Calculus - II K3PZTBCZ83

URI	`m2://res/K3PZTBCZ83`
Kind	course
Creators	Arup Chattopadhyay (instructor), M. Guru Prem Prasad (instructor)
Date	2025-07-13
Scope	in
Ids	course 0022nd079:111103764

Expressions

e1: edition

Language	en
Date	2025-07-13

m1: page, IIT Guwahati (record). nptel 111103764
m2: page, 2025-07-13 (record). nptel 111103764

Contents

part 1: Week 1
session 1: Lec 1: Coordinates Systems 2-D and 3-D
session 2: Lec 2: Vector Algebra R^n
session 3: Lec 3: Euclidean space R^n and some of its properties
session 4: Lec 4: Sequences in R^n
part 2: Week 2
session 5: Lec 5: Functions of Several Variables and Concept of Limit
session 6: Lec 6: Properties of Limit, Iterated Limit and Double limit
session 7: Lec 7: Concept of Continuity and Some of Its Properties
session 8: Lec 8: Properties of Continuous Functions
session 9: Lec 9: Concept of Differentiability for Vector-valued Functions
session 10: Lec 10: Properties of Differentiable Functions, Chain Rule
session 11: Lec 11: Applications of Differentiability
part 3: Week 3
session 12: Lec 12: Concept of Partial Derivates, Examples and Properties
session 13: Lec 13: Higher order Partial Derivatives and notion of Directional Derivatives
session 14: Lec 14: Concept of Total Derivative and related properties
session 15: Lec 15: Gradient Vector and Necessary condition for Differentiability
session 16: Lec 16: Sufficient condition for Differentiability and Chain rule
session 17: Lec 17: Applications: Tangent Plane and Normal Line for a Surface
part 4: Week 4
session 18: Lec 18: Mixed Partial Derivatives and Examples
session 19: Lec 19: Mixed Derivative Theorem and Examples
session 20: Lec 20: Concept of Mean Value Theorem
session 21: Lec 21: Notion of Hessian
session 22: Lec 22: Taylor’s theorem and Linear approximation
part 5: Week 5
session 23: Lec 23: Maxima, Minima and Saddle point
session 24: Lec 24: Necessary condition for extremum and quadratic forms
session 25: Lec 25: Hessian matrix, Method to find the extremum values of f
session 26: Lec 26: Global extrema, Constrained extrema
session 27: Lec 27: The method of Lagrange multiplies, Exact differentials.
part 6: Week 6
session 28: Lec 28: Definition of Double integrals in terms of Upper and Lower sums
session 29: Lec 29: Definition of Double integrals in terms of Riemaan Sum and Properties
session 30: Lec 30: Iterated integral and Fubini’s theorem
session 31: Lec 31: Double integral on simple regions and Fubini’s theorem
session 32: Lec 32: Change of Variables in a Double Integral and Applications
part 7: Week 7
session 33: Lec 33: Definition of Triple integrals as Riemann Integral and Examples
session 34: Lec 34: Triple integral on simple regions and Fubini’s theorem
session 35: Lec 35: More on Triple integral on simple regions and Fubini’s theorem
session 36: Lec 36: Change of Variables in Triple Integral and Examples
part 8: Week 8
session 37: Lec 37: Definition of Vector Fields and visualization of them by arrows
session 38: Lec 38: Integral curves of Vector Fields, conservative and non-conservative vector fields, Gradient
session 39: Lec 39: Necessary and sufficient conditions for a conservative/gradient vector field.
session 40: Lec 40: Concept of Divergence and Curl
session 41: Lec 41: Curl, rotational vector field, Divergence of curl, Laplace operator
part 9: Week 9
session 42: Lec 42: Recall of Curves, Smooth Curves, Piecewise Smooth Curves
session 43: Lec 43: Definition of Scalar Line Integral, Some examples and properties
session 44: Lec 44: Orientation of smooth curve and definition of Vector Line Integral
session 45: Lec 45: Definition of Vector Line Integral, Examples , Properties and Applications
part 10: Week 10
session 46: Lec 46: Definition of surfaces, smooth surfaces, and parametrization of surfaces
session 47: Lec 47: Definition of scalar surface integral and some examples
session 48: Lec 48: Oriented surfaces and the definition of vector surface integral
session 49: Lec 49: Vector surface integral and some examples
part 11: Week 11
session 50: Lec 50: Recall the definition of curves, orientation of curves, Jordan curve theorem.
session 51: Lec 51: Statement, and proof of Green's theorem ona simply connected region
session 52: Lec 52: Application of Green's theorem and Green's theorem for multiply connected regions.
session 53: Lec 53: Application of Green's theorem for multiply connected regions and Examples.
part 12: Week 12
session 54: Lec 54: Recall the definition of surfaces, smooth surfaces, and orientation of surfaces
session 55: Lec 55: Oriented surfaces, Stokes theorem on smooth surfaces with examples
session 56: Lec 56: Stokes theorem on smooth surfaces with finitely many holes, Gauss Divergence theorem and examples
session 57: Lec 57: Gauss Divergence theorem, Application of Divergence theorem and examples
part 13: Live Session
session 58: Live Session 21-08-2025
session 59: Live Session 22-09-2025
session 60: Live Session 10-10-2025

Catalogue records

nptel: 111103764 (manifestation)
nptel_video: 111103764 (manifestation)