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Course11110710840 lectures

Multivariable Calculus

Prof. S. K. Gupta Prof. Sanjeev Kumar · IIT Roorkee

Start with lecture 1 At NPTEL

Lectures

Unit 1

  1. Functions of several variables Video
  2. Limits for multivariable functions-I Video
  3. Limits for multivariable functions-II Video
  4. Continuity of multivariable functions Video
  5. Partial Derivatives-I Video

Unit 2

  1. Partial Derivatives-II Video
  2. Differentiability-I Video
  3. Differentiability-II Video
  4. Chain rule-I Video
  5. Chain rule-II Video

Unit 3

  1. Change of variables Video
  2. Euler's theorem for homogeneous functions Video
  3. Tangent planes and Normal lines Video
  4. Extreme values-I Video
  5. Extreme values-II Video

Unit 4

  1. Lagrange multipliers Video
  2. Taylor's theorem Video
  3. Error approximation Video
  4. Polar-curves Video
  5. Multiple Integrals Video

Unit 5

  1. Change Of Order Of Integration Video
  2. Change of Variables in Multiple Integral Video
  3. Introduction to Gamma Function Video
  4. Introduction to Beta Function Video
  5. Properties of Beta and Gamma Functions-I Video

Unit 6

  1. Properties of Beta and Gamma Functions-II Video
  2. Dirichlet's Integral Video
  3. Applications of Multiple Integrals Video
  4. Vector Differentiation Video
  5. Gradient of a Scalar Field and Directional Derivative Video

Unit 7

  1. Normal Vector and Potential field Video
  2. Gradient(Identities), Divergence and Curl(Identities) Video
  3. Some Identities on Divergence and Curl Video
  4. Line Integral (I) Video
  5. Applications of Line Integrals Video

Unit 8

  1. Green's Theorem Video
  2. Surface Area Video
  3. Surface Integral Video
  4. Divergence Theorem of Gauss Video
  5. Stoke's Theorem Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Roorkee
Department
Mathematics
Teacher
Prof. S. K. Gupta Prof. Sanjeev Kumar
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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