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Module MAU11201: SingleVariable Calculus and Introductory Analysis
 Credit weighting (ECTS)

10 credits
 Semester/term taught

Michaelmas term 201920
 Contact Hours

11 weeks, 5 lectures plus tutorials per week

 Lecturer

Prof. Paschalis Karageorgis
 Learning Outcomes
 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
Twosubject 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. Reassessments if required will consist of 100% exam.