and **The Summer Course on Dynamical Systems V**.

**Six Lectures on Averaging Method and Normalization for Nonlinear Differential Equations.**

**Final update: **

Date : 22nd-23rd August 2013,

Lab Tek III, Bandung Institut of Technology

Programs:

**First day: 22nd of August:**

**Registration : 07:00-08:00****Lecture 1: 08:00 – 09:40****Basic concepts**: Nonlinear differential equations and dynamical systems, asymptotic theory and perturbation method: the Poincare’-Linstedt method. We will apply this method in details for a modified van der Pol equation to compute periodic solution.**Lecture 2: 10:00 – 11:40 The averaging method**: First order averaging method for periodic vector field, second order averaging method of periodic vector field, some concluding remarks on general averaging theory.**Lecture 3: 13:00-14:40 Example**: System of coupled oscillators. This lectures will be devoted to applying the pervious lecture on a classical problem in mechanics: the elastic pendulum. We will do in great details the first order resonance and explain briefly the application of second order averaging to higher order resonance.**Exercise Session: 15:00 – 16:30**

**Second day, 23rd of August: **

**Lecture 4: 08:00-09:40 Introduction to Hamiltonian system of ordinary differential equations**. In this lecture we will present a brief introduction to Hamiltonian system, starting from Lagrangian formalism.**Lecture 5: 10:00-11:00 Restricted three-body problem.**In this part of the lecture we will discuss the linear stability theory in Hamiltonian systems. It is well known that linear stability is too weak for Hamiltonian system, thus a more sophisticated method is in need. As an example, we choose to discuss the Restricted Three Body Problem.**Lecture 6: 13:00 – 14:00****Normalization method**.**Exercise Session 14:00-15:30**

Lectures will be delivered by J.M. Tuwankotta. Lectures note is provided for registered participants. In this series of lectures, we assume minimal knowledge in the theory of dynamical systems.

Expected audience: Researcher in engineering and science who works with dynamical system (system of differential equations to be more precise), PhD student in physics and math or relevant studies.

Registration: please contact: theo@math.itb.ac.id

Registration fee: (to be paid on site)

1. Rp. 300.000,- (for general participants)

2. Rp. 100.000,- (students)

The registration fee includes: Lecture notes.