NOC:Integral and Vector Calculus


Lecture 1 - Partition, Riemann intergrability and One example


Lecture 2 - Partition, Riemann intergrability and One example (Continued...)


Lecture 3 - Condition of integrability


Lecture 4 - Theorems on Riemann integrations


Lecture 5 - Examples


Lecture 6 - Examples (Continued...)


Lecture 7 - Reduction formula


Lecture 8 - Reduction formula (Continued...)


Lecture 9 - Improper Integral


Lecture 10 - Improper Integral (Continued...)


Lecture 11 - Improper Integral (Continued...)


Lecture 12 - Improper Integral (Continued...)


Lecture 13 - Introduction to Beta and Gamma Function


Lecture 14 - Beta and Gamma Function


Lecture 15 - Differentiation under Integral Sign


Lecture 16 - Differentiation under Integral Sign (Continued...)


Lecture 17 - Double Integral


Lecture 18 - Double Integral over a Region E


Lecture 19 - Examples of Integral over a Region E


Lecture 20 - Change of variables in a Double Integral


Lecture 21 - Change of order of Integration


Lecture 22 - Triple Integral


Lecture 23 - Triple Integral (Continued...)


Lecture 24 - Area of Plane Region


Lecture 25 - Area of Plane Region (Continued...)


Lecture 26 - Rectification


Lecture 27 - Rectification (Continued...)


Lecture 28 - Surface Integral


Lecture 29 - Surface Integral (Continued...)


Lecture 30 - Surface Integral (Continued...)


Lecture 31 - Volume Integral, Gauss Divergence Theorem


Lecture 32 - Vector Calculus


Lecture 33 - Limit, Continuity, Differentiability


Lecture 34 - Successive Differentiation


Lecture 35 - Integration of Vector Function


Lecture 36 - Gradient of a Function


Lecture 37 - Divergence and Curl


Lecture 38 - Divergence and Curl Examples


Lecture 39 - Divergence and Curl important Identities


Lecture 40 - Level Surface Relevant Theorems


Lecture 41 - Directional Derivative (Concept and Few Results)


Lecture 42 - Directional Derivative (Concept and Few Results) (Continued...)


Lecture 43 - Directional Derivatives, Level Surfaces


Lecture 44 - Application to Mechanics


Lecture 45 - Equation of Tangent, Unit Tangent Vector


Lecture 46 - Unit Normal, Unit binormal, Equation of Normal Plane


Lecture 47 - Introduction and Derivation of Serret-Frenet Formula, few results


Lecture 48 - Example on binormal, normal tangent, Serret-Frenet Formula


Lecture 49 - Osculating Plane, Rectifying plane, Normal plane


Lecture 50 - Application to Mechanics, Velocity, speed, acceleration


Lecture 51 - Angular Momentum, Newton's Law


Lecture 52 - Example on derivation of equation of motion of particle


Lecture 53 - Line Integral


Lecture 54 - Surface integral


Lecture 55 - Surface integral (Continued...)


Lecture 56 - Green's Theorem and Example


Lecture 57 - Volume integral, Gauss theorem


Lecture 58 - Gauss divergence theorem


Lecture 59 - Stoke's Theorem


Lecture 60 - Overview of Course