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Last updated:
September 23, 2023
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
Description
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)
Course Curriculum
- Lecture 01 – Partition, Riemann Integrability and One Example Unlimited
- Lecture 02 – Partition, Riemann Integrability and One Example (cont.) Unlimited
- Lecture 03 – Condition of Integrability Unlimited
- Lecture 04 – Theorems on Riemann Integrations Unlimited
- Lecture 05 – Examples Unlimited
- Lecture 06 – Examples (cont.) Unlimited
- Lecture 07 – Reduction Formula Unlimited
- Lecture 08 – Reduction Formula (cont.) Unlimited
- Lecture 09 – Improper Integral Unlimited
- Lecture 10 – Improper Integral (cont.) Unlimited
- Lecture 11 – Improper Integral (cont.) Unlimited
- Lecture 12 – Improper Integral (cont.) Unlimited
- Lecture 13 – Introduction to Beta and Gamma Function Unlimited
- Lecture 14 – Beta and Gamma Function Unlimited
- Lecture 15 – Differentiation under Integral Sign Unlimited
- Lecture 16 – Differentiation under Integral Sign (cont.) Unlimited
- Lecture 17 – Double Integral Unlimited
- Lecture 18 – Double Integral over a Region E Unlimited
- Lecture 19 – Examples of Integral over a Region E Unlimited
- Lecture 20 – Change of Variables in a Double Integral Unlimited
- Lecture 21 – Change of Order of Integration Unlimited
- Lecture 22 – Triple Integral Unlimited
- Lecture 23 – Triple Integral (cont.) Unlimited
- Lecture 24 – Area of Plane Region Unlimited
- Lecture 24 – Area of Plane Region Unlimited
- Lecture 25 – Area of Plane Region (cont.) Unlimited
- Lecture 26 – Rectification Unlimited
- Lecture 27 – Rectification (cont.) Unlimited
- Lecture 28 – Surface Integral Unlimited
- Lecture 29 – Surface Integral (cont.) Unlimited
- Lecture 30 – Surface Integral (cont.) Unlimited
- Lecture 31 – Volume Integral, Gauss Divergence Theorem Unlimited
- Lecture 32 – Vector Calculus Unlimited
- Lecture 33 – Limit, Continuity, Differentiability Unlimited
- Lecture 34 – Successive Differentiation Unlimited
- Lecture 35 – Integration of Vector Function Unlimited
- Lecture 36 – Gradient of a Function Unlimited
- Lecture 37 – Divergence and Curl Unlimited
- Lecture 38 – Divergence and Curl Examples Unlimited
- Lecture 39 – Divergence and Curl Important Identities Unlimited
- Lecture 40 – Level Surface Relevant Theorems Unlimited
- Lecture 41 – Directional Derivative (Concept and Few Results) Unlimited
- Lecture 42 – Directional Derivative (Concept and Few Results) (cont.) Unlimited
- Lecture 43 – Directional Derivatives, Level Surfaces Unlimited
- Lecture 44 – Application to Mechanics Unlimited
- Lecture 45 – Equation of Tangent, Unit Tangent Vector Unlimited
- Lecture 46 – Unit Normal, Unit Binormal, Equation of Normal Plane Unlimited
- Lecture 47 – Introduction and Derivation of Serret-Frenet Formula, Few Results Unlimited
- Lecture 48 – Example on Binormal, Normal Tangent, Serret-Frenet Formula Unlimited
- Lecture 49 – Osculating Plane, Rectifying Plane, Normal Plane Unlimited
- Lecture 50 – Application to Mechanics, Velocity, Speed, Acceleration Unlimited
- Lecture 51 – Angular Momentum, Newton’s Law Unlimited
- Lecture 52 – Example on Derivation of Equation of Motion of Particle Unlimited
- Lecture 53 – Line Integral Unlimited
- Lecture 54 – Surface Integral Unlimited
- Lecture 55 – Surface Integral (cont.) Unlimited
- Lecture 56 – Green’s Theorem and Example Unlimited
- Lecture 57 – Volume Integral, Gauss Theorem Unlimited
- Lecture 58 – Gauss Divergence Theorem Unlimited
- Lecture 59 – Stokes’ Theorem Unlimited
- Lecture 60 – Overview of Course Unlimited
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