# LO1 Use applications of number theory in practical engineering situations

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Higher National Certificate/Diploma in Engineering

Assignment Brief

 Unit Number and Title 39: Further Mathematics (level 5) Academic Year 2022-2023 Unit Tutor Assignment Title Analyse and Model Engineering Systems Issue Date 22 May 2023 Submission Date 22 July 2023 IV Name & Date Unit Learning Outcomes LO1 Use applications of number theory in practical engineering situations LO3 Approximate solutions of contextualised examples with graphical and numerical methods LO2 Solve systems of linear equations relevant to engineering applications using matrix methods LO4 Review models of engineering systems using ordinary differential equations

Submission Format

The submission is in the form of an individual report.

• the assignment must be submitted in a report format.
• it must have appropriate structure and approach.
• must append a bibliography in Harvard Referencing format

When completing the assignment and producing evidence, each learner must produce individual and authentic evidence for each task within the assignment.

## Scenario:

You are working as an Engineering Research Technician in a research and development laboratory where good analytical skills and understanding of mathematics is essential for everyday work. Your line manager has informed you that you need to improve and update your present Mathematical skills to work effectively & contribute to the research team. The essential skills include Number theory, Matrices, graphical and numerical methods, Models of engineering systems using ordinary differential equations .

To test your suitability for this position in research, the following tasks have been compiled for you to complete.

## Unit Learning outcomes

LO1 Use applications of number theory in practical engineering situations Task 1.0

1.1

(a) Sum the following numbers expressed in their respective bases: 3A16 , E716 and 658

(b) Multiply 101112 by 11012

(c) Convert each number into denary, along with the answer to verify your result.

.2

Determine in rectangular form of complex numbers ,the current flowing in each of the above circuits.

1.3

Convert the answers in (1.2) in polar and exponential form of complex numbers.

1.4

Use de Moivre’s Theorem to determine the three cubic roots of one expresiing the answers in both polar and Cartesian form.

1.5

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

## LO2 Solve systems of linear equations relevant to engineering applications using matrix methods

Task 2.0

2.1 determine the determinant of 3x3 matrix :

2.1  a d.c circuit comprises three closed loops. Applying kirchhoff’’s laws to the closed loops gives the following equations for current flow in mA.:

2x+3y -4 z=26 x - 5y -3z =-87

-7x+2y+6z =12

2.21  represent the above linear vector equations in matrix form and use Gaussian elimination to find the currents x,y& z .

2.22  solve the system using the inverse matrix method.

2.23  Validate the matrix solutions using computer software.

Assignment Brief Continues.........

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