Short Title:Mathematics 2
Full Title:Mathematics 2
Module Code:MATH H1019
 
Credits: 5
NFQ Level:6
Field of Study:Mechanics and metal work
Module Delivered in 5 programme(s)
Reviewed By:DIARMUID RUSH
Module Author:Ciaran O Sullivan
Module Description:The aim of Mathematics 2 is to enable the student to master a broad range of standard mathematical techniques in linear algebra, analysis and calculus to a high level of proficiency. This proficiency is required to support engineering subjects and forms the basis for further mathematical study in year 2.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Write down geometric transformations as matrices and use matrices to implement geometric transformations.
LO2 Use matrix techniques to describe, solve and interpret the solution to systems of linear equations of the type occurring in engineering problems.
LO3 Use vectors to describe and solve geometric problems in 3D.
LO4 Recognise different engineering signal types such as even, odd, monotonic, convex, concave, piecewise ( constant and linear) and rational functions.
LO5 Apply knowledge of engineering functions to solve models (growth and decay models).
LO6 Extend the differential calculus to parametrically defined functions.
LO7 Apply differential calculus to analyse the graph of a function and to solve problems in mechanics and other engineering contexts.
LO8 Use the definition of integration to integrate an exact function.
LO9 Integrate the basic monomials, exponential, logarithmic and trigonometric functions of the type occurring in engineering and use linearity to integrate sums of such.
LO10 Use Simpson’s and the Trapezoid rules to evaluate definite integrals numerically, with an estimate of the error.
LO11 Apply integration to find a variety of areas and volumes and to solve problems in mechanics and other engineering contexts.
LO12 Demonstrate a sound knowledge of the vocabulary and syntax of a modern programming language.
LO13 Perform programming basics such as the assembling of programmes/scripts which correctly use variable assignment, comments and indentation and are able to debug and test such programmes.
LO14 Use programming control structures (selection structures and repetition)
Pre-requisite learning
Co-requisite Modules
No Co-requisite modules listed
 

Module Content & Assessment

Content (The percentage workload breakdown is inidcative and subject to change) %
Geometry and Matrices:
Matrix definition. Matrix algebra. Matrix determinant, special matrices and the matrix of a geometric transformation. Matrix multiplication as geometric composition. Inverse matrix formula for 2X2.
15.00%
Linear Algebra:
Systems of linear equations in matrix form. Solution of system of linear equations using row reduction (Gaussian elimination). Interpretation of the solution of systems of linear equations.
15.00%
Vectors and Matrices:
Vector and Scalar products with geometric and engineering context application. Using vectors to calculate planes in 3D .
7.00%
Functions:
Application of engineering functions to 1-D models such as growth and decay models.Types of function (even, odd, convex, concave, monotone, continuous, differentiable). Piecewise defined functions. Rational functions. Curves in 2D described in parametrized (vector) form.
8.00%
Further Differentiation:
Second derivatives. Parametric differentiation. Applying differentiation to engineering problems.
10.00%
Function investigation using differentiation:
Increasing and decreasing functions. Stationary points. Classifying stationary points. Points of inflexion.
10.00%
Indefinite Integration:
The anti-derivative. Linearity of the integral. Application to position, velocity and acceleration calculations.
10.00%
Definite Integration:
Calculations and properties. Fundamental Theorem of Calculus. Area under a graph. Area between two curves. Solids of revolution. Simpson’s rule and Trapezoid rule.
10.00%
Programming Skills:
Programming Basics: documentation (use of comments and indentation), Use of built-in I/O and mathematical functions, debugging and testing. Datatypes: Numbers, characters, arrays. Control Structures: selection structures ( if etc. using conditional expressions), repetition structures (for).
15.00%
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Continuous Assessment High threshold test on vectors and linear algebra. 1,2,3 10.00 Week 5
Assignment Exercises and lab test on the use of appropriate software [for example MATLAB] to manipulate matrices, solve simultaneous equations and visualize engineering functions. 1,2,3,4,5,7,11 10.00 Week 10
Continuous Assessment High threshold coursework (test or assignment) on application of calculus 4,5,6,7 10.00 Week 12
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination 1,2,3,4,5,6,7,8,9,10,11 70.00 End-of-Semester

IT Tallaght reserves the right to alter the nature and timings of assessment

 

Module Workload

Workload: Full Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture No Description 3.00 Every Week 3.00
Lab Computer lab on using Matlab augmented by tutorial work on problem sheet questions. 1.00 Every Week 1.00
Independent Learning Review of lecture material between lectures, completion of problem sheet questions, completion of computer assignments. Synthesis of course material ahead of final semester exam. 3.00 Every Week 3.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture PT Workload same at FT 3.00 Every Week 3.00
Lab Computer lab on using Matlab augmented by tutorial work on problem sheet questions. 1.00 Every Week 1.00
Independent Learning Review of lecture material between lectures, completion of problem sheet questions, completion of computer assignments. Synthesis of course material ahead of final semester exam. 3.00 Every Week 3.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
 

Module Resources

Recommended Book Resources
  • Kuldeep Singh 2011, Engineering Mathematics Through Applications, Palgrave MacMillan [ISBN: 9780230274792]
  • Glyn James... [et al.], Modern engineering mathematics, Pearson Prentice Hall Harlow [ISBN: ISBN: 9780132391443]
  • Tony Croft,, Foundation Maths, 4ed Ed., Pearson Education [ISBN: ISBN: 9780131979215]
  • Brian Hahn,Daniel T. Valentine 2016, Essential MATLAB for Engineers and Scientists, Academic Press [ISBN: 0081008775]
Recommended Article/Paper Resources
  • David Zarrouk, Moshe Mann, Nir Degani, Tal Yehuda, Nissan Jarbi and Amotz Hess 2016, Single actuator wave-like robot (SAW): design, modeling, and experiments, Bioinspir. Biomim. 11 (2016) 046004
Other Resources
 

Module Delivered in

Programme Code Programme Semester Delivery
TA_EBIOM_B B.Eng (Hons) in Biomedical Design 2 Mandatory
TA_EAMEC_B B.Eng(Hons) in Mechanical Engineering [Ab Initio] 2 Mandatory
TA_EBIOM_D Bachelor of Engineering in Biomedical Design 2 Mandatory
TA_EAMEC_D Bachelor of Engineering in Mechanical Engineering 2 Mandatory
TA_EAUTO_D Bachelor of Mechanical Engineering (Automation) 2 Mandatory