Information Package / Course Catalogue
Introduction to Nonlinear Physics
Course Code: FİZ329
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

To present the need for nonlineer equations as explaining phenomenons in physics and present the difference in physical meaning and solutions between linear and nonlinear differential equations

Course Content

Constructing, solving and learning the physical meaning of solutions of basic differential equations in physics.

Name of Lecturer(s)
Learning Outcomes
1.. Must classify differential equations as linear and nonlinear equations, present the difference between the basic solution methods of above ones and present the physical meanings of them.
2.Must solve first order nonlinear differential equations geometrically and reach the constant, stable and unstable points.
3.Must classify the bifurcation of first order nonlinear differential equations and present their normal forms.
4.Must classify the static points of second order linear differential equations and must give examples.
5.. Must classify the static points of second order linear differential equations and must give examples.
6.Must write the Jacobi matrix of systems and must determine the stability of stable points using it.
7.Must solve some kind of nonlinear differential equations by using simple perturbation methods.
Recommended or Required Reading
1.Differantial Equations,,Shepley L.Ross,
2.NonlinearDynamics and Chaos,S.H.Strogatz
3.3. Introduction to Nonlinear Dynamics and Chaos,www.cns.gatech.edu/~roman/phys4267/index.html
Weekly Detailed Course Contents
Week 1 - Theoretical
The classification of differential equations as lineer and nonlinear ones, presenting the difference between their physical meanings and solution methods.
Week 2 - Theoretical
Introduction to geometric solutions of nonlinear equations.
Week 3 - Theoretical
Raching the equilibrium points and stable and unstable equilibrium points of 1st order nonlinear differential equations and discusing physical meanings of those.
Week 4 - Theoretical
Introduction to variation of equilibrium(constant) points of 1st order nonlineer differential equations with respect to parameter and bifurcation concept; discussion of the meaning of those.
Week 5 - Theoretical
The classification of bifurcation in 1st order nonlineer differential equations and normal forms.
Week 6 - Theoretical
The representation of second order lineer differential equations as two 1st order equation and classification of equilibrium points.
Week 7 - Theoretical
The representation of second order non-lineer differential equations as two 1st order equation and classification of equilibrium points.
Week 8 - Intermediate Exam
Midterm
Week 9 - Theoretical
Jacobi matrix and determination of stability of equilibrium points.,
Week 10 - Theoretical
The variatiof of stability of equilibrium points with respect to parameter in 2nd order nonlineer differential equations and bifurcation.
Week 11 - Theoretical
New bifurcation and limit cycle in 2nd order nonlineer differential equations.
Week 12 - Theoretical
The investigation of the conditions of being limit cycle of periodic vbrations in 2nd order nonlineer differential equations.
Week 13 - Theoretical
The conditions of global stability in nonlineer differential equations and indice theory
Week 14 - Theoretical
Examples in nonlineer systems and the investigation of the phase spece.
Week 15 - Theoretical
Introduction to solution of nonlineer differential equations with perturbation method.
Assessment Methods and Criteria
Type of AssessmentCountPercent
Quiz2%10
Midterm Examination1%30
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory143384
Quiz25112
Midterm Examination118220
Final Examination130232
TOTAL WORKLOAD (hours)148
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
PÇ-16
PÇ-17
PÇ-18
OÇ-1
3
4
OÇ-2
2
3
OÇ-3
4
4
OÇ-4
3
3
3
OÇ-5
3
3
OÇ-6
3
3
OÇ-7
3
4
Adnan Menderes University - Information Package / Course Catalogue
2026