Vectors, Geometry and Dynamics
This course introduces students to vector algebra, coordinate geometry and elementary mechanics. It builds the mathematical foundation needed for analysing quantities with magnitude and direction, solving geometry problems, and interpreting basic motion and force systems.
Major outline
- Scalars, vectors, vector representation and types of vectors.
- Vector addition, subtraction and scalar multiplication.
- Linear combinations, span, linear dependence and independence.
- Components, direction ratios and direction cosines.
- Dot product, cross product, projections and area applications.
- Coordinate geometry, straight lines, circles, tangents and normals.
- Conic sections: parabola, ellipse and hyperbola.
- Kinematics, projectiles, Newton’s laws, work, energy, power and equilibrium.