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In this video, a geodesic is calculated when a curve is rotated about the line (y-axis) & it is shown that a curve is a catenary in the calculus of variations using Euler's equations. #DrPrashantPatil#CalculusOfVariations#18MAT31_Module04#Lecture13 For more videos and playlist of Engineering Mathematics go through the playlists 1)18MAT31- TRANSFORM CALCULUS, FOURIER SERIES AND NUMERICAL TECHNIQUES: 1) Laplace Transforms [18MAT31-Module 01]: • Laplace Transforms 2) Inverse Laplace Transform [18MAT31-Module 01]: • Inverse Laplace Transform || Dr Prash... 3) Fourier Series | 18mat31 | Module 02 | Dr Prashant Patil • Fourier Series | 18mat31 | Module 02 ... 4) Numerical Methods for ODE | 18mat31 | Module 04 & 05 | Dr Prashant Patil • Numerical Methods for ODE | Module 04... 5) Calculus of Variations | 18mat31 | Module 05 | Dr Prashant Patil • Calculus of Variations | 18mat31 | Mo... 2)18MAT21- Advanced Calculus and Numerical Techniques: 1) Vector Calculus [18MAT21-Module 01]: • Vector Calculus || 21MAT21 || 2) Ordinary Differential Equation of Higher order[18MAT21-Module 02]: • Ordinary Differential Equation of Hig... 3) Partial Differential Equations [18MAT21-Module 03]: • Partial Differential Equations | 18ma... 4) Infinite Series [18MAT21-Module 04]: • Infinite Series [18MAT21-Module 04] 3) 18MAT41- Complex Analysis, Probability and Statistical Methods: 1) Conformal Transformations[18MAT41-Module 02] • Conformal Transformations || 18MAT41 ... 2) Complex Integration[18MAT41-Module 02] • Complex Integration || 18MAT41 || Dr... 3) Probability Distributions[18MAT41-Module 03] • Probability Distributions[18MAT41-Mod... 4) Joint Probability Distribution and Sampling [18MAT41-Module 05] • Joint Probability Distribution and Sa... 4)18MATDIP41- Additional Mathematics II: 1) Probability[18MATDIP41-Module05] • 18MATDIP41 | Additional Mathematics I...