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 2 programme(s)
Reviewed By:FIONA CRANLEY
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 Solve a variety of trigonometric equations involving engineering waves and use a variety of trigonometric identities.
LO4 Recognise different engineering signal types such as even, odd, monotonic, convex, concave, piecewise and rational functions,
LO5 Use partial fractions to break down rational functions.
LO6 Use differential calculus to find and classify the stationary points of a function.
LO7 Extend the differential calculus to parametrically defined functions.
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 Apply integration to find a variety of areas and volumes.
LO11 Use Simpson’s and the Trapezoid rules to evaluate definite integrals numerically, with an estimate of the error.
LO12 Use vectors to describe and solve geometric problems in 3D involving lines and planes.
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.
12.00%
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. Rank of a matrix.
23.00%
Functions:
Types of function (even, odd, convex, concave, monotone, continuous, differentiable). Rational functions, their graph and partial fractions. Trigonometric functions: solving trigonometric equations, compound angle formulae, product formulae.
15.00%
Function investigation using differentiation:
Increasing and decreasing functions. Stationary points. Classifying stationary points and the second derivative test.
6.00%
Further Differentiation:
Inverse functions. Parametric differentiation. Applied max/min problems.
8.00%
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. The definite integral as a limit of sums. Simpson’s rule and Trapezoid rule.
13.00%
Vectors and Matrices:
Vector and Scalar triple product with geometric application. Lines and planes in 3D and geometric problems involving them done using vectors. Curves and surfaces in 3D described in parametrized vector form.
13.00%
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. 1,2,12 10.00 Week 4
Assignment Exercises and lab test on the use of appropriate software [for example MATLAB] to manipulate matrices, solve simultaneous equations and visualize engineering functions. 1,2,4,6,8,10,11,12 10.00 Week 9
Continuous Assessment High threshold test on calculus 6,7,8,9 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 1,2,3,4,5,6,7,8,9,10,11,12 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 2.00 Every Week 2.00
Lab Computer lab on using Matlab augmented by tutorial work on problem sheet questions. 4.00 Every Third Week 1.33
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. 3.67 Every Week 3.67
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 3.33
 

Module Resources

Required Book Resources
  • Kuldeep Singh, Engineering mathematics through applications [ISBN: ISBN 0333922247]
Recommended Book Resources
  • CALMAT learning environment - MOLS lessons as prescribed.
  • Glyn James... [et al.], Modern engineering mathematics, Pearson Prentice Hall Harlow [ISBN: ISBN: 9780132391443]
  • Dexter J. Booth,, Engineering Mathematics [ISBN: ISBN: 9781403942463]
  • Tony Croft,, Foundation Maths, 4ed Ed., Pearson Education [ISBN: ISBN: 9780131979215]
This module does not have any article/paper resources
This module does not have any other resources
 

Module Delivered in

Programme Code Programme Semester Delivery
TA_EAMEC_B B.Eng(Hons) in Mechanical Engineering [Ab Initio] 2 Mandatory
TA_EAMEC_D Bachelor of Engineering in Mechanical Engineering 2 Mandatory