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Vector-Valued Functions - Introduction: 01. Introduction

Vector-Valued Functions - Introduction: 02. Graphing Example

Vector-Valued Functions - Introduction: 03. Graphing Example 2

Vector-Valued Functions - Introduction: 04. Algebra

Vector-Valued Functions - Introduction: 05. Algebra Example

Vector-Valued Functions - Introduction: 06. Cycloid Example

Vector-Valued Functions - Introduction: 07. Displacement

Vector-Valued Functions - Introduction: 08. Displacement Example

Vector-Valued Functions - Introduction: 09. Average Change

Vector-Valued Functions - Calculus: 01. Limits

Vector-Valued Functions - Calculus: 02. Limits Example

Vector-Valued Functions - Calculus: 03. Continuity

Vector-Valued Functions - Calculus: 04. Derivatives

Vector-Valued Functions - Calculus: 05. Derivatives Example

Vector-Valued Functions - Calculus: 06. Tangent Vectors

Vector-Valued Functions - Calculus: 07. Tangent Line Example

Vector-Valued Functions - Calculus: 08. Tangent Line Example 2

Vector-Valued Functions - Calculus: 09. Smooth Curves

Vector-Valued Functions - Calculus: 10. Derivative Rules

Vector-Valued Functions - Calculus: 11. Derivative Rules Example

Vector-Valued Functions - Calculus: 12. Integration

Vector-Valued Functions - Calculus: 13. Integration Example

Vector-Valued Functions - Calculus: 14. Integration Example 2

Vector-Valued Functions - Motion: 01. Introduction

Vector-Valued Functions - Motion: 02. Example

Vector-Valued Functions - Motion: 03. Whirling Ball Example

Vector-Valued Functions - Motion: 04. Projectile Motion

Vector-Valued Functions - Motion: 05. Projectile Example

Vector-Valued Functions - Motion: 06. Distance

Vector-Valued Functions - Motion: 07. Distance Example

Vector-Valued Functions - Unit Tangent and Normal Vectors: 01. Tangent Vectors

Vector-Valued Functions - Unit Tangent and Normal Vectors: 02. Tangent Example

Vector-Valued Functions - Unit Tangent and Normal Vectors: 03. Tangent Example 2

Vector-Valued Functions - Unit Tangent and Normal Vectors: 04. Normal Vectors

Vector-Valued Functions - Unit Tangent and Normal Vectors: 05. Normal Example

Vector-Valued Functions - Unit Tangent and Normal Vectors: 06. Normal Example 2

Vector-Valued Functions - Unit Tangent and Normal Vectors: 07. Acceleration

Vector-Valued Functions - Unit Tangent and Normal Vectors: 08. Acceleration Example

Vector-Valued Functions - Unit Tangent and Normal Vectors: 09. Acceleration Example 2

Vector-Valued Functions - Curvature: 01. Arc Length Parameter

Vector-Valued Functions - Curvature: 02. Example

Vector-Valued Functions - Curvature: 03. Properties

Vector-Valued Functions - Curvature: 04. Curvature

Vector-Valued Functions - Curvature: 05. Line Example

Vector-Valued Functions - Curvature: 06. Formulas and Circle Example

Vector-Valued Functions - Curvature: 07. Osculating Circle

Roger Penrose - Is Mathematics Invented or Discovered?

Description:

Dive into an extensive 4.5-hour video series on vector-valued functions, covering introductory concepts, calculus applications, motion analysis, unit tangent and normal vectors, and curvature. Begin with graphing examples and algebraic operations, then progress to limits, derivatives, and integration of vector-valued functions. Explore practical applications in physics, including displacement, projectile motion, and acceleration. Master advanced topics such as unit tangent and normal vectors, arc length parameterization, and curvature calculations. Conclude with a thought-provoking discussion on the nature of mathematics featuring Roger Penrose.

APEX Calculus - Vector-Valued Functions

Sean Fitzpatrick

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#Mathematics #Calculus #Vector Calculus #Art & Design #Visual Arts #3D Design #Motion #Geometry #Curvature

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