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Course11110409221 lectures

Differential Calculus in Several Variables

Prof. S Dutta · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Differential Calculus Of Sevral Variables

  1. Introduction to Several Variables and Notion Of distance in Rn Video
  2. Countinuity And Compactness Video
  3. Countinuity And Connectdness Video
  4. Derivatives: Possible Definition Video
  5. Matrix Of Linear Transformation Video

Directional derivatives , chain rule

  1. Examples for Differentiable function Video
  2. Sufficient condition of differentiability Video
  3. Chain Rule Video
  4. Mean Value Theorem Video
  5. Higher Order Derivatives Video

Taylor’s formula and maximum minimum for real valued functions

  1. Taylor\'s Formula Video
  2. Maximum And Minimum Video
  3. Second derivative test for maximum, minimum and saddle point Video
  4. We formalise the second derivative test discussed in Lecture 2 and do examples. Video
  5. Specialisation to functions of two variables Video

Implicit Function Theorem and Application\'s

  1. Implicit Function Theorem Video
  2. Implicit Function Theorem -a Video
  3. Application of IFT: Lagrange\'s Multipliers Method Video
  4. Application of IFT: Lagrange\'s Multipliers Method- b Video
  5. Application of IFT: Lagrange\'s Multipliers Method - c Video
  6. Application of IFT: Inverse Function Theorem - c Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. S Dutta
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
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