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Qualification - Higher National Diploma in Construction and the Built Environment

Unit Number - Unit 28

Unit Name - Further Mathematics for Construction

Assignment Title - Further Maths

Learning Outcome 1: Apply instances of number theory in practical construction situations.
Learning Outcome 2: Solve systems of linear equations relevant to construction applications using matrix methods
Learning Outcome 3: Approximate solutions of contextualised examples with graphical and numerical methods
Learning Outcome 4: Review models of construction systems using ordinary differential equations

LO1

Task 1
a. Convert each number into denary,

• 11001.01

• 4D

b. calculate the following in both binary and denary

•11001+1001

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Task 2
Apply de'Moivre's theorem or otherwise to solve for Zo and C from these expressions given below :
Z0=Z/Y and C=Z*Y
Where:
• Z is a complex number.
• Y is also a complex number.
• Re (Z0) >0 and Re (C) >0
Find Z0 and C when:
Z = 1 + 5 j,Y = 1 - 3 j

Task 3

a. Simplify the following equation:
G = 1 x e j2Π x 2 x ej0.5 x 0.5x e j0.75

b. Express the following expression in complex exponential form:

v=20sin (1000t-30°)

Task 4

Find a formula for cos (3θ) in terms of cos (θ) and sin (θ) using de Moivre's Theorem.

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LO2

Task 1

1252_Mathematics for Construction.jpg

a) Determine the vector Z when θ = Π/2, Z = Rθ x ( X - Y )

b) Determine the determinant of the matrix Rθ when θ = Π/4

c) Determine the inverse of Rθ When θ = Π/4

d) Solve the following equation for

Task 2

You have been asked by the structural engineering department to find the determinant and inverse of the following matrix

Task 4
You have been asked to the following set of equations that have been obtained from the structural engineering Department and verify your calculations using computer methods
2x2 + x3 = -8
x1 - 2x2 - x3 = 0
- x1 + x2 + 2x3 = 3

LO3

Assignment Brief and Guidance

Task 1
The engineering department has developed the following equation for the bending moment of a beam and you have asked to investigate its behaviour
M ( x) = x3 - 3x2 - 4
The Beam is 4m long and the design team suspect the is problem if the bending moment is zero in the range between 3-4m and you have been asked to
a) Plot the bending moment at 0.5m interval for the range 0 ≤ x ≤ 4m 0 ≤ x ≤ 4 and determine if the bending moment is zero in range 3m ≤ x ≤ 4m
b) Use the graph to estimate where the bending moment is zero
c) Use the bisection method to numerically estimate the exact location where the bending moment is zero
d) Newton-Raphson method to obtain the required location
e) Compare the results of the above method to determine which gives a best solution

Task 2
The following offsets are taken from a chain line to an irregular boundary towards right side of the chain line.

chainage 0 25 50 75 100 125 150

Offset 'm' 3.6 5.0 6.5 5.5 7.3 6.0 4.0

Common distance d =25m
You have been asked to estimate the area using the following methods and compare and comment on their difference and accuracy.
a) Trapezium Rule
b) Simpson's Rule

Task 3
The equation governing a body travelling in a water channel is given by the following equation
dv/dt = 1 - v2

Plot the velocity time graph for the object and determine the final velocity and the time taken to reach this velocity

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LO4

Assignment Brief and Guidance

TASK 1

The equation of catenary is given by the following second order differential equation
y " = 5
x = 0, y = 100
x = 100, y = 100

Solve the above differential equation and plot the curve at 10m intervals.

Task 2
The differential equation governing the motion of a particle is given by the following differential equation
y ''+ 5 y = 0
t = 0, y = 20
Solve the above and plot the results and determine the amplitude and frequency of the oscillations

Task 3
A new series of tests is carried out and the equation modified to
y ''+ 2 y + 5 = 0
y = 20, t = 0

Use Laplace transforms or any other method to solve the new equations and plot the function and comment on the results.

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Are You Looking for Further Mathematics for Construction Assignment Help?


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  • Unit 4 Construction practice & management Assignment Help
  • Unit 7 Surveying, measuring & setting out Assignment Help
  • Unit 2 Construction Technology Assignment Help
  • Unit 1 Individual project Assignment Help
  • Unit 3 Science & materials Assignment Help
  • Unit 14 Building information modelling Assignment Help
  • Unit 5 Legal & statutory responsibilities in construction Assignment Help
  • Unit 6 Construction information (drawing, detailing, specification) Assignment Help