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