Vector Algebra and Foundational Geometry - Vectors (Undergraduate Foundation)
356
21 hrs
[OAU, Ife] MTH 104: VectorsThis comprehensive learning track guides you through the complete world of vector analysis. We begin with the fundamentals of vector algebra and its application to foundational geometry. You will then master scalar, vector, and triple products before using them to construct the vector equations of lines, planes, and conics. The journey culminates in advanced topics, including vector calculus, its applications in classical mechanics, and an introduction to differential geometry.
Vectors are the essential language used to describe our physical world, making their mastery non-negotiable for any serious student of science or engineering. This track is designed to build your intuition for spatial reasoning and equip you with a powerful problem-solving toolkit. You will see direct applications in mechanics, analyzing forces and motion; in geometry, calculating angles and distances; and in calculus, modeling dynamic change over time.
While this track is tailored to the first-year university curriculum for MTH 104 at Obafemi Awolowo University, Ile-Ife, Nigeria, it is an invaluable resource for a wide range of learners. It is ideal for any undergraduate student in mathematics, physics, engineering, or computer science seeking a comprehensive understanding of vector analysis. Furthermore, it serves as an excellent and thorough refresher for professionals who wish to solidify their foundational knowledge of this critical subject.
This comprehensive learning track guides you through the complete world of vector analysis. We begin with the fundamentals of vector algebra and its application to foundational geometry. You will then master scalar, vector, and triple products before using them to construct the vector equations of lines, planes, and conics. The journey culminates in advanced topics, including vector calculus, its applications in classical mechanics, and an introduction to differential geometry. Vectors are the essential language used to describe our physical world, making their mastery non-negotiable for any serious student of science or engineering. This track is designed to build your intuition for spatial reasoning and equip you with a powerful problem-solving toolkit. You will see direct applications in mechanics, analyzing forces and motion; in geometry, calculating angles and distances; and in calculus, modeling dynamic change over time. While this track is tailored to the first-year university curriculum for MTH 104 at Obafemi Awolowo University, Ile-Ife, Nigeria, it is an invaluable resource for a wide range of learners. It is ideal for any undergraduate student in mathematics, physics, engineering, or computer science seeking a comprehensive understanding of vector analysis. Furthermore, it serves as an excellent and thorough refresher for professionals who wish to solidify their foundational knowledge of this critical subject.
[FUTA, Akure] MTS 104: Introductory Applied MathematicsThis learning track is designed for first-year students at the Federal University of technology, Akure (FUTA) and aligns with the second-semester coverage of introductory applied mathematics. It opens with vectors—what they are, how they work, and where they show up in real-world problems. From there, you’ll explore the geometry of circles and conic sections, gradually building up to the core ideas in basic dynamics.
The lessons are short, clear, and practical—just the way we like it on UniDrills. Everything’s broken down to help you build strong intuition and problem-solving skills, especially if this is your first time engaging with applied math in this form.
If you're not a FUTA student, no worries. The structure and explanations are broadly relevant, and the track works just as well for anyone looking to master these foundational topics in science and engineering.
This learning track is designed for first-year students at the Federal University of technology, Akure (FUTA) and aligns with the second-semester coverage of introductory applied mathematics. It opens with vectors—what they are, how they work, and where they show up in real-world problems. From there, you’ll explore the geometry of circles and conic sections, gradually building up to the core ideas in basic dynamics. The lessons are short, clear, and practical—just the way we like it on UniDrills. Everything’s broken down to help you build strong intuition and problem-solving skills, especially if this is your first time engaging with applied math in this form. If you're not a FUTA student, no worries. The structure and explanations are broadly relevant, and the track works just as well for anyone looking to master these foundational topics in science and engineering.
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.