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September 23, 2023

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Description

Multivariable Calculus. Instructors: Dr. S. K. Gupta and Dr. Sanjeev Kumar, Department of Mathematics, IIT Roorkee.

This course is a basic course offered to UG and PG students of Engineering/Science background. It contains various topics related to the calculus of the functions of two or more variables. In particular, this course includes topics like differentiation and integration of the functions of two or more variables together with their various applications. This course also includes the calculus of vector functions with different applications. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Functions of Several Variables Unlimited
  • Lecture 02 – Limits for Multivariable Functions Unlimited
  • Lecture 03 – Limits for Multivariable Functions (cont.) Unlimited
  • Lecture 04 – Continuity of Multivariable Functions Unlimited
  • Lecture 05 – Partial Derivatives Unlimited
  • Lecture 06 – Partial Derivatives (cont.) Unlimited
  • Lecture 07 – Differentiability Unlimited
  • Lecture 08 – Differentiability (cont.) Unlimited
  • Lecture 09 – Chain Rule Unlimited
  • Lecture 10 – Chain Rule (cont.) Unlimited
  • Lecture 11 – Change of Variables Unlimited
  • Lecture 12 – Euler’s Theorem for Homogeneous Functions Unlimited
  • Lecture 13 – Tangent Planes and Normal Lines Unlimited
  • Lecture 14 – Extreme Values Unlimited
  • Lecture 15 – Extreme Values (cont.) Unlimited
  • Lecture 16 – Lagrange Multipliers Unlimited
  • Lecture 17 – Taylor’s Theorem Unlimited
  • Lecture 18 – Error Approximation Unlimited
  • Lecture 19 – Polar Curves Unlimited
  • Lecture 20 – Multiple Integral Unlimited
  • Lecture 21 – Change of Order in Integration Unlimited
  • Lecture 22 – Change of Variables in Multiple Integral Unlimited
  • Lecture 23 – Introduction to Gamma Function Unlimited
  • Lecture 24 – Introduction to Beta Function Unlimited
  • Lecture 25 – Properties of Beta and Gamma Functions Unlimited
  • Lecture 26 – Properties of Beta and Gamma Functions (cont.) Unlimited
  • Lecture 27 – Dirichlet’s Integral Unlimited
  • Lecture 28 – Applications of Multiple Integrals Unlimited
  • Lecture 29 – Vector Differentiation Unlimited
  • Lecture 30 – Gradient of a Scalar Field and Directional Derivative Unlimited
  • Lecture 31 – Normal Vector and Potential Field Unlimited
  • Lecture 32 – Gradient (Identities), Divergence and Curl (Definitions) Unlimited
  • Lecture 33 – Some Identities on Divergence and Curl Unlimited
  • Lecture 34 – Line Integral Unlimited
  • Lecture 35 – Applications of Line Integrals Unlimited
  • Lecture 36 – Green’s Theorem Unlimited
  • Lecture 37 – Surface Area Unlimited
  • Lecture 38 – Surface Integral Unlimited
  • Lecture 39 – Divergence Theorem of Gauss Unlimited
  • Lecture 40 – Stoke’s Theorem Unlimited

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