On successful completion of this module students will be able to
Determine whether a given relation is a function or not, and
whether an inverse function exists.
Find limits and determine whether given functions are continuous or
Differentiate functions and use derivatives to graph functions,
solve extremal problems and related rates problems.
Integrate functions using substitution, integration by parts,
partial fractions and reduction formulae.
Find areas, volumes, length of curves, averages and work done.
Solve simple first order differential equations and higher order
linear homogeneous differential equations.
Determine whether a given sequence or series converges or not.
Determine where a given power series converges absolutely,
converges conditionally or diverges.
This course is mainly the study of the theory and practical uses of the
Differential and Integral Calculus. Topics covered include
Limits and Continuity
Derivatives: Theory and Applications
Integration: Theory and Applications
Modelling and Differential Equations
Sequences and Series
Textbook: The textbook that will be followed is
Calculus, by Anton, Bivens, Davis
Publisher, Wiley and Son
None for students admitted to the Mathematics, Theoretical Physics or
This module will be examined in a 3 hour examination in Trinity term. Continuous assessment will contribute 15% to the final grade for the module at the annual
examination session. Re-assessments if required will consist of 100% exam.