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Integral and Vector Calculus

Integral and Vector Calculus. Instructor: Prof. Hari Shankar Mahato, Department of Mathematics, IIT Kharagpur. This course will cover a detailed introduction to integral and vector calculus. We'll start with the concepts of partition, Riemann sum and Riemann Integrable functions and their properties. We then move to antiderivatives and will look into a few classical theorems of integral calculus such as a fundamental theorem of integral calculus. We'll then study improper integral, their convergence and learn about a few tests which conform the convergence. Afterwards we'll look into multiple integrals, Beta and Gamma functions, Differentiation under the integral sign. (from nptel.ac.in)

Lecture 49 - Osculating Plane, Rectifying Plane, Normal Plane


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Lecture 01 - Partition, Riemann Integrability and One Example
Lecture 02 - Partition, Riemann Integrability and One Example (cont.)
Lecture 03 - Condition of Integrability
Lecture 04 - Theorems on Riemann Integrations
Lecture 05 - Examples
Lecture 06 - Examples (cont.)
Lecture 07 - Reduction Formula
Lecture 08 - Reduction Formula (cont.)
Lecture 09 - Improper Integral
Lecture 10 - Improper Integral (cont.)
Lecture 11 - Improper Integral (cont.)
Lecture 12 - Improper Integral (cont.)
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 (cont.)
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 (cont.)
Lecture 24 - Area of Plane Region
Lecture 25 - Area of Plane Region (cont.)
Lecture 26 - Rectification
Lecture 27 - Rectification (cont.)
Lecture 28 - Surface Integral
Lecture 29 - Surface Integral (cont.)
Lecture 30 - Surface Integral (cont.)
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) (cont.)
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 (cont.)
Lecture 56 - Green's Theorem and Example
Lecture 57 - Volume Integral, Gauss Theorem
Lecture 58 - Gauss Divergence Theorem
Lecture 59 - Stokes' Theorem
Lecture 60 - Overview of Course