Module: Integral Calculus

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Integral Calculus
Module Code	MS113 (ITS) / MTH1014 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Niamh O'Sullivan
Module Teachers	-
NFQ level	6	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

None

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	150	Self-study
Total Workload: 186

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

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	n/a	4%	Week 6
In Class Test	n/a	4%	Week 12
Short Answer Questions	n/a	12%	As required

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 3

Indicative Reading List

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

Other Resources

None