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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)

Lecture 36 - Green's Theorem

Green's Theorem: Statement of Green's theorem, Relation between line and double integral in 2D, applications, examples.

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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