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MTH108:DIFFERENTIAL EQUATIONS L:3 T:0 P:0 Course Objectives: • The objective of the course is to acquaint with the knowledge of various ordinary and partial differntial equations. • It aims at indepth understading of various analytical and numerical methods needed for solving different differential equations. • To provide solution of some standard partial differential equations and initial value problems arising in different fields of engineering . Unit I Differential Equations Of Higher Order : Introduction to linear differential equation, Solution of linear differential equation, Linear dependence and linear independence of solution, Method of solution of linear differential equation- Differential operator, Solution of second order homogeneous linear differential equation with constant coefficient, Method of reduction of order for variable coefficient linear homogenous second order equation, Solution of higher order homogenous linear differential equations with constant coefficient Unit II Linear Differential Equation-1 : Solution of non-homogeneous linear differential equations with constant coefficients using operator method, Method of variation of parameters, Method of undetermined coefficient Unit III Linear Differential Equation-2 : Solution of Euler-Cauchy equation, Simultaneous Differential Equations, Solution of first order systems by matrix method, Method of undetermined coefficients to find particular integral Unit IV Numerical Methods For Solutions Of Differential Equations : Existence and Uniqueness of solutions, Picard Method, Taylor Series Method, Euler's Method, Runge kutta Method, Predictor corrector Method (Milne's Method) Unit V Methods of Solving Initial Value Problems : Introduction to Laplace transforms, Properties of laplace transforms, Inverse laplace transforms, Convolution theorem, Laplace transform solution of initial value problems Unit VI Partial Differential Equation : Introduction to partial differential equation, Method of Separation of Variables, Solution of wave equation, Solution of Heat equation, Solution of Laplace equation Text Books: 1. Advanced Engineering Mathematics by R.K. Jain, S.R.K. Iyengar, NAROSA PUBLISHING HOUSE, 4th Edition, (2014) References: 1. Higher Engineering Mathematics by Dr. B.S. Grewal, KHANNA PUBLISHERS, 43th Edition, (2014) Credits:3 Page:1/1 Print Date : 5/19/2015 8:02:02 AM

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  • MTH108:DIFFERENTIAL EQUATIONS

    L:3 T:0 P:0

    Course Objectives:

    The objective of the course is to acquaint with the knowledge of various ordinary and partial differntial equations.

    It aims at indepth understading of various analytical and numerical methods needed for solving different differential equations.

    To provide solution of some standard partial differential equations and initial value problems arising in different fields of engineering .

    Unit IDifferential Equations Of Higher Order : Introduction to linear differential equation, Solution of linear differential equation, Linear dependence and linear independence of solution, Method of solution of linear differential equation- Differential operator, Solution of second order homogeneous linear differential equation with constant coefficient, Method of reduction of order for variable coefficient linear homogenous second order equation, Solution of higher order homogenous linear differential equations with constant coefficient

    Unit IILinear Differential Equation-1 : Solution of non-homogeneous linear differential equations with constant coefficients using operator method, Method of variation of parameters, Method of undetermined coefficient

    Unit IIILinear Differential Equation-2 : Solution of Euler-Cauchy equation, Simultaneous Differential Equations, Solution of first order systems by matrix method, Method of undetermined coefficients to find particular integral

    Unit IV

    Numerical Methods For Solutions Of Differential Equations : Existence and Uniqueness of solutions, Picard Method, Taylor Series Method, Euler's Method, Runge kutta Method, Predictor corrector Method (Milne's Method)

    Unit VMethods of Solving Initial Value Problems : Introduction to Laplace transforms, Properties of laplace transforms, Inverse laplace transforms, Convolution theorem, Laplace transform solution of initial value problems

    Unit VIPartial Differential Equation : Introduction to partial differential equation, Method of Separation of Variables, Solution of wave equation, Solution of Heat equation, Solution of Laplace equation

    Text Books:

    1. Advanced Engineering Mathematics by R.K. Jain, S.R.K. Iyengar, NAROSA PUBLISHING HOUSE, 4th Edition, (2014)

    References:

    1. Higher Engineering Mathematics by Dr. B.S. Grewal, KHANNA PUBLISHERS, 43th Edition, (2014)

    Credits:3

    Page:1/1 Print Date : 5/19/2015 8:02:02 AM


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