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