Overview

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.

Syllabus

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?.