June 23, 07

MA 108: Differential Equations-I (3-1-0-4)
Exact operations, integrating factors and Bernoulli equations.
Orthogonal trajectories. Lipschitz condition, Picard's theorem, examples on
nonuniqueness.
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.

Text/References
1. E. Kreyszig, Advanced Engineering Mathematics, 8th ed., John Wiley, 1999.
2. W. E. Boyce and R. DiPrima, Elementary Differential Equations, 8th ed.,
John Wiley, 2005.
3. T. M. Apostol, Calculus, Volumes 1 and 2, 2nd ed., Wiley Eastern, 1980.