## Mathematics III

**Module 1. Instructor: Dr. P. N. Agrawal, Department of Mathematics, IIT Roorkee**

Solution of ODE of First Order and First Degree, Linear Differential Equations of the First Order, Approximate Solution of an Initial Value Problem, Series Solution of Homogeneous Linear Differential Equations, Bessel Functions and Their Properties, Laplace Transformation, Applications of Laplace Transformation, One Dimensional Wave Equation, One Dimensional Heat Equation.

**Module 2. Instructor: Dr. Tanuja Srivastava, Department of Mathematics, IIT Roorkee**

Introduction to Differential Equation, First Order Differential Equations and Their Geometric Interpretation, Differential Equations of First Order and Higher Degree, Linear Differential Equations of Second Order, Euler-Cauchy Theorem, Higher Order Linear Differential Equations, Higher Order Non-homogeneous Linear Equations, Boundary Value Problems, Sturm Liouville Boundary Value Problems, Fourier Series, Convergence of the Fourier Series, Fourier Integrals, Fourier Transforms, Partial Differential Equation, Solution of One Dimensional Wave Equation, Fourier Integral and Transform Method for Heat Equation, Three Dimensional Laplace Equations, Solution of Dirichlet Problem, Numerical Method for Laplace and Poisson Equations.

(from **nptel.ac.in**)

Solution of ODE of First Order and First Degree |

References |

Mathematics IIIInstructors: Dr. P. N. Agrawal and Dr. Tanuja Srivastava, Department of Mathematics, IIT Roorkee. Differential Equations. |