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
not

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.

Module Content

This course is mainly the study of the theory and practical uses of the
Differential and Integral Calculus. Topics covered include

Functions

Limits and Continuity

Derivatives: Theory and Applications

Integration: Theory and Applications

Transcendental Functions

Modelling and Differential Equations

Sequences and Series

Textbook: The textbook that will be followed is
Calculus, by Anton, Bivens, Davis
Publisher, Wiley and Son

Module Prerequisite

None for students admitted to the Mathematics, Theoretical Physics or
Two-subject Moderatorships.

Assessment Detail

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.