**AUTUMN - 2001**

**
Teaching Plan
:**

[K] refers to the text book by E. Kreyszig, ``Advanced Engineering
Mathematics", 8th Edition, John Wiley and Sons(1999).

No. | Topic | § in [K] | No.of Lec. |

1. | Basic concepts, Geometric meaning, | ||

Direction fields | 1.1-1.2 | 1 | |

2. | 1st order linear equations, homogeneous | ||

and non homogeneous | 1 | ||

3. | Solution Method for Nonlinear equations, | ||

Separation of variables | 1.3-1.4 | 1 | |

4. | Exact Differential equations, integrating factors | ||

Bernoulli Equation, Orthogonal trajectories | 1.5-1.8 | 2 | |

5. | Existence Uniqueness: Picards iteration | 1.9 | 1 |

6. | 2nd order Linear Differential equations: homogeneous | ||

equation with constant coefficients | 2.1-2.3 | 1 | |

Mass spring system | 2.5-2.6 | 1 | |

Existence Uniqueness, Wronskian, | |||

Non homogeneous equation | 2.7-2.8 | 2 | |

Method of undetermined coefficients, | 2.9-2.10 | 1 | |

variation of parameters method | 2.11-2.12 | 1 | |

7. | Higher Order equations: Wronskian | ||

Existence of solution: Solution Methods | |||

for constant coefficients | 2.13-2.14 | 2 | |

8. | System of ODE: Conversion of higher order ode, | ||

basic concepts | 3.1-3.2 | 1 | |

Homogeneous systems | 3.3-3.4 | 1 | |

Nonhomogeneous System | 3.6 | 1 | |

9. | Laplace Transform | 5.1-5.7 | 5 |

10. | Linear equation with variable coefficients: Solution | ||

Motivation for Power series Method | 2.6, 4.1 | 1 | |

**After
Mid Semester**

No |
Topic |
in [K] | No. of Lec. |

1 | Sequence and Series, Convergence Tests | 14.1, A- 3.3 | 2 |

2 | Improper Integrals | Handout 2 | 1 |

3 | Uniform convergence, and Power Series | 14.5, 14.2 | 3 |

4 | Series solution: Legendre's Equation, Legendre polynomials | 4.3 | 1 |

5 | Frobenius method, Bessels Function, Bessel Function of 2nd kind | 4.4 - 4.6 | 3 |

6 | Convergence of Picard's iterates | Handout 3 | 1 |

7 | Qualitative Theory: Stability of Linear systems, Phase plane analysis Critical points, Linearised stability | Handout 4 3.3 - 3.4, 3.5 | 3 |

8 | Sturm - Liouville Problems: Eigenvalues and Eigenfunctions and properties | Handout 5 4.7 - 4.8 | 3 |

9 | Fourier Series: expansions, approximation by trigonometric polynomials Fourier integrals with Applications | 10.1- 10.4, 10.7 - 10.10 | 4 |

About the course
Course contents
__Teaching Plan__