Learning Outcome 1: Solve systems of linear equations relevant to engineering applications using matrix methods
Learning Outcome 2: Calculate the determinant of a set of given linear equations using a 3 x 3 matrix P5 Solve a system of three linear equations using Gaussian elimination
Learning Outcome 3: Determine the solution of a set of given engineering linear equations using the inverse Matrix method for a 3 x 3 matrix
Learning Outcome 4: Validate solutions for the given engineering linear equations using appropriate computer software
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Introduction: The understanding of more advanced mathematics is important within an engineering curriculum to support and broaden abilities within the applied subjects at the core of all engineering programmes. Students are introduced to additional topics that will be relevant to them as they progress to the next level of their studies, advancing their knowledge of the underpinning mathematics gained in Unit 2: Engineering Maths.
The unit will prepare students to analyse and model engineering situations using mathematical techniques. Among the topics included in this unit are - number theory, complex numbers, matrix theory, linear equations, numerical integration, numerical differentiation, and graphical representations of curves for estimation within an engineering context. Finally, students will expand their knowledge of calculus to discover how to model and solve engineering problems using first and second order differential equations.
On successful completion of this unit students will be able to use applications of number theory in practical engineering situations, solve systems of linear equations relevant to engineering applications using matrix methods, approximate solutions of contextualised examples with graphical and numerical methods, and review models of engineering systems using ordinary differential equations.
Unique Numbers
You will be given a set of numbers - these are unique values for your assessment. (*) denotes student number
Note: due to student number system your answer may not be realistic. Adopt an accurate real-world approach to using your number correctly.
Task 1 - Mechanical HND
You latest role in the design department is to participate in a development team who are trying to improve the efficiency of their simply piston engines. The relationship between the displacement s, velocity v and the acceleration a of the piston you are working with is given by:
Set Mech A
s+2v+2a=4 3s-v+4a=25 3s+2v-a=-4
Set Mech B
s+2v+3a=5 2s-3v-a=3 -3s+4v+5a=3
Set Mech C 3s+4v-3a=2 -2s+2v+2a=15 7s-5v+4a=26
Set Mech D
s+v+a=6 2s+3v-2a=2 3s+4v+3a=30
Calculate the determinant for the matrix created from this set of linear equations
Task 1 - Electrical HND
You are involved in a simple circuit design to control the speed of certain aspects of the machining processes to be used at the manufacturing company you work for. From your previous experience using Kirchoffs Laws to determine the current equations in the electrical network and show that-
Set Elec A
i1+2i2+2i3=4 3i1-i2+4i3=25 3i1+2i2-i3=-4
Set Elec B
i1+2i2+3i3=5 2i1-3i2-i3=3 -3i1+4i2+5i3=3
Set Elec C 3i1+4i2-3i3=2 -2i1+2i2+2i3=15 7i1-5i2+4i3=26
Set Elec D
i1+i2+i3=6 2i1+3i2-2i3=2 3i1+4i2+3i3=30
Calculate the determinant for the matrix created from this set of linear equations
Task 2
To check the exact values for the unknowns in your given equations. Solve the set of 3 linear equations identified using Gaussian Elimination.
Task 3
Further to using Gaussian Elimination use Inverse Matrix Method to solve and confirm results for the set of 3 linear equations you have been given.
Task 4
Then you can finally validate solutions for the equations in Task 1-3 using appropriate computer software (Use MATLAB to confirm Q1).