of Second Order PDE Lecture 44 - Classification and Canonical Form of Second Order PDE (cont.) Lecture 45 - Classification and Characteristic Curves of Second Order PDEs Lecture 46 - Review of Integral Transform: Laplace Transform and its Properties Lecture 47 - Review of Integral Transform: the Application of Laplace Transform Lecture 48 - Review of Integral Transform: Fourier Integral Lecture 49 - Laplace Equation Lecture 50 - Laplace Equation (cont.) Lecture 51 - Laplace Equation (cont.) Lecture 52 - Laplace and Poisson Equations Lecture 53 - One Dimensional Wave Equations and its Solutions I Lecture 54 - One Dimensional Wave Equations and its Solutions II Lecture 55 - One Dimensional Wave Equations and its Solutions III Lecture 56 - Two Dimensional Wave Equation and its Solution Lecture 57 - Solution of Nonhomogeneous Wave Equation: Riemann Method Lecture 58 - Solution of Homogeneous Diffusion Equation Lecture 59 - Solution of Homogeneous Diffusion Equation (cont.) Lecture 60 - Duhamel's Principle

 References Ordinary and Partial Differential Equations and Applications Instructors: Dr. P. N. Agrawal and Dr. D. N. Pandey, Department of Mathematics, IIT Roorkee. Differential equation are used to express many general laws of nature.