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Quick 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

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

Data ScientistChemistPhysicistBiologist

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 Frequently Asked Questions (FAQ's)

1: What background knowledge do I need for the Introduction to Non Linear Dynamics online course?

You should have a solid understanding of calculus and basic linear algebra before enrolling in this course.

2: How will the Introduction to Non Linear Dynamics certification benefit me in my field of study?

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.

3: Will I need any specific software or tools for the Introduction to Non Linear Dynamics online course?

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.

4: Are there any prerequisites for enrolling in the Introduction to Non Linear Dynamics certification course?

Yes, you should have a basic understanding of calculus and linear algebra to effectively grasp the concepts covered in this course.

5: What can I expect to learn by the end of 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.