# InfoCoBuild

## Multivariable Calculus

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)

 Functions of Several Variables

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

 References Multivariable Calculus Instructors: Dr. S. K. Gupta and Dr. Sanjeev Kumar, Department of Mathematics, IIT Roorkee. This course contains various topics related to the calculus of the functions of two or more variables.