Short Title:Mathematics 1
Full Title:Mathematics 1
Module Code:MATH H1018
 
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 first aim of Mathematics 1 is to allow a thorough revision and consolidation of key basic mathematical topics that have been encountered by students prior to entry to higher education. The second aim is to deepen the students understanding of key mathematical ideas regarding engineering functions, iteration and calculus in such a way as to support other engineering modules.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Manipulate and solve algebraic expressions and equations.
LO2 Apply the basic techniques of trigonometry to solve problems in engineering.
LO3 Find the equation of a straight line through data.
LO4 Find the centre and radius of a circle.
LO5 Convert co-ordinates from Cartesian to polar form.
LO6 Perform algebra involving complex numbers.
LO7 Graph functions, identify 1-1 functions, apply the algebra of functions, recognise and do calculations with periodic functions, log and exponential functions.
LO8 Apply the standard techniques of differential calculus.
LO9 Apply the differential calculus to simple 1-variable problems in engineering.
LO10 Manipulate vectors and apply them to simple problems in engineering
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) %
Review Material:
Arithmetic: Arithmetic of real numbers, indices, fractions, scientific form. Algebraic expressions and formulae: Precedence rules. Manipulation of algebraic expressions. Manipulation of algebraic fractions. Factorisation of quadratic expressions. Recognition of the graphs of simple quadratic forms. Co-ordinate geometry: Cartesian co-ordinates. Equation of a straight line. Plotting simple linear laws, y-intercept and slope. Distance in 2D. Area of a triangle. Equation of a circle. Tangent to a circle. Complex numbers: Definition of a complex numbers. Conjugate of a complex number. Argand diagram representation. Addition and subtraction of complex numbers. Trigonometry: Right-angled triangles. Sin, cos and tan. Sectors and arcs. Sin, cos and tan as lengths in the unit circle. Pythagoras’ theorem. Solution of right-angled triangles. Sine and cosine rules. Functions: Basic concepts/notation. Domain and range. Injective, surjective, bijective functions.
25.00%
Algebra:
Negative and fractional indices. Logarithms. Error estimates. Transposition of formulae. Solution of linear equations. Gradient and intercept with reference to straight lines. Proportion. Solution of simple inequalities. Simultaneous equations. Simultaneous linear inequalities as regions in the plane. Graph of quadratic expression y = x2. Rewriting a quadratic expression by completion of the square. Graphs of a general quadratic expression. Solution of quadratic equations. Graphs of cubics. Standard form of conics.
22.00%
Trigonometry:
Radian measure. Cosecant, secant and cotangent. Fundamental identities arising from Pythagoras’ theorem.
3.00%
Vectors:
Scalars and vectors. Addition and subtraction of vectors. Modulus of a vector. Unit vectors. Resolution into component form. Scalar product.
17.00%
Complex Numbers:
Modulus and argument of a complex number. Multiplication and division of complex numbers in both Cartesian and polar forms. Solution of equations of the form zn = a where a is a real number.
4.00%
Functions:
Plotting functions. Alteration of a functional description as a result of transformations in the plane. Function inverses. Limit of a function. Power law, exponential and logarithmic functions. Simplification of expressions using the rules of logs. Solving equations involving logarithmic and exponential functions. Growth and decay model problems. Definition of periodic functions. Graphs of trigonometric functions.
22.00%
Rate of change and differentiation:
Average and instantaneous rate of change. Definition of derivative of a function at a point. Geometric interpretation of the derivative. The chain rule. The equations of tangent and normal to the graph of a function. Differentiation: Use of a table of derived functions. Use of the multiple, sum, product and quotient rules.
7.00%
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Short Answer Questions Diagnostic test to identify for students key areas of consolidation in the first 3 weeks of term. 1,2,3,4,6 0.00 Week 1
Continuous Assessment High threshold test at the end of review material. 1,2,3,4,5,6 15.00 Week 4
Assignment Assignment to plot functions and investigate polynomial, power law, exponential, logarithmic and trigonometric functions using appropriate software tools (for example Excel and MATLAB) 7 10.00 Week 9
Continuous Assessment High threshold test on rules on vectors and rules of differentiation. 8,10 5.00 Week 10
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 70.00 End-of-Semester
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.

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 labs on graphing engineering function and using excel. Followed by tutorial work on problem sheets. 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 No Description 2.00 Every Week 2.00
Lab Computer labs on graphing engineering function and using excel. Followed by tutorial work on problem sheets. 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 0 333 922247.]
Recommended Book Resources
  • CALMAT learning environment - MOLS lessons as prescribed, n/a
  • Glyn James... [et al.], Modern engineering mathematics, Pearson Prentice Hall Harlow [ISBN: ISBN 9780132391443]
  • Dexter J. Booth,, Engineering Mathematics [ISBN: 9781403942463]
  • Tony Croft,, Foundation Maths [ISBN: 9780131979215]
  • Anthony Croft, Robert Davison, Martin Hargreaves, Engineering mathematics [ISBN: ISBN 0130268585]
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] 1 Mandatory
TA_EAMEC_D Bachelor of Engineering in Mechanical Engineering 1 Mandatory