Special Mathematics Lecture
Contact:
Serge Richard (richard@math.nagoyau.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

Registration to NUEMI :
here

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

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 wlimit 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 SturmLiouville 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
LotkaVolterra Equation, by Peng Qi and Kanazawa Tomoaki
About the preliminaries of Sarkovskii's theorem, by Sarun Mukdapitak

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.
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