Short Title: Mathematics 1 Mathematics 1
Module Code: MATH H1018

 Credits: 5
 NFQ Level: 6
Field of Study: Mechanics and metal work
Module Delivered in 6 programme(s)
Reviewed By: DIARMUID RUSH
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 Convert co-ordinates from Cartesian to polar form.
LO5 Manipulate vectors and apply them to simple problems in engineering
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 Solve a variety of trigonometric equations involving engineering waves.
LO9 Apply the standard techniques of differential calculus.
LO10 Safely backup electronic data by managing files and folders using a file management system.
LO11 Use common Mathematical, Engineering and Financial formulae in a spreadsheet.
LO12 Plot linear data, draw inferences, find the equation of the line of best fit and use appropriate software (e.g. Excel) to plot linear data and find its equation.
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. Negative and fractional indices. Algebraic expressions and formulae: Precedence rules. Manipulation of algebraic expressions. Manipulation of algebraic fractions. Factorisation of quadratic expressions. Functions: Basic concepts/notation. Domain and range. Recognition of the graphs of simple quadratic forms. Transposition of formulae. Solution of linear equations. 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. Complex numbers: Definition of a complex numbers. Conjugate of a complex number. Argand diagram representation. Addition and subtraction of complex numbers. Trigonometry: Radian measure. Right-angled triangles. Sin, cos and tan. Sectors and arcs. Sin, cos and tan as lengths in the unit circle. Pythagorasâ€™ theorem. Solution of right-angled triangles. Sine and cosine rules.
28.00%
Further Algebra:
Simultaneous equations. Rewriting a quadratic expression by completion of the square. Graphs of a general quadratic expression. Solution of quadratic equations. Graphs of cubics.
12.00%
Vectors:
Scalars and vectors. Addition and subtraction of vectors. Modulus of a vector. Unit vectors. Resolution into component form. Scalar product.
13.00%
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. Solving equations involving logarithmic and exponential functions. Definition of periodic functions. Graphs of trigonometric functions. Trigonometric functions: sin, cos and tan. Compound angle formulae. Solving trigonometric equations in an engineering context.
17.00%
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.
15.00%
Complex Numbers:
Modulus and argument of a complex number. Multiplication and division of complex numbers in both Cartesian and polar forms. De Moivre Theoerm
5.00%
Software Skills:
File management: Managing Files and the Computer Interface: Directory structure. Searching for files. Copy and rename. Spreadsheets: Basic concepts. Entering data to cells. Selecting cells, rows, columns and ranges. Copying/moving cells. Inserting/deleting cells, rows and columns. Entering formulae. Cell referencing. Using the function wizard. Plotting charts & graphs: line/curve fitting.
10.00%
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 5 weeks of term. 1,2,3,6 1.00 Week 1
Continuous Assessment High threshold test at the end of review material. 1,2,3,4,6 14.00 Week 5
Assignment Assignment to (a) collect, plot and interpolate linear data; (b)to plot polynomial, power law, exponential, logarithmic and trigonometric functions using appropriate software tools (for example Excel or Geogrebra). 3,7,10,11,12 10.00 Week 10
Continuous Assessment High threshold coursework ( test or assignment) on rules on vectors and rules of differentiation. 5,9 5.00 Week 12
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination 1,2,3,4,5,6,7,9 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

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 Contact Hours 4.00
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 Contact Hours 4.00

## Module Resources

Recommended Book Resources
• Kuldeep Singh, 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 [ISBN: 9780131979215]
• Anthony Croft, Robert Davison, Martin Hargreaves, Engineering mathematics [ISBN: ISBN 0130268585]
This module does not have any article/paper resources
Other Resources

## Module Delivered in

Programme Code Programme Semester Delivery
TA_EBIOM_B B.Eng (Hons) in Biomedical Design 1 Mandatory
TA_EAMEC_B B.Eng(Hons) in Mechanical Engineering [Ab Initio] 1 Mandatory
TA_EBIOM_D Bachelor of Engineering in Biomedical Design 1 Mandatory
TA_EAEEE_D Bachelor of Engineering in Energy and Environmental Engineering 1 Mandatory
TA_EAMEC_D Bachelor of Engineering in Mechanical Engineering 1 Mandatory
TA_EAUTO_D Bachelor of Mechanical Engineering (Automation) 1 Mandatory