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 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 |
| References |
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.
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