Introduction to Non Linear Dynamics
Explore nonlinear dynamics and gain skills across various scientific disciplines with the Introduction to Non Linear Dynamics certification by NPTEL.
Online
6 WeeksQuick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The Introduction to Non Linear Dynamics certification course introduces students to the complexities of dynamic systems through analytical methods and real-world examples. It offers a practical understanding of phenomena in physics, biology, chemistry, and engineering, covering topics like bifurcations, phase plane analysis, and limit cycles.
Students will explore the behavior of one-dimensional and two-dimensional flows, learning about stability analysis, classification of linear systems, and the dynamics of oscillators. The Introduction to Non Linear Dynamics certification by NPTEL equips students with analytical skills and problem-solving abilities crucial for navigating nonlinear phenomena in diverse scientific contexts.
The Highlights
- Online Course
- 6 Weeks Duration
- Offered by IIT Madras
Courses and Certificate Fees
| Certificate Availability | Certificate Providing Authority |
|---|---|
| yes | IIT Madras (IITM) |
Eligibility Criteria
Academic Qualifications
You need to have studied calculus and basic linear algebra before taking the Introduction to Non Linear Dynamics certification course.
Certification Qualifying Details
To receive the Introduction to Non Linear Dynamics certification by NPTEL, you need a minimum average assignment score of 10/25 and an exam score of 30/75.
What you will learn
After completing the Introduction to Non Linear Dynamics certification syllabus, you will gain a comprehensive understanding of complex dynamic systems. You will also learn to analyze and interpret phenomena in physics, biology, chemistry, and engineering.
Upon completion of the Introduction to Non Linear Dynamics training, you will explore first-order differential equations and bifurcations. You will also explore concepts like stability analysis and numerical methods and develop a solid foundation for understanding nonlinear behavior.
Who it is for
The Introduction to Non Linear Dynamics online course is suitable for students in physics, biology, chemistry, and engineering who are interested in gaining an understanding of nonlinear dynamics and its applications. This course can also be beneficial for:
Admission Details
Follow these steps to join the Introduction to Non Linear Dynamics classes:
Step 1: Browse the URL below:
https://swayam.gov.in/NPTEL
Step 2: Click on the “Sign-in/ Register” button
Step 3: Log in using a Google account-enabled email address
Step 4: Select your preferred course. Review the course details and fill out the required fields
Step 5: Click on the "Join" button
The Syllabus
- Geometrical intuition
- Fixed points, and stability
- Local stability analysis
- Existence and Uniqueness
- Impossibility of Oscillations
- Potentials
- Numerical methods
- Saddle node
- Normal forms
- Transcritical
- Pitch fork
- Imperfect bifurcations
- Example
- Numerics (XPP-Auto)
- Saddle-node, Transcritical and Pitchfork
- Choice of bifurcation parameter
- Hopf
- Poincare Maps
- Uniform oscillator
- Non-uniform oscillator
Linear systems
- Definitions and examples
- Classification of linear systems
Phase plane
- Phase portraits
- Existence, uniqueness and topological consequences
- Fixed points and linearisation
- Examples: population dynamics
- Ruling out closed orbits
- Poincare-Bendixson theorem
- Lienard systems
- Weakly nonlinear oscillators
- Higher-order systems, and the existence of Chaos
- Importance of time delays and noise
Evaluation process
The Introduction to Non Linear Dynamics certification offers an optional exam. Your final score is determined by averaging the best 8 out of 12 assignments (25%) and your proctored exam score (75%).
IIT Madras (IITM) Frequently Asked Questions (FAQ's)
You should have a solid understanding of calculus and basic linear algebra before enrolling in this course.
This course will equip you with analytical skills and problem-solving abilities that are applicable across various scientific disciplines, such as physics, biology, chemistry, and engineering.
While not mandatory, familiarity with numerical methods and software tools such as MATLAB, Python with NumPy and SciPy libraries, or XPP-Auto for bifurcation analysis may be beneficial.
Yes, you should have a basic understanding of calculus and linear algebra to effectively grasp the concepts covered in this course.
You will have gained a comprehensive understanding of nonlinear dynamics, including topics such as bifurcations, phase plane analysis, limit cycles, and the dynamics of oscillators.