Special Mathematics Lecture

Contact:
Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 247 in Sci. Bldg. A

Differential equations and dynamical systems (Fall 2021)

Registration code : 0063611
Schedule : Wednesday (18.30 - 20.00) in room 207 of Science Building A and on Zoom

• Syllabus : pdf file

• Registration to NU-EMI : here

• Class dates :
  October 6, 13, 20, 27
  November 3, 10, 17, 24
  December 1, 8, 15, 22
  January 5, 12, 19
  

• Pictures : October, December, January

• The cumulative notes : The cumulative notes

• Weekly summaries : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

• Program :
  1) Introduction through examples
  2) First order linear systems
  3) Initial value problems
  4) Dynamical systems
  5) Examples in 2D
  6) Dynamical systems in higher dimensions
  7) Discrete dynamical systems

• Study sessions : Are organized on an individual basis by students. For any information, contact Yesui , Duc , Hiep, Tom, Qi.

• For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements. These submissions can take place at any time during the semester. If you have any question, contact me or Ziyu Liu.

• Works submitted by the students :
  Unique Solution to the Exponential Function Problem, by Vic Austen
  Deriving the logistic equation, by Yat Ming Luk, Rafi Rizqy Firdaus, Iksoo Jun, Aaron Ontangco
  on exp(A+B) = exp(A) exp(B) if and only A and B commute, by Li Yucheng
  About the Jordan canonical form, by Li Yucheng
  On the properties of the norm of matrices, by Vic Austen
  On the logistic equation with constant harvesting, by Vic Austen
  About the derivative of t → exp(tA), by Li Yucheng
  On the exponential of a nilpotent matrix, by Nguyen Duc Thanh
  About the solution of a linear system for a time dependent matrix A, by Li Yucheng
  About Cauchy sequence and converging sequence, by Yat Ming Luk, Rafi Rizqy Firdaus, Iksoo Jun, Aaron Ontangco
  Inverse triangle inequality, by Mitsuki Nagaura and Peng Qi
  Inverse triangle inequality, by Yui Hatanaka and Yesui Baatar
  Cauchy and converging sequences: a sequence of sequences..., by Sirawich Saranakomkoop
  About invariant sets, by Li Yucheng
  Proof that w-limit sets are close and invariant, by Li Yucheng
  The solution of first order differential equation, by Guan Xinye
  About an example of limit set of a set, by Li Yucheng
  LRC circuits, by Guan Xinye
  The solution of a discrete time inhomogeneous system, by Li Yucheng
  Lyapunov and asymptotical stability, by Nguyen Duc Thanh
  Proof of contraction principle, by Peng Qi
  About the Jordan block decomposition, by Kuboki Yuya
  Euler equation, by Nguyen Hoang Hiep and Jotaro Kobayashi
  Wronskian for the solutions of a second order autonomous differential equation , by Nguyen Hoang Hiep and Jotaro Kobayashi
  Solutions of one differential equation, by Nguyen Hoang Hiep and Jotaro Kobayashi
  Resonance catastrophe, by Nguyen Hoang Hiep and Jotaro Kobayashi
  Expression for the tent map, by Keito Masuda
  Bendixson's criterion, by Nguyen Hoang Hiep and Nguyen Duc Thanh
  The logistic equation, by Mitsuki Nagaura
  Brownian motion of a harmonic oscillator, by Dam Truyen Duc
  On 1D discrete time dynamical systems with period 3, by Dam Truyen Duc
  Two exercises on the dependence on initial conditions, by Kuboki Yuya
  The logistic equation and the Bernoulli equation, by Qiuling Low
  About the tent map, and the Hausdorff dimension of its repeller, by Keito Masuda
  The itinerary map, by Vic Austen
  An exercise related to Sturm-Liouville problems, by Yui Hatanaka
  The Complete Picture For Planar Systems of Differential Equations, by Yat Ming Luk, Rafi Rizqy Firdaus, Iksoo Jun, Aaron Ontangco
  Reduction of order (d'Alembert), by Nirunpornputha Weerawit
  Lotka-Volterra Equation, by Peng Qi and Kanazawa Tomoaki
  About the preliminaries of Sarkovskii's theorem, by Sarun Mukdapitak
  

• Additional information or links :
  Supplementary notes on Green function's method, by Ziyu Liu
  Dynamical systems: a case method approach, by O. Knill, plenty of illustrations, very attracting.
  

• References : (electronic version available upon request)
  [ASY] CHAOS, an introduction to dynamical systems, by K. Alligood, T. Sauer, J. Yorke, long, but contains many examples.
  [HK] A first course in dynamics, by B. Hasselblatt, A. Katok, a very classical, mathematical reference.
  [HSD] Differential equations, dynamical systems, and an introduction to chaos, by M. Hirsch, S. Smale, R. Devaney, probably one of the main source for this course.
  [N] Ordinary differential equations, by V. Noonburg, accessible, but only on differential equations.
  [P] Differential equations and dynamical systems,by L. Perko, mathematically oriented and precise. The differential equations' part looks great.
  [S] Nonlinear dynamics and chaos, by S. Strogatz, contains many examples and exercises with solutions.
  [T] Ordinary differential equations and dynamical systems, by S. G. Teschl, excellent reference, probably use in a simpler formulation.