This course on Vector-Valued Functions aims to teach students the concepts and applications related to vector-valued functions, calculus, motion, unit tangent and normal vectors, and curvature. By the end of the course, students will be able to graph vector-valued functions, calculate limits and derivatives, understand motion in terms of vectors, determine unit tangent and normal vectors, and analyze curvature. The course utilizes examples and exercises to help students grasp the material effectively. This course is intended for learners interested in advanced calculus topics and applications in physics and engineering.
Overview
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?.
Taught by
Sean Fitzpatrick
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