Short Title:  Mathematics 2 

Full Title:  Mathematics 2 

Field of Study:  Mechanics and metal work 

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 Simpsonâ€™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. 
Prerequisite learning 

Corequisite Modules
 No Corequisite 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 antiderivative. 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. Simpsonâ€™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 Work  30.00% 
End of Module Formal Examination  70.00% 
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 
EndofSemester Final Examination 
1,2,3,4,5,6,7,8,9,10,11,12 
70.00 
EndofSemester 
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 ResourcesRequired 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
