Course Details

1 Title of the course
(L-T-P-C)
Differential Equations - I (2nd Half)
(3-1-0-4)
2 Pre-requisite courses(s) Nil
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
  1. E. Kreyszig, Advanced engineering mathematics (10th Edition), John Wiley (1999)
  2. W. E. Boyce and R. DiPrima, Elementary Differential Equations (8th Edition), John Wiley (2005)