Lecture 1 - Coordinates Systems 2-D and 3-D
Lecture 2 - Vector Algebra R^n
Lecture 3 - Euclidean space R^n and some of its properties
Lecture 4 - Sequences in R^n
Lecture 5 - Functions of Several Variables and Concept of Limit
Lecture 6 - Properties of Limit, Iterated Limit and Double limit
Lecture 7 - Concept of Continuity and Some of Its Properties
Lecture 8 - Properties of Continuous Functions
Lecture 9 - Concept of Differentiability for Vector-valued Functions
Lecture 10 - Properties of Differentiable Functions, Chain Rule
Lecture 11 - Applications of Differentiability
Lecture 12 - Concept of Partial Derivates, Examples and Properties
Lecture 13 - Higher order Partial Derivatives and notion of Directional Derivatives
Lecture 14 - Concept of Total Derivative and related properties
Lecture 15 - Gradient Vector and Necessary condition for Differentiability
Lecture 16 - Sufficient condition for Differentiability and Chain rule
Lecture 17 - Applications: Tangent Plane and Normal Line for a Surface
Lecture 18 - Mixed Partial Derivatives and Examples
Lecture 19 - Mixed Derivative Theorem and Examples
Lecture 20 - Concept of Mean Value Theorem
Lecture 21 - Notion of Hessian
Lecture 22 - Taylor’s theorem and Linear approximation
Lecture 23 - Maxima, Minima and Saddle point
Lecture 24 - Necessary condition for extremum and quadratic forms
Lecture 25 - Hessian matrix, Method to find the extremum values of f
Lecture 26 - Global extrema, Constrained extrema
Lecture 27 - The method of Lagrange multiplies, Exact differentials
Lecture 28 - Definition of Double integrals in terms of Upper and Lower sums
Lecture 29 - Definition of Double integrals in terms of Riemaan Sum and Properties
Lecture 30 - Iterated integral and Fubini’s theorem
Lecture 31 - Double integral on simple regions and Fubini’s theorem
Lecture 32 - Change of Variables in a Double Integral and Applications
Lecture 33 - Definition of Triple integrals as Riemann Integral and Examples
Lecture 34 - Triple integral on simple regions and Fubini’s theorem
Lecture 35 - More on Triple integral on simple regions and Fubini’s theorem
Lecture 36 - Change of Variables in Triple Integral and Examples
Lecture 37 - Definition of Vector Fields and visualization of them by arrows
Lecture 38 - Integral curves of Vector Fields, conservative and non-conservative vector fields, Gradient
Lecture 39 - Necessary and sufficient conditions for a conservative/gradient vector field
Lecture 40 - Concept of Divergence and Curl
Lecture 41 - Curl, rotational vector field, Divergence of curl, Laplace operator
Lecture 42 - Recall of Curves, Smooth Curves, Piecewise Smooth Curves
Lecture 43 - Definition of Scalar Line Integral, Some examples and properties
Lecture 44 - Orientation of smooth curve and definition of Vector Line Integral
Lecture 45 - Definition of Vector Line Integral, Examples, Properties and Applications
Lecture 46 - Definition of surfaces, smooth surfaces, and parametrization of surfaces
Lecture 47 - Definition of scalar surface integral and some examples
Lecture 48 - Oriented surfaces and the definition of vector surface integral
Lecture 49 - Vector surface integral and some examples
Lecture 50 - Recall the definition of curves, orientation of curves, Jordan curve theorem
Lecture 51 - Statement, and proof of Green's theorem ona simply connected region
Lecture 52 - Application of Green's theorem and Green's theorem for multiply connected regions
Lecture 53 - Application of Green's theorem for multiply connected regions and Examples
Lecture 54 - Recall the definition of surfaces, smooth surfaces, and orientation of surfaces
Lecture 55 - Oriented surfaces, Stokes theorem on smooth surfaces with examples
Lecture 56 - Stokes theorem on smooth surfaces with finitely many holes, Gauss Divergence theorem and examples
Lecture 57 - Gauss Divergence theorem, Application of Divergence theorem and examples
