Module Specification
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
1. Module Title CHAOS AND DYNAMICAL SYSTEMS
2. Module Code MATH322
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester First Semester
7. CATS Level Level 6 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Dr BN Vasiev Mathematical Sciences B.Vasiev@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Dr A Alpers Mathematical Sciences Andreas.Alpers@liverpool.ac.uk
13. Board of Studies
14. Mode of Delivery
15. Location Main Liverpool City Campus
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
16. Study Hours 24

   24

       48
17.

Private Study

 102
18.

TOTAL HOURS

 150
 
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other
19. Timetable (if known)            
 
20. Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

 
21. Modules for which this module is a pre-requisite:

 
22. Co-requisite modules:

 
23. Linked Modules:

 
24. Programme(s) (including Year of Study) to which this module is available on a mandatory basis:
25. Programme(s) (including Year of Study) to which this module is available on a required basis:
26. Programme(s) (including Year of Study) to which this module is available on an optional basis:
27. Aims
 

To develop expertise in dynamical systems in general and study particular systems in detail.
 
28. Learning Outcomes
 

(LO1) After completing the module students will be able to understand the possible behaviour of dynamical systems with particular attention to chaotic motion;
 

(LO2) After completing the module students will be familiar with techniques for extracting fixed points and exploring the behaviour near such fixed points;
 

(LO3) After completing the module students will understand how fractal sets arise and how to characterise them.
 

(S1) Problem solving skills
 

(S2) Numeracy
 
29. Teaching and Learning Strategies
 

Material is presented during lectures (3 hours per week). Tutorials (1 hour per week) are used for consolidation and practice, and for help with individual questions.
 
30. Syllabus
   

Introduction (1 lecture) Discrete-time dynamical systems with one variable (10 lectures) Fractal sets (3 lectures) Discrete-time dynamical systems with several variables (5 lectures) Systems of autonomous coupled first-order differential equations (8 lectures) Models of dynamical systems (9 lectures)
 
31. Recommended Texts
  Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
 

Assessment
32. EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  Final Assessment 60 50
33. CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  Homework 5 0 10
  Homework 4 0 10
  Homework 3 0 10
  Homework 2 0 10
  Homework 1 0 10