Module Details

Module Code: MATH7030
Title: Calculus & Laplace Transforms
Long Title: Calculus & Laplace Transforms
NFQ Level: Intermediate
Valid From: Semester 1 - 2019/20 ( September 2019 )
Duration: 1 Semester
Credits: 5
Field of Study: 4610 - Mathematics
Module Delivered in: 3 programme(s)
Module Description: This module introduces concepts in further calculus including partial differentiation and various methods of integration. An introduction to the theory of Laplace transforms completes the module.
 
Learning Outcomes
On successful completion of this module the learner will be able to:
# Learning Outcome Description
LO1 Recall the techniques of differentiation and apply them to problems relevant to the student discipline.
LO2 Apply partial differentiation to analyse small changes, error analysis and rates of change.
LO3 Apply various integration techniques. Calculate the mean and root mean square value of periodic and non periodic functions.
LO4 Apply the Laplace transform method in solving ordinary differential equations
LO5 Use computer software package to explore further calculus problems and integral transforms.
Dependencies
Module Recommendations

This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named MTU module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).
9693 MATH6060 Maths for Physical Sciences
13601 MATH6019 Technological Maths 2 & Maple
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list.
No incompatible modules listed
Co-requisite Modules
No Co-requisite modules listed
Requirements

This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.
No requirements listed
 
Indicative Content
Differential Calculus
Review the fundamental rules of differentiation including product, quotient and chain rules. Introduce functions of several variables. Partial differentiation with application to small changes, error analysis and rates of change.
Integral Calculus
Review the fundamental techniques of integration including the method of substitution. Further integration techniques to include integration by parts and partial fractions. Applications of definite integrals including the calculation of the mean and root mean square (rms) of periodic and non periodic functions.
Introduction to Laplace Transforms
Definition of the Laplace transform. Determining the Laplace transform of basic functions. First shift theorem. Laplace transform of a derivative. Inverse Laplace transforms. Application to solving differential equations - including the damped harmonic oscillator.
Module Content & Assessment
Assessment Breakdown%
Coursework40.00%
End of Module Formal Examination60.00%

Assessments

Coursework
Assessment Type Short Answer Questions % of Total Mark 15
Timing Week 6 Learning Outcomes 1,2,3
Assessment Description
Differential Calculus
Assessment Type Short Answer Questions % of Total Mark 15
Timing Week 10 Learning Outcomes 3,4
Assessment Description
Integration techniques and Laplace Transform
Assessment Type Practical/Skills Evaluation % of Total Mark 10
Timing Every Second Week Learning Outcomes 5
Assessment Description
Computer software package labs
End of Module Formal Examination
Assessment Type Formal Exam % of Total Mark 60
Timing End-of-Semester Learning Outcomes 1,2,3,4
Assessment Description
End-of-Semester Final Examination
Reassessment Requirement
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.

The University reserves the right to alter the nature and timings of assessment

 

Module Workload

Workload: Full Time
Workload Type Contact Type Workload Description Frequency Average Weekly Learner Workload Hours
Lecture Contact Formal Lecture Every Week 3.00 3
Tutorial Contact Worksheets Every Week 1.00 1
Lab Contact Computer algebra software laboratory Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact Exercise Sheets and Skills Practice Every Week 2.00 2
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 5.00
Workload: Part Time
Workload Type Contact Type Workload Description Frequency Average Weekly Learner Workload Hours
Lecture Contact Formal Lecture Every Week 2.00 2
Tutorial Contact Worksheets Every Second Week 0.50 1
Lab Contact Computer algebra software laboratory Every Second Week 0.50 1
Independent & Directed Learning (Non-contact) Non Contact Worksheets Every Week 4.00 4
Total Hours 8.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 3.00
 
Module Resources
Recommended Book Resources
  • Stroud K A. (2013), Engineering Mathematics, 7th Edition. Palgrave, [ISBN: 978-113703120].
Supplementary Book Resources
  • Bird J.. (2017), Engineering Mathematics, 8th Edition. Routledge, [ISBN: 978-113867359].
  • Stewart, J.. (2015), Calculus, 8th Edition. Brooks Cole, [ISBN: 1285740629].
This module does not have any article/paper resources
Other Resources
 
Module Delivered in
Programme Code Programme Semester Delivery
CR_SINEN_8 Bachelor of Science (Honours) in Instrument Engineering 4 Mandatory
CR_SPHYS_7 Bachelor of Science in Applied Physics and Instrumentation 4 Mandatory
CR_SPHYS_6 Higher Certificate in Science in Applied Physics and Instrumentation 4 Mandatory