Raffi Hovasapian: Multivariable Calculus

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Raffi Hovasapian: Multivariable Calculus
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Author : Raffi Hovasapian
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Language: English
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Professor Raffi Hovasapian helps students develop their Multivariable Calculus intuition with in-depth explanations of concepts before reinforcing an understanding of the material through varied examples.

This course is appropriate for those who have completed single-variable calculus. Topics covered include everything from Vectors to Partial Derivatives, Lagrange Multipliers, Line Integrals, Triple Integrals, and Stokes’ Theorem. Professor Hovasapian has degrees in Mathematics, Chemistry, and Classics and over 10 years of teaching experience.

Table of Contents
I. Vectors
Points and Vectors 28:23
Scalar Product and Norm 30:25
More on Vectors and Norms 38:18
Inequalities and Parametric Lines 33:19
Planes 29:59
More on Planes 34:18

II. Differentiation of Vectors
Maps, Curves and Parameterizations 29:48
Differentiation of Vectors 39:40

III. Functions of Several Variables
Functions of Several Variable 29:31
Partial Derivatives 23:31
Higher and Mixed Partial Derivatives 30:48

IV. Chain Rule and The Gradient
The Chain Rule 28:03
Tangent Plane 42:25
Further Examples with Gradients and Tangents 47:11
Directional Derivative 41:22
A Unified View of Derivatives for Mappings 39:41

V. Maxima and Minima
Maxima and Minima 36:41
Further Examples with Extrema 32:48
Lagrange Multipliers 32:32
More Lagrange Multiplier Examples 27:42
Lagrange Multipliers, Continued 31:47

VI. Line Integrals and Potential Functions
Line Integrals 36:08
More on Line Integrals 28:04
Line Integrals, Part 3 29:30
Potential Functions 40:19
Potential Functions, Continued 31:45
Potential Functions, Conclusion and Summary 28:22

VII. Double Integrals
Double Integrals 29:46
Polar Coordinates 36:17
Green’s Theorem 38:01
Divergence and Curl of a Vector Field 37:16
Divergence and Curl, Continued 33:07
Final Comments on Divergence and Curl 16:49

VIII. Triple Integrals
Triple Integrals 27:24
Cylindrical and Spherical Coordinates 35:33

IX. Surface Integrals and Stokes’ Theorem
Parameterizing Surfaces and Cross Product 41:29
Tangent Plane and Normal Vector to a Surface 37:06
Surface Area 32:48
Surface Integrals 46:52
Divergence and Curl in 3-Space 23:40
Divergence Theorem in 3-Space 34:12
Stokes’ Theorem, Part 1 22:01
Stokes’ Theorem, Part 2 20:32

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