## Trinity College Dublin, The University of Dublin

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# Module MAU11201: Single-Variable Calculus and Introductory Analysis

Credit weighting (ECTS)
10 credits
Semester/term taught
Michaelmas term 2019-20
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 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. Re-assessments if required will consist of 100% exam.