NOC:Calculus of Several Real Variables


Lecture 1 - Vectors in plane and space


Lecture 2 - Inner product and distance


Lecture 3 - Application to real world problems


Lecture 4 - Matrices and determinants


Lecture 5 - Cross product of two vectors


Lecture 6 - Higher dimensional Euclidean space


Lecture 7 - Functions of more than one real-variable


Lecture 8 - Partial derivatives and Continuity


Lecture 9 - Vector-valued maps and Jacobian matrix


Lecture 10 - Chain rule for partial derivatives


Lecture 11 - The Gradient Vector and Directional Derivative


Lecture 12 - The Implicit Function Theorem


Lecture 13 - Higher Order Partial Derivatives


Lecture 14 - Taylor's Theorem in Higher Dimension


Lecture 15 - Maxima and Minima for Several Variables


Lecture 16 - Second Derivative Test for Maximum and Minimum


Lecture 17 - Constrained Optimization and The Lagrange Multiplier Rule


Lecture 18 - Vector Valued Function and Classical Mechanics


Lecture 19 - Arc Length


Lecture 20 - Vector Fields


Lecture 21 - Multiple Integral - I


Lecture 22 - Multiple Integral - II


Lecture 23 - Multiple Integral - III


Lecture 24 - Multiple Integral - IV


Lecture 25 - Cylindrical and Spherical Coordinates


Lecture 26 - Multiple Integrals and Mechanics


Lecture 27 - Line Integral - I


Lecture 28 - Line Integral - II


Lecture 29 - Parametrized Surfaces


Lecture 30 - Area of a surface Integral


Lecture 31 - Area of parametrized surface


Lecture 32 - Surface Integrals


Lecture 33 - Green's Theorem


Lecture 34 - Stoke's Theorem


Lecture 35 - Examples of Stoke's Theorem


Lecture 36 - Gauss Divergence Theorem


Lecture 37 - Facts about vector fields