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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)

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.