Vector Calculus

Video Lectures

Displaying all 44 video lectures.
Lecture 1
Line Integral: Proof of Green's Theorem (Part I)
Play Video		 Line Integral: Proof of Green's Theorem (Part I)
In this video lesson, GMath Calculus Donny Lee gives a proof of a special case of Green's Theorem where the graph can be described in two ways.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 2
Line Integral: Using Green's Theorem
Play Video		 Line Integral: Using Green's Theorem
In this video lesson, GMath Calculus Donny Lee gives a short example using Green's Theorem.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 3
Line Integral: Proof of Green's Theorem (Part II)
Play Video		 Line Integral: Proof of Green's Theorem (Part II)
In this video lesson, GMath Calculus Donny Lee gives a proof of a special case of Green's Theorem where the graph can be described in two ways.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 4
Line Integral: Green's Theorem
Play Video		 Line Integral: Green's Theorem
In this video lesson, GMath Calculus Donny Lee gives a short introduction to Green's Theorem, which concerns turning a closed loop integral into a double integral given certain conditions.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 5
Line Integral: Physical Meaning
Play Video		 Line Integral: Physical Meaning
In this video lesson, GMath Calculus Donny Lee studies a concept in mechanics with the line integral and that is the line integral gives us the work done by a vector field on moving a point along the curve C.

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Lecture 6
Line Integral for Piecewise-Smooth Curve
Play Video		 Line Integral for Piecewise-Smooth Curve
In this video lesson, GMath Calculus Donny Lee teaches a few properties of the line integral when dealing with piecewise-smooth curves..

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 7
Line Integral Piecewise-Smooth Curve Example
Play Video		 Line Integral Piecewise-Smooth Curve Example
In this video lesson, GMath Calculus Donny Lee gives an example showing how we use the line integral for a piecewise-smooth curve.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 8
Terms of a Curve: Initial, Terminal Point and Closed Curve
Play Video		 Terms of a Curve: Initial, Terminal Point and Closed Curve
In this video lesson, GMath Calculus Donny Lee teaches some terms of a curve first. This is needed to better understand the line integral..

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 9
Line Integral: Short Example
Play Video		 Line Integral: Short Example
In this video lesson, GMath Calculus Donny Lee gives a basic example of implementing the line integral. You must substitute the parametric equations into both the vector field and position vector and then integrate.

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Lecture 10
Line Integral: Definition
Play Video		 Line Integral: Definition
In this video lesson, GMath Calculus Donny Lee teaches the definition of the Line Integral. Pay close attention that the line integral requires a vector field and a position vector of a curve C.

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Lecture 11
Vector Calculus: Finding Unit Tangent and Normal Explicitly
Play Video		 Vector Calculus: Finding Unit Tangent and Normal Explicitly
In this video lesson, GMath Calculus Donny Lee shows a method of finding the Unit Tangent and Unit Normal vector.

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Lecture 12
Vector Integral Calculus: Directional Derivative (Part II)
Play Video		 Vector Integral Calculus: Directional Derivative (Part II)
In this video lesson, GMath Calculus Donny Lee explains the directional derivative of phi at the point P0 in the direction of unit vector u.

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Lecture 13
Finding Directional Derivative
Play Video		 Finding Directional Derivative
In this video lesson, GMath Calculus Donny Lee provides a follow up with his previous video on the directional derivative, here is a short example. Situable for those taking vector calculus or enginnering math in general.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 14
Finding the Tangent Plane
Play Video		 Finding the Tangent Plane
In this video lesson, GMath Calculus Donny Lee gives a short example finding the Tangent Plane of a given scalar surface function. Situable for those taking vector calculus or enginnering math in general.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 15
Lines of Force (Part I)
Play Video		 Lines of Force (Part I)
In this video lesson, GMath Calculus Donny Lee gives an Introduction to Vector Fields and their related Lines of Force as seen in Physics namely sreamlines or magnetic lines. Situable for those taking a module on vector calculus or enginnering mathematics.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 16
Lines of Force (Part II)
Play Video		 Lines of Force (Part II)
In this video lesson, GMath Calculus Donny Lee gives an introduction to Vector Fields and their related Lines of Force as seen in Physics namely streamlines or magnetic lines. Situable for those taking a module on vector calculus or enginnering mathematics.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 17
Introduction to Vector Fields (Part I)
Play Video		 Introduction to Vector Fields (Part I)
In this video lesson, GMath Calculus Donny Lee gives an introduction to Vector Fields. Situable for those taking a module on vector calculus or enginnering mathematics.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 18
Introduction to Vector Fields (Part II)
Play Video		 Introduction to Vector Fields (Part II)
In this video lesson, GMath Calculus Donny Lee gives an introduction to Vector Fields. Situable for those taking a module on vector calculus or enginnering mathematics.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 19
Fundamental Theorem fo Space Curves (Part I)
Play Video		 Fundamental Theorem fo Space Curves (Part I)
In this video lesson, GMath Calculus Donny Lee gives a long 3-part video on the 'Fundamental Theorem of Space Curves', a theorem in Vector Differential Caculus.

Note: View this only if you are taking a course in vector calculus. If not, it could just be a waste of your time..

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 20
Fundamental Theorem fo Space Curves (Part II)
Play Video		 Fundamental Theorem fo Space Curves (Part II)
In this video lesson, GMath Calculus Donny Lee gives a long 3-part video on the 'Fundamental Theorem of Space Curves', a theorem in Vector Differential Caculus.

Note: View this only if you are taking a course in vector calculus. If not, it could just be a waste of your time.

Check out www.gaussianmath.com for an indepth study and more calculus related lessons.
Lecture 21
Fundamental Theorem fo Space Curves (Part III)
Play Video		 Fundamental Theorem fo Space Curves (Part III)
Lecture 22
Theorem on Directional Derivative
Play Video		 Theorem on Directional Derivative
Lecture 23
Torsion (Part I)
Play Video		 Torsion (Part I)
Lecture 24
Torsion (Part II)
Play Video		 Torsion (Part II)
Lecture 25
Gradient Vector Field (Part I)
Play Video		 Gradient Vector Field (Part I)
Lecture 26
Gradient Vector Field (Part II)
Play Video		 Gradient Vector Field (Part II)
Lecture 27
How to Find Lines of Force (Part I)
Play Video		 How to Find Lines of Force (Part I)
Lecture 28
How to Find Lines of Force (Part II)
Play Video		 How to Find Lines of Force (Part II)
Lecture 29
Frenet Serret Equations
Play Video		 Frenet Serret Equations
Lecture 30
Directional Derivative (Part I)
Play Video		 Directional Derivative (Part I)
Lecture 31
The Circular Helix (Part I)
Play Video		 The Circular Helix (Part I)
Lecture 32
The Circular Helix (Part II)
Play Video		 The Circular Helix (Part II)
Lecture 33
Unit Binormal (Part I)
Play Video		 Unit Binormal (Part I)
Lecture 34
Unit Binormal (Part II)
Play Video		 Unit Binormal (Part II)
Lecture 35
Multiple Approach (Part I)
Play Video		 Multiple Approach (Part I)
Lecture 36
Multiple Approach (Part II)
Play Video		 Multiple Approach (Part II)
Lecture 37
Parametrize the Arc Length
Play Video		 Parametrize the Arc Length
Lecture 38
The First Derivative
Play Video		 The First Derivative
Lecture 39
Functions of One-Variable (Part I)
Play Video		 Functions of One-Variable (Part I)
Lecture 40
Introduction
Play Video		 Introduction
Lecture 41
Acceleration Components
Play Video		 Acceleration Components
Lecture 42
Curvature (Part II)
Play Video		 Curvature (Part II)
Lecture 43
Velocity Acceleration
Play Video		 Velocity Acceleration
Lecture 44
Curvature (Part I)
Play Video		 Curvature (Part I)