Unit 34 Further Mathematics for Construction Assignment Brief
| Qualification | Higher National Diploma in Construction and the Built Environment |
| Module Code | P5E34 |
| Module Title | Further Mathematics for Construction |
| Unit code | M/618/8110 |
| Unit level | 5 |
| Credit value | 15 |
Submission Requirement
| Font | Times New Roman |
| Font Size | 12 font |
| Spacing | Single Line Spacing |
| Margin | 2 cm (Left-side only) |
| Printing | 1-Sided |
| Number of Words (Approx.) | 1) At least 2 pages answer of each question (400-500 words) excluding diagrams or pictures |
Learning Outcomes
By the end of this unit, students will be able to:
LO1 Apply instances of number theory in practical construction situations
LO2 Solve systems of linear equations relevant to construction applications using matrix methods
LO3 Approximate solutions of contextualised examples with graphical and numerical methods
LO4 Review models of construction systems using ordinary differential equations.
Assignment Brief and Guidance
Scenario
A multi-disciplinary Engineering Consultancy has contracted you as an Engineering Mathematics tutor
to support the recruits of Apprentice Engineers. They have asked you to produce a workbook for the apprentices.
Part A
Task 1
P1
Complete the following arithmetic and then convert to the identified number system
- 1011001₂ × 101100₂, convert the answer to Octal number system
- 4A6₁₆ + 3C4F₁₆ Convert to Denary number system
Task 2
P2
Using complex numbers determine the magnitude and direction of the resultant force for the force system below.
Task 3
P2/P3
A delta-connected impedance ZA of an electrical circuit is given by:
ZA = (Z1Z2 + Z2Z3 + Z3Z1) / Z2
Determine ZA given:
- Z1 = (10 + 0i) Ω
- Z2 = (0 − 10i) Ω
- Z3 = (10 + 10i) Ω
Give your answer in polar, cartesian and exponential form.
Task 4
P3
If z1 = 12∠125° and z2 = 3∠72°
Determine:
- z1z2
- z1 / z2
Task 5
P2/P3
If v = Vei(ωt+α) and i = Iei(ωt+β)
then show that the impedance (z) is given by
z = V/I [ cos(α − β) + i sin(α − β) ]
Task 6
M1
An electro mechanical circuit will perform repetitive cycles of operation,
hence the total impedance of the circuit is given by the complex equation.
Simplify this equation to give ZT in cartesian and polar form.
ZT = (3 + 5i)5 × (6 + 3.6i)3
Task 7
D1
Check that the following identities are valid using De Moivre’s Theorem:
cos 3θ = cos³θ − 3cosθsin²θ
sin 3θ = 3cos²θsinθ − sin³θ
Task 9
P10
The settlement of soil in a foundation is described by a second-order differential equation.
- Find the general solution for the depth of settlement.
- Determine the particular solution given the stated boundary conditions.
Task 10
P10
The deflection of a beam under a varying load can be modelled by the differential equation.
Find the general equation for the deflection.
Task 11
P10
In coastal engineering, the behaviour of waves in a medium can be modelled by a differential equation.
Determine a general solution for the equation when:
f(x) = 3cos(kx)
Task 12
P11
Using Laplace transform determine the particular solution for the differential equation
given the boundary condition y(0) = 0.
Task 13
P11
In a building’s heating system, the temperature T(t) of a room is modelled by a second-order differential equation.
Solve using Laplace transforms and determine T(t) given:
- T(0) = 20
- T'(0) = 5
Task 14
M4/D4
- Analyse how first-order differential equations are used to solve structural or environmental problems.
- Evaluate first- and second-order differential equations when generating solutions to construction problems.
Learning Outcomes and Assessment Criteria
| Pass | Merit | Distinction |
| LO1 Apply instances of number theory in practical construction situations | D1 Test the correctness of a trigonometric identity using de Moivre’s Theorem. | |
| P1 Apply addition and multiplication methods to numbers that are expressed in different base systems. P2 Solve construction problems using complex number theory.P3 Perform arithmetic operations using the polar and exponential form of complex numbers. |
M1 Deduce solutions of problems using de Moivre’s Theorem. | |
| LO2 Solve systems of linear equations relevant to construction applications using matrix methods | ||
| P4 Ascertain the determinant of a 3 × 3 matrix. P5 Solve a system of three linear equations using Gaussian elimination. |
M2 Determine solutions to a set of linear equations using the inverse matrix method. | |
| Pass | Merit | Distinction |
| LO3 Approximate solutions of contextualised examples with graphical and numerical methods | D2 Validate all analytical matrix solutions using appropriate computer software.D3 Critique the use of numerical estimation methods, commenting on their applicability and the accuracy of the methods. | |
| P6 Estimate solutions of sketched functions using a graphical estimation method. P7 Identify the roots of an equation using two different iterative techniques.P8 Determine the numerical integral of construction functions using two different methods. |
M3 Evaluate construction problems to formulate mathematical models using numerical and graphical methods. | |
| LO4 Review models of construction systems using ordinary differential equations | ||
| P9 Determine first-order differential equations using analytical methods. P10 Determine second-order homogeneous and non-homogenous differential equations using analytical methods.P11 Calculate solutions to linear ordinary differential equations using Laplace transforms. |
M4 Analyse how first-order differential equations are used to solve structural or environmental problems. D4 Evaluate first- and second-order differential equations when generating the solutions to construction problems. |
|
Recommended Resources
Print resources
BIRD, J. (2017), Higher Engineering Mathematics, Routledge
SINGH, K. (2011), Engineering Mathematics Through Applications, Macmillan International Higher Education
STROUD, K., BOOTH, D. (2001), Engineering Mathematics, Industrial Press Inc.
Links
This unit links to the following related units:
- Unit 3: Science & Materials
- Unit 7: Surveying, Measuring & Setting-out
- Unit 8: Mathematics for Construction
- Unit 9: Principles of Heating, Ventilation and Air Conditioning
- Unit 10: Measurement & Estimating
- Unit 16: Principles of Public Health Engineering
- Unit 21: Geotechnics & Soil Mechanics
- Unit 31: Advanced Structural Design
- Unit 33: Construction Technology for Complex Buildings Projects
- Unit 37: Advanced Heating, Ventilation and Air Conditioning Design & Installation
- Unit 38: Advanced Quantities for Complex Building Projects
- Unit 41: Highway Engineering
- Unit 43: Advanced Surveying & Measurement
- Unit 49: Advanced Electrical Design & Installation
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