Multivariable Calculus

INTENDED AUDIENCE: UG & PG students

COURSE OUTLINE: 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.

Multivariable Calculus.
Lecture 01: Functions of several variables.
Lecture 02: Limits for multivariable functions-I.
Lecture 03: Limits for multivariable functions-II.
Lecture 04: Continuity of multivariable functions.
Lecture 05: Partial Derivatives-I.
Lecture 06: Partial Derivatives-II.
Lecture 07: Differentiability-I.
Lecture 08: Differentiability-II.
Lecture 09: Chain rule-I.
Lecture 10: Chain rule-II.
Lecture 11: Change of variables.
Lecture 12: Euler’s theorem for homogeneous functions.
Lecture 13: Tangent planes and Normal lines.
Lecture 14: Extreme values-I.
Lecture 15: Extreme values-II.
Lecture 16: Lagrange multipliers.
Lecture 17: Taylor’s theorem.
Lecture 18: Error approximation.
Lecture 19: Polar-curves.
Lecture 20: Multiple Integrals.
Lecture 21-Change of order of Integration.
Lecture 22-Change of Variables in Multiple Integral.
Lecture 23-Introduction to Gamma Function.
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Lecture 40.