Module: Integral Calculus

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Integral Calculus
Module Code	MTH1014 (ITS: MS113)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

Description

This module is aimed at students, starting with knowledge of higher level leaving certificate mathematics and differential calculus, to gain a sound grasp of integral calculus. Students on the module are expected to master fundamental techniques of integral calculus through doing a substantial number of exercises. It also exposes students to applications of calculus in economics and finance, and lays the foundations for further courses in calculus, analysis, probability and statistics.

Learning Outcomes

1. understand the concept of definite integral and know the basic properties of definite integrals
2. understand the concept of area of regions with curvilinear boundaries, be able to find area between curves
3. understand the concept of indefinite integral as anti-derivative
4. integrate important elementary functions, using the rules of integration
5. prove important results about the logarithm, exponential, and trigonometric functions
6. apply their knowledge of integration to solve real world problems in economics and finance

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	Lecture
Tutorial	12	Group tutorial
Independent Study	90	Self-study
Total Workload: 126

Section Breakdown
CRN	20780	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Niamh O'Sullivan	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
Assignment	Written Homework	10%	As required
Assignment	Written Homework	10%	As required
Formal Examination	2 hour exam	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Riemann Sums
Sums and summation notation,

Area as a limit of sums

Definite Integral
The definite integral and fundamental theorem of calculus

Indefinite Integral
The indefinite integral and basic rules of integration.

Methods of Integration
Integration by parts, substitution and using partial fractions

Applications of integration
area and volume; applications in economics, finance & actuarial maths; the natural logarithm; Taylor’s theorem

Indicative Reading List

Books:

G. Thomas, M. Weir, J. Hass: 2013, Thomas' Calculus: Early Transcendentals, 13, Pearson, 978-032188407
David Alexander Brannan: 2006, A first course in mathematical analysis, Cambridge University Press, Cambridge, 9780521864398
Jan Mikusi?ski, Piotr Mikusi?ski: 1993, An introduction to analysis, Wiley & Sons, New York, 9780471599777
Michael Spivak: 1994, Calculus, Cambridge Univ. Press, Houston, 9780521867443

Articles:
None

Other Resources

None