Semester IIComments Off on (Mathematics-II) DIFFERENTIAL EQUATIONS
Objectives of the Course:
To provide an understanding of analytical solution of first and second order differential equations.
Differential equations and their classification, formation of differential equations. Differential equations of first order. Methods of solution of differential equations of first order and first-degree: Separable equations, homogenous equations, equations reducible to homogenous, exact differential equations, integrating factor, linear equations, Bernoulli equations, orthogonal trajectories in Cartesian and polar coordinates, application of first order differential equations. Non-linear first order differential equations.
Higher order linear differential equations: Homogeneous linear equations of order n with constant coefficients, auxiliary/characteristics equations. Solution of higher order differential equation according to the roots of auxiliary equation. Non-homogenous linear equations. Working rules for finding particular integral. Cauchy Euler Equation. Introduction to partial differential equations.
Text and references:
Erwin Kreyszig, “Advanced Engineering Mathematics”, John Wiley & Sons,
John Polking, Al Boggess, David Arnold “Differential Equations”, Prentice Hall, ISBN: 0131437380
Stephen Goode, “Differential Equations and Linear Algebra”, Prentice Hall, ISBN: 013263757X.