## Syllabus

**Tentative Syllabus:**

- Dimensional analysis and scaling
- Asymptotic analysis
- Perturbation methods
- Some basics in functional analysis
- Calculus of Variations
- Orthogonal expansions and generalized Fourier series
- Sturm-Liouville problems

**Script: ** Script_MATH46_2020.pdf

**Topics by Weeks:**

Week | Brief Description | Section in Textbook | Section in Textbook |
---|---|---|---|

1 | Dimensional analysis | 2.1, 2.2 | 1.1 |

2 | Scaling | 2.3 | 1.2 |

3 | Asymptotic analysis & regular perturbation | 3, 4.1 | 2.1 |

4 | Pitfalls of regular perturbation & asymptotic expansion of integrals | 4.2, 5 | 2.2, 2.6 |

5 | Functional analysis (crash course) | 6 | - |

6 | Calculus of variations - part 1 | 7.1 - 7.3 | 3.1 - 3.3.2 |

7 | Calculus of variations - part 2 | 7.4, 7.5 | 3.3.3, 3.4 |

8 | Orthogonal expansions - part 1 | 8.1, 8.2 | 4.1 |

9 | Orthogonal expansions - part 2 | 8.3, 8.4 | 4.1 |

10 | Sturm-Liouville problems | 9 | 4.2 |