Course Details

1	Title of the course (L-T-P-C)	Differential Equations - I (3-1-0-4)
2	Pre-requisite courses(s)
3	Course content	Exact equations, integrating factors and Bernoulli equations. Orthogonal trajectories. Lipschitz condition, Picard's theorem, examples on non-uniqueness. Linear differential equations generalities. Linear dependence and Wronskians. Dimensionality of space of solutions, Abel-Liouville formula. Linear ODE's with constant coefficients, the characteristic equations. Cauchy-Euler equations. Method of undetermined coefficients. Method of variation of parameters. Laplace transform generalities. Shifting theorems. Convolution theorem.
4	Texts/References	E. Kreyszig, Advanced engineering mathematics (10th Edition), John Wiley (1999) W. E. Boyce and R. DiPrima, Elementary Differential Equations (8th Edition), John Wiley (2005)

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