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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

Go to the Course Home or watch other lectures:

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