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📘Differential Equations with Separable Variables Basic Level (Part 2/5).

We continue with our series of solved exercises on Basic-Level Separable Differential Equations. In this second installment, you will fin...

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Osculating Circle of a Parabola + Summary of TNB Vectors and Curvature Formulas

In this video, I go over the osculating circle, which lies on the same osculating plane and has the same tangent and normal vector as a ...

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Osculating Circle of a Parabola + Summary of TNB Vectors and Curvature Formulas

▶️ Watch on 3Speak In this video, I go over the osculating circle, which lies on the same osculating plane and has the same tangent and ...

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The TNB Frame: Normal and Osculating Planes + Example on a Circular Helix

In this video, I go over the TNB Frame for space curves and their associated Normal and Osculating Planes, which have applications in th...

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The TNB Frame: Normal and Osculating Planes + Example on a Circular Helix

▶️ Watch on 3Speak In this video, I go over the TNB Frame for space curves and their associated Normal and Osculating Planes, which have...

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Normal and Binormal Vectors + Example on a Circular Helix

In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from the unit tangent v...

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Normal and Binormal Vectors + Example on a Circular Helix

▶️ Watch on 3Speak In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from...

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Curvature of a Plane Curve y = f(x) + Example on a Parabola

In this video, I go over the curvature of the special case of a plane curve with equation y = f(x), by selecting x as the parameter and ...

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Curvature Cross Product Formula: Proof and Example on Twisted Cubic

In this video, I derive a more convenient formula for the curvature of a space curve, which involves the cross product of the first two ...

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Curvature Cross Product Formula: Proof and Example on Twisted Cubic

▶️ Watch on 3Speak In this video, I derive a more convenient formula for the curvature of a space curve, which involves the cross produc...

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Curvature: Definition and Curvature of a Circle is 1/Radius

In this video, I go over the definition of curvature, which describes how quickly a curve changes direction at a given point. It is defi...

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Curvature: Definition and Curvature of a Circle is 1/Radius

▶️ Watch on 3Speak In this video, I go over the definition of curvature, which describes how quickly a curve changes direction at a give...

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Parameterizations and Arc Length Function

In this video, I show that a curve can be represented by multiple different vector functions, called parameterizations of the curve, and...

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Arc Length of a Space Curve + Example on Circular Helix

In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented...

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Vector Functions: Arc Length and Curvature

In this video, I go over further into vector functions and this time do a deep dive into the arc length and curvature of a space curve. ...

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Vector Functions: Arc Length and Curvature

https://youtu.be/i9ForOVH5Bk ▶️ Watch on 3Speak - Odysee - BitChute - Rumble - Telegram - YouTube - PDF Notes - Hive Notes - Summary - Sec...

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Steemit

Laboratory Project: Bezier Curves Part 5

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Steemit

Bezier Curves: A Brief History

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Steemit

Polar Coordinates: Example 1

https://youtu.be/q_kpqPpoLqE PDF Notes - Hive Notes In this video I go over a quick example on polar coordinates and illustrate how to pl...

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Steemit

Polar Coordinates: Infinite Representations

https://youtu.be/QJYbnO7NzCk PDF Notes - Notes In this video I go over further into Polar Coordinates and this time elaborate on one of t...

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Steemit

Polar Coordinates: Cartesian Connection

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Exercise 5: Proof of Formula 6: Chain Rule for Vector Functions

▶️ Watch on 3Speak In this video I prove Formula 6 of the differentiation rules for vector functions and this time show that the derivat...

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Exercise 4: Proof of Formula 5: Derivative of Cross Product of Vector Functions via Definition

▶️ Watch on 3Speak In this video I once again prove Formula 5 of the Differentiation Rules for Vector Functions but this time obtain the...

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Exercise 4: Proof of Formula 5: Derivative of Cross Product of Vector Functions by Components

In this video I prove Formula 5 of the differentiation rules for vector functions, and this time derive the derivative of the cross prod...

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Exercise 4: Proof of Formula 5: Derivative of Cross Product of Vector Functions by Components

▶️ Watch on 3Speak In this video I prove Formula 5 of the differentiation rules for vector functions, and this time derive the derivativ...

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Exercise 3: Proof of Formulas 2 and 3: Derivative of a Function Multiplied by a Vector Function

▶️ Watch on 3Speak In this video I prove formulas 2 and 3 of the differentiation rules for vector functions and show that the derivative...

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Exercise 3: Proof of Formulas 2 and 3: Derivative of a Function Multiplied by a Vector Function

In this video I prove formulas 2 and 3 of the differentiation rules for vector functions and show that the derivative of a vector functi...

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Exercise 2: Proof of Formula 1: Derivative of Addition of Vector Functions

In this video I go over Formula 1 of the differentiation rules for vector functions and show the derivative of the addition (or subtract...

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Exercise 2: Proof of Formula 1: Derivative of Addition of Vector Functions

▶️ Watch on 3Speak In this video I go over Formula 1 of the differentiation rules for vector functions and show the derivative of the ad...

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Exercise 1: Tangent Vector Points in the Direction of Increasing t

▶️ Watch on 3Speak In this video I show that the derivative or tangent vector of a curve defined by a vector function always points in t...