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Course11110512267 lectures

Integral and Vector Calculus

Prof. Hari Shankar Mahato · IIT Kharagpur

Start with lecture 1 At NPTEL

Lectures

WEEK 1

  1. Lecture 1 : Partition, Riemann intergrability and One example Video
  2. Lecture 2 : Partition, Riemann intergrability and One example (Contd.) Video
  3. Lecture 3 : Condition of integrability Video
  4. Lecture 4 : Theorems on Riemann integrations Video
  5. Lecture 5 : Examples Video

WEEK 2

  1. Lecture 06: Examples (Contd.) Video
  2. Lecture 07: Reduction formula Video
  3. Lecture 08: Reduction formula (Contd.) Video
  4. Lecture 09: Improper Integral Video
  5. Lecture 10: Improper Integral (Contd.) Video

WEEK 3

  1. Lecture 11 : Improper Integral (Contd.) Video
  2. Lecture 12 : Improper Integral (Contd.) Video
  3. Lecture 13 : Introduction to Beta and Gamma Function Video
  4. Lecture 14 : Beta and Gamma Function Video
  5. Lecture 15 :Differentiation under Integral Sign Video

WEEK 4

  1. Lecture 16 : Differentiation under Integral Sign (Contd.) Video
  2. Lecture 17 : Double Integral Video
  3. Lecture 18 : Double Integral over a Region E Video
  4. Lecture 19 : Examples of Integral over a Region E Video
  5. Lecture 20 : Change of variables in a Double Integral Video

WEEK 5

  1. Lecture 21: Change of order of Integration Video
  2. Lecture 22: Triple Integral Video
  3. Lecture 23: Triple Integral (Contd.) Video
  4. Lecture 24: Area of Plane Region Video
  5. Lecture 25: Area of Plane Region (Contd.) Video

WEEK 6

  1. Lecture 26 :Rectification Video
  2. Lecture 27 : Rectification (Contd.) Video
  3. Lecture 28 : Surface Integral Video
  4. Lecture 29 : Surface Integral (Contd.) Video
  5. Lecture 30 : Surface Integral (Contd.) Video

WEEK 7

  1. Lecture 31: Volume Integral, Gauss Divergence Theorem Video
  2. Lecture 32: Vector Calculus Video
  3. Lecture 33: Limit, Continuity, Differentiability Video
  4. Lecture 34: Successive Differentiation Video
  5. Lecture 35: Integration of Vector Function Video

WEEK 8

  1. Lecture 36: Gradient of a Function Video
  2. Lecture 37: Divergence & Curl Video
  3. Lecture 38: Divergence & Curl Examples Video
  4. Lecture 39: Divergence & Curl important Identities Video
  5. Lecture 40: Level Surface Relevant Theorems Video

WEEK 9

  1. Lecture 41: Directional Derivative (Concept & Few Results) Video
  2. Lecture 42: Directional Derivative (Concept & Few Results) (Contd.) Video
  3. Lecture 43: Directional Derivatives, Level Surfaces Video
  4. Lecture 44: Application to Mechanics Video
  5. Lecture 45: Equation of Tangent, Unit Tangent Vector Video

WEEK 10

  1. Lecture 46: Unit Normal, Unit binormal, Equation of Normal Plane Video
  2. Lecture 47: Introduction and Derivation of Serret-Frenet Formula, few results Video
  3. Lecture 48: Example on binormal, normal tangent, Serret-Frenet Formula Video
  4. Lecture 49: Osculating Plane, Rectifying plane, Normal plane Video
  5. Lecture 50: Application to Mechanics, Velocity, speed , acceleration Video

WEEK 11

  1. Lecture 51: Angular Momentum, Newton's Law Video
  2. Lecture 52: Example on derivation of equation of motion of particle Video
  3. Lecture 53: Line Integral Video
  4. Lecture 54: Surface integral Video
  5. Lecture 55: Surface integral (Contd.) Video

WEEK 12

  1. Lecture 56: Green's Theorem & Example Video
  2. Lecture 57: Volume integral, Gauss theorem Video
  3. Lecture 58: Gauss divergence theorem Video
  4. Lecture 59: Stoke's Theorem Video
  5. Lecture 60: Overview of Course Video

Live Session

  1. Live Session 07-04-2021 Video
  2. Live Session 21-04-2021 Video
  3. Live Session 20-02-2020 Video
  4. Live Session 16-03-2020 Video
  5. Live Session 03-03-2022 Video
  6. Live Session 01-04-2022 Video
  7. Live Session 18-04-2022 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Mathematics
Teacher
Prof. Hari Shankar Mahato
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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