Course Code | MA 108 |

Course Name | Ordinary Differential Equations |

Offered to | UG |

Pre-requisites | NIL |

Lecture | 2 |

Tutorial | 1 |

Practical | 0 |

Credit | 4 |

Reference | 1. E. Kreyszig, Advanced engineering mathematics (8th Edition), John Wiley (1999). 2. W. E. Boyce and R. DiPrima, Elementary Di?erential Equations (8th Edition), John Wiley (2005). 3. T. M. Apostol, Calculus, Volume 2 (2nd Edition), Wiley Eastern, 1980. |

Description | Exact equations, integrating factors and Bernoulli equations. Orthogonal tra jectories. Lipschitz condition, Picard302222s theorem, examples on nonuniqueness. Linear di?erential equations generalities. Linear dependence and Wronskians. Dimensionality of space of solutions, Abel-Liouville formula. Linear ODE302222s with constant coe?cients, the characteristic equations. Cauchy-Euler equations. Method of undetermined coe?cients. Method of variation of parameters. Laplace transform generalities. Shifting theorems. |