This course on vectors aims to teach students about space coordinates, introduction to vectors, dot products, cross products, lines, and planes. By the end of the course, students will be able to understand and apply concepts related to vectors in 3D space. The course covers skills such as calculating distances, lengths, angles, and areas using vectors. The teaching method involves theoretical explanations followed by examples for better understanding. This course is intended for learners interested in advanced calculus and mathematics, particularly those looking to deepen their knowledge of vectors in three-dimensional space.
Overview
Syllabus
Vectors: Space Coordinates - 01. Cartesian coordinates in 3D.
Vectors: Space Coordinates - 02. Distance.
Vectors: Space Coordinates - 03. Length of a line segment.
Vectors: Space Coordinates - 04. Spheres.
Vectors: Space Coordinates - 05. Example: Sphere.
Vectors: Space Coordinates - 06. Planes.
Vectors: Space Coordinates - 07. Example: Planes.
Vectors: Space Coordinates - 08. Cylinders.
Vectors: Space Coordinates - 09. Example: Cylinders.
Vectors: Space Coordinates - 10. Surfaces of Revolution.
Vectors: Space Coordinates - 11. Example: Surfaces of Revolution.
Vectors: Space Coordinates - 12. Quadric Surfaces.
Vectors: Space Coordinates - 13. Example: Quadric Surfaces.
Vectors: Introduction - 01. Introduction.
Vectors: Introduction - 02. Example: Sketch.
Vectors: Introduction - 03. Algebraic Addition.
Vectors: Introduction - 04. Algebraic Scalar Multiplication.
Vectors: Introduction - 05. Example: Addition.
Vectors: Introduction - 06. Example: Subtraction.
Vectors: Introduction - 07. Example: Scalar Multiplication.
Vectors: Introduction - 08. Scalar Multiplication and Magnitude.
Vectors: Introduction - 09. Unit Vectors.
Vectors: Introduction - 10. Example: Unit Vectors.
Vectors: Introduction - 11. Parallel Vectors.
Vectors: Introduction - 12. Example: Weight hanging from two chains.
Vectors: Dot Products - 01. Introduction.
Vectors: Dot Products - 02. Example.
Vectors: Dot Products - 03. Properties.
Vectors: Dot Products - 04. Geometric Formula.
Vectors: Dot Products - 05. Example: Angles.
Vectors: Dot Products - 06. Orthogonality.
Vectors: Dot Products - 07. Orthogonal Projection.
Vectors: Dot Products - 08. Example: Projection.
Vectors: Dot Products - 09. Orthogonal Decomposition.
Vectors: Dot Products - 10. Work.
Vectors: Cross Products - 01. Introduction.
Vectors: Cross Products - 02. Example.
Vectors: Cross Products - 03. Determinant Formula.
Vectors: Cross Products - 04. Example.
Vectors: Cross Products - 05. Properties.
Vectors: Cross Products - 06. Angles.
Vectors: Cross Products - 07. Application: Area of a Parallelogram.
Vectors: Cross Products - 08. Application: Area of a Triangle.
Vectors: Cross Products - 09. Application: Volume of a Parallelepiped.
Vectors: Lines - 01. Introduction.
Vectors: Lines - 02. Example.
Vectors: Lines - 03. Example.
Vectors: Lines - 04. Comparing lines.
Vectors: Lines - 05. Distance from a Point to a Line.
Vectors: Lines - 06. Example: Distance (point to line).
Vectors: Lines - 07. Distance Between Skew Lines.
Vectors: Lines - 08. Example: Distance (Between Skew Lines).
Vectors: Planes - 01. Introduction.
Vectors: Planes - 02. Example: Plane Through 3 Points.
Vectors: Planes - 03. Example: Plane Orthogonal to Line.
Vectors: Planes - 04. Example: Intersection of two Planes.
Vectors: Planes - 05. Example: Intersection of two planes (algebraic solution).
Vectors: Planes - 06. Example: Intersection of a Line and Plane.
Vectors: Planes - 07. Distance.
Vectors: Planes - 08. Example: Distance.
Taught by
Sean Fitzpatrick
