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Integral and Vector Calculus
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Integral and Vector Calculus
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- 1 Integral and Vector Calculus
- 2 Lecture 01 : Partition, Riemann intergrability and One example
- 3 Lecture 02 : Partition, Riemann intergrability and One example (Contd.)
- 4 Lecture 03 : Condition of integrability
- 5 Lecture 04 : Theorems on Riemann integrations
- 6 Lecture 05 : Examples
- 7 Lecture 06 : Examples (Contd.)
- 8 Lecture 07 : Reduction formula
- 9 Lecture 08 : Reduction formula (Contd.)
- 10 Lecture 09 : Improper Integral
- 11 Lecture 10 : Improper Integral (Contd.)
- 12 Lecture 11 : Improper Integral (Contd.)
- 13 Lecture 12 : Improper Integral (Contd.)
- 14 Lecture 13 : Introduction to Beta and Gamma Function
- 15 Lecture 14 : Beta and Gamma Function
- 16 Lecture 15 : Differentiation under Integral Sign
- 17 Lecture 16 : Differentiation under Integral Sign (Contd.)
- 18 Lecture 17 : Double Integral
- 19 Lecture 18 : Double Integral over a Region E
- 20 Lecture 19 : Examples of Integral over a Region E
- 21 Lecture 20 : Change of variables in a Double Integral
- 22 Lecture 21 : Change of order of Integration
- 23 Lecture 22 : Triple Integral
- 24 Lecture 23 : Triple Integral (Contd.)
- 25 Lecture 24 : Area of Plane Region
- 26 Lecture 25 : Area of Plane Region (Contd.)
- 27 Lecture 26 : Rectification
- 28 Lecture 27 : Rectification (Contd.)
- 29 Lecture 28 : Surface Integral
- 30 Lecture 29 : Surface Integral (Contd.)
- 31 Lecture 30 : Surface Integral (Contd.)
- 32 Lecture 31 : Volume Integral, Gauss Divergence Theorem
- 33 Lecture 32 : Vector Calculus
- 34 Lecture 33 : Limit, Continuity, Differentiability
- 35 Lecture 34 : Successive Differentiation
- 36 Lecture 35 : Integration of Vector Function
- 37 Lecture 36 : Gradient of a Function
- 38 Lecture 37 : Divergence & Curl
- 39 Lecture 38 : Divergence & Curl Examples
- 40 Lecture 39 : Divergence & Curl important Identities
- 41 Lecture 40 : Level Surface Relevant Theorems
- 42 Lecture 41 : Directional Derivative (Concept & Few Results)
- 43 Lecture 42 : Directional Derivative (Concept & Few Results) (Contd.)
- 44 Lecture 43 : Directional Derivatives, Level Surfaces
- 45 Lecture 44 : Application to Mechanics
- 46 Lecture 45 : Equation of Tangent, Unit Tangent Vector
- 47 Lecture 46 : Unit Normal, Unit binormal, Equation of Normal Plane
- 48 Lecture 47 : Introduction and Derivation of Serret-Frenet Formula, few results
- 49 Lecture 48 : Example on binormal, normal tangent, Serret-Frenet Formula
- 50 Lecture 49 : Osculating Plane, Rectifying plane, Normal plane
- 51 Lecture 50 : Application to Mechanics, Velocity, speed , acceleration
- 52 Lecture 51 : Angular Momentum, Newton's Law
- 53 Lecture 52 : Example on derivation of equation of motion of particle
- 54 Lecture 53 : Line Integral
- 55 Lecture 54 : Surface integral
- 56 Lecture 55 : Surface integral (Contd.)
- 57 Lecture 56 : Green's Theorem & Example
- 58 Lecture 57 : Volume integral, Gauss theorem
- 59 Lecture 58 : Gauss divergence theorem
- 60 Lecture 59 : Stoke's Theorem
- 61 Lecture 60 : Overview of Course
