# ATML-Ordinary Diff. Equations (2011)

Venue: |
M. S. University of Baroda, Vadodara |

Dates: |
2 Jun - 15 Junl, 2011 |

Convener(s) |
Speakers, Syllabus and Time table |
Applicants/Participants |

Name |
Tarun Das |

Mailing Address |
Department of Mathematics, Faculty of Science The M. S. University of Baroda, Vadodara - 390002 |

## Speakers

### Confirmed Speakers:

- S. Baskar, IIT Bombay
- Tarun Das, The M. S. University of Baroda
- P. S. Datti, TIFR Bangalore
- A. S. Vasudeva Murthy, TIFR Bangalore
- V. Raghavendra, IIT Kanpur
- V. O. Thomas, The M. S. University of Baroda
- Mythily Ramaswamy TIFR Bangalore
- K Sandeep, TIFR Bangalore
- Hari Kataria, The M.S. University of Baroda
- B. Rai, University of Allahabad

### Speakers: Unity of Mathematics

- S G Dani, TIFR, Mumbai
- Dinesh Singh, University of Delhi

### Course Associates:

- Rasmita Kar, IIT Kanpur
- Sejal Shah, The M. S. University of Baroda

## Proposed Syllabus

**Linear systems:** Basic Matrix Theory, Matrix Functions, Differentiation and Integration of Matrix Functions, Diagonalization, Exponentials of Operators, The Fundamental Theorem of Linear Systems, Linear Systems in **R ^{2}** , Solving Linear Systems Using Eigen Values and Eigen Vectors, Distinct Real Eigen Values, Complex Eigen Values, Repeated Eigen Values, Jordan Forms, Phase Plane and Linear Systems, Stability Theory, Non Homogeneous Linear Systems.

**Non-linear systems- Local Theory:** Some Preliminary Concepts and Definitions, The Fundamental Existence-Uniqueness Theorem, Dependance on Initial Conditions and Parameters, The Maximal Interval of Existence, The Flow Defined by a Differential Equation, Linearization, The Stable Manifold Theorem, The Hartman-Grobman Theorem, Stability and Liapunov Functions, Saddles, Nodes, Foci and Centers, Nonhyperbolic Critical Points in **R ^{2}** , Center Manifold Theory, Normal Form Theory, Gradient and Hamiltonian Systems.

## References:

- Differential Equations and Dynamical Systems (3rd Edition) by Lawrence Perko, Springer.
- Elementary Differential Equations and Boundary Value Problems (7th Edition) by William E. Boyce and Richard C DiPrima, John Wiley and Sons Inc.
- Theory of Ordinary Differential Equations by Earl A. Coddington and Norman Levinson, Tata McGraw Hill Publishing Comp.Ltd.

Sr. No. |
Name |
Affiliation |
---|---|---|

1 | Akhil Mittal | Sardar Vallabhbhai Institute of Technology, Vasad |

2 | Amit Kumar Singh | University of Allahabad, Allahabad |

3 | Anand Kumar | Central University of Rajasthan, Kishangarh |

4 | Anisa Mohmad Husen Chorwadwala | IISER, Pune |

5 | Anuj Kumar Jhankal | Birla Institute of Technology, Mersa |

6 | Bapan Ghosh | Bengal Engineering and Science University, Shibpur |

7 | Dharitri Manpritsinh Rathod | The M. S. University of Baroda, Vadodara |

8 | Dhaval Thakkar | The M. S. University of Baroda, Vadodara |

9 | Diddi Kumaraswamy | Christu Jyoti Institute of Technology & Science,Yeshwanthapur, Jangaon |

10 | Heramb Balakrishna Aiya | St. Xaviers College of Arts, Science And Commerce, Mapusa - Goa |

11 | Jitendra Singh | Institute of Technology, Banaras Hindu University, Varanasi |

12 | Jyoti Rajaram Thorwe | Shivaji University, Kolhapur |

13 | Krihna Basappa Chavaraddi | Government First Grade College, Yellpur |

14 | Mahesh K B | Government First Grade College, Mangalore |

15 | Nishant Parmar | The M. S. University of Baroda, Vadodara |

16 | Pabitra Debnath | St. Xavier's College, Kolkata |

17 | Pankajini Tripathy | KMBB College of Engineering and Technology, Orissa |

18 | Pasupula Rami Reddy | University of Hyderabad, Hyderabad |

19 | Piyush Patel | The M. S. University of Baroda, Vadodara |

20 | Prabhugouda Mallanagouda Patil | JSS's Banashankari Arts, Commerce amd Shanti, Kumar Gubbi Science College, Dharwad |

21 | Prakash Uttam Sansare | Birla College of Arts, Science and Commerce, Kalyan |

22 | Pramod Machindra Dhakane | S.B.E.S College of Science, Aurangabad |

23 | Preeti Jain | Banasthali University, Banasthali |

24 | Saurabh Chandra Maury | University of Allahabad, Allahabad |

25 | Saurabh Kumar Agrawal | Banaras Hindu University, Varanasi |

26 | Sharan Gopal | University of Hyderabad, Hyderabad |

27 | Shyam Sunder Iyer | National Institute of Technology, Thiruchirappalli |

28 | Snehal Suryakant Mitragotri | Shivaji University, Kolhapur |

29 | Umesh Ramesh Swami | College of Engineering Pune, Pune |

30 | Veeararaghan Piramanantham | Bharathidasan University,Tiruchirappalli |

**How to reach**

**How to reach the venue:**

Vadodara (also known as Baroda) is well connected by rail to all the major metros in the country including Delhi, Mumbai, Kolkata, Chennai, Bangalore and Hyderabad. Vadodara is also well connected to Mumbai and Delhi by air.

Ahmedabad is one of the important cities in western India. It is about 110 Kilometers from Vadodara and is very well connected to Vadodara through roadways as well as railways.

Department of Mathematics, Faculty of Science is just at a walking distance from the railway station and the bus station. University guest house and hostel are within one kilometer range from the railway station and bus stand. Vadodara airport is about 6 kms from the department.