# Vector Calculus

## Video Lectures

Displaying all 44 video lectures.

Lecture 1Play 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 2Play Video |
Line Integral: Using Green's TheoremIn 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 3Play 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 4Play Video |
Line Integral: Green's TheoremIn 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 5Play Video |
Line Integral: Physical MeaningIn 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. Check out www.gaussianmath.com for an indepth study and more calculus related lessons. |

Lecture 6Play Video |
Line Integral for Piecewise-Smooth CurveIn 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 7Play Video |
Line Integral Piecewise-Smooth Curve ExampleIn 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 8Play Video |
Terms of a Curve: Initial, Terminal Point and Closed CurveIn 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 9Play Video |
Line Integral: Short ExampleIn 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. Check out www.gaussianmath.com for an indepth study and more calculus related lessons. |

Lecture 10Play Video |
Line Integral: DefinitionIn 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. Check out www.gaussianmath.com for an indepth study and more calculus related lessons. |

Lecture 11Play Video |
Vector Calculus: Finding Unit Tangent and Normal ExplicitlyIn this video lesson, GMath Calculus Donny Lee shows a method of finding the Unit Tangent and Unit Normal vector. Check out www.gaussianmath.com for an indepth study and more calculus related lessons. |

Lecture 12Play 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. Check out www.gaussianmath.com for an indepth study and more calculus related lessons. |

Lecture 13Play Video |
Finding Directional DerivativeIn 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 14Play Video |
Finding the Tangent PlaneIn 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 15Play 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 16Play 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 17Play 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 18Play 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 19Play 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 20Play 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 21Play Video |
Fundamental Theorem fo Space Curves (Part III) |

Lecture 22Play Video |
Theorem on Directional Derivative |

Lecture 23Play Video |
Torsion (Part I) |

Lecture 24Play Video |
Torsion (Part II) |

Lecture 25Play Video |
Gradient Vector Field (Part I) |

Lecture 26Play Video |
Gradient Vector Field (Part II) |

Lecture 27Play Video |
How to Find Lines of Force (Part I) |

Lecture 28Play Video |
How to Find Lines of Force (Part II) |

Lecture 29Play Video |
Frenet Serret Equations |

Lecture 30Play Video |
Directional Derivative (Part I) |

Lecture 31Play Video |
The Circular Helix (Part I) |

Lecture 32Play Video |
The Circular Helix (Part II) |

Lecture 33Play Video |
Unit Binormal (Part I) |

Lecture 34Play Video |
Unit Binormal (Part II) |

Lecture 35Play Video |
Multiple Approach (Part I) |

Lecture 36Play Video |
Multiple Approach (Part II) |

Lecture 37Play Video |
Parametrize the Arc Length |

Lecture 38Play Video |
The First Derivative |

Lecture 39Play Video |
Functions of One-Variable (Part I) |

Lecture 40Play Video |
Introduction |

Lecture 41Play Video |
Acceleration Components |

Lecture 42Play Video |
Curvature (Part II) |

Lecture 43Play Video |
Velocity Acceleration |

Lecture 44Play Video |
Curvature (Part I) |