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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Integral Calculus
Module Code MS113
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Ben Quigley
Semester 2: Ben Quigley
Autumn: Ben Quigley
Module TeachersNiamh O'Sullivan
Ben Quigley
NFQ level 6 Credit Rating 5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
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



Workload Full-time hours per semester
Type Hours Description
Lecture24Lecture
Tutorial12Group tutorial
Independent Study150Self-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 Assessment20% Examination Weight80%
Course Work Breakdown
TypeDescription% of totalAssessment Date
In Class Testn/a4%Week 6
In Class Testn/a4%Week 12
Short Answer Questionsn/a12%As required
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
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
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