In this video, Amit Sir explores the Legendre conditions in the calculus of variations. These conditions are essential for determining whether a function provides a minimum or maximum solution in variational problems. Amit Sir provides clear explanations, building on previous concepts like Euler-Lagrange equations, to offer deeper insights into the nature of extremal functions. This lecture is perfect for undergraduate and graduate students looking to strengthen their understanding of the calculus of variations, especially those preparing for competitive exams like IIT JAM, CSIR NET, and GATE.
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𝗟𝗲𝗰𝘁𝘂𝗿𝗲: 04 Part (04) by Amit Sir
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• • Calculus of Variations...
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📚 Topics Covered:
Legendre Conditions and Examples
Proper Field
Central Field
Example
Extremal Field
Jacobi Condition
Example
Example
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This video is about;
What is Legendre's necessary condition?
What is the Legendre's principle?
What is an example of Legendre's equation?
What is the Legendre condition in the calculus of variations?
What is Legendre's theorem?
What is the condition of the Jacobi method?
What is the Jacobi's theorem state?
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17 сен 2024
