Module Handbook-Mathematics-Universitas Brawijaya
Module Handbook
Module Name: Introduction to Continuous Dynamical System
Module Level: Bachelor
Abbreviation, if Applicable: MAM 62308 Sub-Heading, if Applicable:
Courses included in the module, if applicable:
Introduction to Continuous Dynamical System
Semester/term: 4th/second years
Module Coordinator(s): Chair of the Lab. Applied Analysis and Numerical Computation Lectures(s) 1. Dr. Wuryansari Muharini Kusumawinahyu, M.Si.
2. Indah Yanti, S.Si., M.Si.
3. Zuraidah Fitriah, S.Si., M.Si.
Language Bahasa Indonesia
Classification within the curriculum
Elective Studies
Teaching format / class hours per week during semester:
100 minutes lectures per week.
Workload: Total workload is 3 ECTS, which consists of 1.67 hours lectures, 2 hours structured activities, 2 hours independent learning, 16 week per semester, and a total 90.67 hours per semester including mid exam and final exam.
Credit Points: 2
Requirements according to
the examination
regulations:
The student has attended at least 80% of Introduction to Continuous Dynamical System classes and is registered as the examinee in the academic information system
Recommended prerequisites
Students have taken Ordinary Differential Equation course (MAM61302) and have participated in the final examination of the course.
Module Handbook-Mathematics-Universitas Brawijaya Course learning outcomes
(CLO)
After completing this course, the student should have
CLO 1 : understanding some basic terminologies related to continuous dynamic systems, such as system solutions, orbits of solution, equilibrium points, stability of equilibrium points, phase portraits, and directional fields
CLO 2 : ability to solve a linear continuous dynamical system and relates the behavior of the solution to the stability property of the equilibrium point
CLO 3 : ability to determine the equilibrium point of a non-linear continuous dynamical system and determine its stability through the linearization process
CLO 4 : ability to present the solution geometrically in the form of phase portrait and directional field and interpret the result
CLO 5 : understanding the concept of bifurcation and ability to check the occurrence of bifurcation
Content: 1. Linear autonomous dynamical system: analytical solution, equilibrium point, stability of equilibrium point, directional field, phase portrait a. One-dimension Linear autonomous dynamical system
b. Two-dimension Linear autonomous dynamical system
2. Non-linear autonomous dynamical system: equilibrium point, linearization, stability of equilibrium point, directional field, phase portrait
3. Bifurcation on continuous dynamical system
Study / exam
achievements:
The final mark will be weighted as follows:
No. Assessment methods (component, activities). Weight
1. Class activity 10 %
2. Quiz 10 %
3. Assignment 20 %
4. Middle examination 30 %
5. Final examination 30 %
Final grades is defined as follow: A : 80 < Final Mark ≤ 100 B+ : 75 < Final Mark ≤ 80
B : 69 < Final Mark ≤ 75
C+ : 60 < Final Mark ≤ 69
C : 55 < Final Mark ≤ 60
D+ : 50 < Final Mark ≤ 55
D : 44 < Final Mark ≤ 50
E : 0 ≤ Final Mark ≤ 44
Forms of Media Slides and LCD projectors, mathematical software such as MAPLE or Matlab, and whiteboards, internet connection for online learning
Learning Methods Lecture, discussion, assignment delivery
Literature 1. Robinson, R.C., 2004, An Introduction to Dynamical Systems, Continuous and Discrete, Prentice Hall.
2. Boyce, W. E. and R. C. Di Prima, 2012, Elementary Differential Equations and Boundary Value Problems, 10th ed, John Willey &
Sons, Inc., Canada.
3. Kreyszig, E., 2011, Advanced Engineering Mathematics, 10th edition, John Wiley & sons, inc.
Notes:
Module Handbook-Mathematics-Universitas Brawijaya
