To introduce geometric ideas and develop the basic skills in handling them.

To study the line, circle, ellipse, hyperbola, parabola,  cubics and many other curves.

To study theoretical aspects of parametric, algebraic and projective curves.

To study and sketch curves using an appropriate computer package.

After completing this module students should be able to:

- use a computer package to study curves and their evolution in both parametric and algebraic forms.

-determine and work with tangents, inflexions, curvature, cusps, nodes, length and other features.

-calculate envelopes and evolutes.

- solve the position and shape of some algebraic curves including conics.

The first learning outcome is assessed by coursework, the others by both coursework and examination.

Ellipse, hyperbola, parabola:  canonical forms from the general equation.

Parametric, polar, complex, and algebraic equations.

Parametric and algebraic curves, tangents, contact, inflexions, vertices, cusps.

Curvature, evolutes.

Envelopes, caustics, orthotomics.

Algebraic curves, multiplicity, singular points, branches.

Projective curves, points at infinity, bounded curves, asymptotes.