Vector Algebra and Geometry - Vectors (Undergraduate Foundation)

Vectors are the primary tool for describing quantities with both magnitude and direction. This course provides a complete foundation in their algebraic and geometric properties. We move systematically from the basic definition and classification of vectors to the core operations of vector algebra: addition and scalar multiplication. The curriculum then progresses to essential geometric applications, including position vectors, Cartesian components, direction cosines, the division of lines, vector projections, and centroids. A command of vector algebra is not optional; it is essential for any technical or scientific discipline. This knowledge is the bedrock of classical mechanics, electromagnetism, and fluid dynamics. Engineers use these principles to analyse forces, computer scientists use them to build 3D graphics engines, and data scientists apply them in advanced linear algebra. This course provides the indispensable mathematical toolkit required for these fields. Upon completion, you will be able to perform all fundamental vector operations with precision. You will resolve vectors into Cartesian components and use direction cosines. You will solve geometric problems involving position vectors, the internal and external division of lines, and collinearity. Furthermore, you will master the calculation of vector projections and the determination of centroids in geometric systems. This course is designed for first-year undergraduate students in Engineering, Physics, Mathematics, and Computer Science. It serves as a critical foundation for anyone beginning studies that rely on applied mathematics. It is also a rigorous and efficient refresher for professionals or advanced students who need to solidify their understanding of foundational vector principles before tackling more complex material.

21 hrs

Enrolment valid for 12 months
This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.
GET 209: Engineering Mathematics I
GET 209: Engineering Mathematics I
Master the mathematical language of engineering. This programme delivers the complete analytical toolkit required for a successful engineering career, covering single-variable calculus, multivariable calculus, linear algebra, and vector analysis. It provides the essential foundation for all subsequent engineering courses. This programme is for second-year undergraduate students across all engineering disciplines. It delivers the official NUC CCMAS curriculum for Engineering Mathematics, providing the core training required for advanced modules in mechanics, thermodynamics, and circuit theory. Model and analyse complex physical systems using calculus, linear algebra, and vector analysis. You will be equipped to solve problems in dynamics, statics, and field theory, providing the quantitative proficiency required for advanced engineering study and professional practice.

Master the mathematical language of engineering. This programme delivers the complete analytical toolkit required for a successful engineering career, covering single-variable calculus, multivariable calculus, linear algebra, and vector analysis. It provides the essential foundation for all subsequent engineering courses. This programme is for second-year undergraduate students across all engineering disciplines. It delivers the official NUC CCMAS curriculum for Engineering Mathematics, providing the core training required for advanced modules in mechanics, thermodynamics, and circuit theory. Model and analyse complex physical systems using calculus, linear algebra, and vector analysis. You will be equipped to solve problems in dynamics, statics, and field theory, providing the quantitative proficiency required for advanced engineering study and professional practice.

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MTH 210: Vector Analysis
MTH 210: Vector Analysis
Vector analysis is the mathematical backbone of classical mechanics, electromagnetism, and fluid dynamics. This learning track delivers the complete NUC CCMAS MTH 210 curriculum, rigorously progressing from fundamental vector algebra to the advanced differential and integral calculus of scalar and vector fields used in complex engineering and scientific modelling. This programme is targeted at undergraduates in engineering, physics, mathematics, and computer science. It provides the essential mathematical toolkit for students entering disciplines that rely on applied mathematics and spatial analysis, and serves as a rigorous refresher for professionals needing to solidify their command of vector principles. You will master the full spectrum of vector operations including dot, cross, and triple products, and apply them to solve geometric problems and vector equations. You will acquire the skills to analyze the differential geometry of curves using the Frenet-Serret framework and apply the powerful gradient, divergence, curl, and Laplacian operators in various coordinate systems. Completion establishes the critical mathematical foundation demanded for advanced studies in continuum mechanics, electrodynamics, and theoretical physics.

Vector analysis is the mathematical backbone of classical mechanics, electromagnetism, and fluid dynamics. This learning track delivers the complete NUC CCMAS MTH 210 curriculum, rigorously progressing from fundamental vector algebra to the advanced differential and integral calculus of scalar and vector fields used in complex engineering and scientific modelling. This programme is targeted at undergraduates in engineering, physics, mathematics, and computer science. It provides the essential mathematical toolkit for students entering disciplines that rely on applied mathematics and spatial analysis, and serves as a rigorous refresher for professionals needing to solidify their command of vector principles. You will master the full spectrum of vector operations including dot, cross, and triple products, and apply them to solve geometric problems and vector equations. You will acquire the skills to analyze the differential geometry of curves using the Frenet-Serret framework and apply the powerful gradient, divergence, curl, and Laplacian operators in various coordinate systems. Completion establishes the critical mathematical foundation demanded for advanced studies in continuum mechanics, electrodynamics, and theoretical physics.

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Course Chapters

1. Introduction
5
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.
Concept Overviews
5 Lessons
1:43:14
2. Vector Algebra
6
5
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.
Concept Overviews
6 Lessons
1:46:52
Problem Walkthroughs
5 Lessons
2:38:43
3. Position Vectors
1
2
Meaning and algebra of position vectors.
Concept Overviews
1 Lesson
10:04
Problem Walkthroughs
2 Lessons
1:30:40
4. Vector Components
4
5
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.
Concept Overviews
4 Lessons
1:42:33
Problem Walkthroughs
5 Lessons
1:56:04
5. Division of a Line
3
3
Ratio Division of a line internally and externally; collinearity of points.
Concept Overviews
3 Lessons
1:03:54
Problem Walkthroughs
3 Lessons
2:06:50
6. Vector Projections
2
2
Projection of a vector on another vector; projection of a vector on a plane.
Concept Overviews
2 Lessons
39:13
Problem Walkthroughs
2 Lessons
1:09:25
7. Centroids
2
2
Mean centre (geometric centre) of a number of points; weighted mean centres.
Concept Overviews
2 Lessons
20:28
Problem Walkthroughs
2 Lessons
36:22