Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Geometry of Curves
Code MATH248
Coordinator Dr O Karpenkov
Mathematical Sciences
O.Karpenkov@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2020-21 Level 5 FHEQ Second Semester 15

Aims

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.

Learning Outcomes

(LO1) 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.

(LO2) After completing this module students should be able to determine and work with tangents, inflexions, curvature, cusps, nodes, length and other features.

(LO3) After completing this module students should be able to determine the position and shape of some algebraic curves including conics.

(S1) Problem solving skills

(S2) Numeracy

(S3) IT skills

(S4) Adaptability

Syllabus
 

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.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
MATH101 Calculus I; MATH102 CALCULUS II; MATH103 MATH103 - Introduction to Linear Algebra 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Final Assessment - open book and remote Standard UoL penalties apply Assessment Schedule: Semester 2  1 hour time on task    50       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Computer Practical      15       
Class Test - open book and remote  around 60-90 minutes    35