Short Title:  Mathematics 1 

Full Title:  Mathematics 1 

Field of Study:  Mechanics and metal work 

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 coordinates from Cartesian to polar form. 
LO6 
Perform algebra involving complex numbers. 
LO7 
Graph functions, identify 11 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 1variable problems in engineering. 
LO10 
Manipulate vectors and apply them to simple problems in engineering 
Prerequisite learning 

Corequisite Modules
 No Corequisite 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.
Coordinate geometry: Cartesian coordinates. Equation of a straight line. Plotting simple linear laws, yintercept 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: Rightangled triangles. Sin, cos and tan. Sectors and arcs. Sin, cos and tan as lengths in the unit circle. Pythagorasâ€™ theorem. Solution of rightangled 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 Pythagorasâ€™ 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 Work  30.00% 
End of Module Formal Examination  70.00% 
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 
EndofSemester Final Examination 
1,2,3,4,5,6,7,8,9,10 
70.00 
EndofSemester 
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 ResourcesRequired 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
