Vector Algebra and Geometry - Introduction to Vectors
315
21 hrs
$ 7.15
MTH 104: VectorsIntroduction to vectors, covering vector algebra, geometry, products, vector equations of geometries, vector differentiation, integration and their applications to mechanics and differential geometry.
Curated for first-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
Introduction to vectors, covering vector algebra, geometry, products, vector equations of geometries, vector differentiation, integration and their applications to mechanics and differential geometry. Curated for first-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
Course Chapters
1Introduction
Definitions of scalars, vectors and tensors; representation of a vector by a directed line segment; kinds of vectors - free, localized, equal, null, unit, like and unlike vectors.
Chapter lessons
2.Definition57:41
2Vector Algebra
Vector addition - triangle and parallelogram laws; multiplication of a vector by a scalar; relations on mid-points of sides of a triangle; vector algebra on quadrilaterals and other polygons; parallel vectors; laws of vector algebra.
Chapter lessons
6.Parallel vectors27:49
3Position Vectors
4Vector Components
Meaning of vector components; resolution of vectors into components in two and three dimensions; unit vectors, direction cosines and angle between two vectors in the three-dimensional Cartesian coordinate system.
Chapter lessons
4.Direction cosines22:13
5Division of a Line
Ratio division of a line internally and externally; collinearity of points.
Chapter lessons
3.Collinearity21:26
6Vector Projections
Projection of a vector on another vector; projection of a vector on a plane.
Chapter lessons
1.On another vector20:58
7Centroids
Mean centre (geometric centre) of a number of points; weighted mean centres.
Chapter lessons
1.Centroid8:07
Meaning and analysis of the centroid of a number of points.
2.Weighted mean12:21
Meaning and analysis of the weighted mean of a number of points.
3.Worked examples (1)15:07
Worked examples on centroids and weighted means of a number of points.
4.Worked examples (2)21:15
More worked examples on centroids and weighted means of a number of points.