BEng/MEng Mechanical Engineering with an Integrated Foundation Year

The Foundation Year Bursary  is available to UK students who are registered on an undergraduate foundation year here and who has had a full financial assessment carried out by Student Finance.

Details of country-specific funding available to international students can be found within our  International country profiles .

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability, therefore, we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships please visit our  undergraduate student finance pages  and the Department funding pages that you intend to progress to after successfully completing the Foundation Year.

The course unit aims to provide a basic course in various mathematical topics to students in Foundation Year.

On completion of the course the successful student will be able to:

- Calculate interpolating functions and values using linear and quadratic interpolation formulae and their inverses

- Select and apply numerical differentiation formulae to approximate derivatives, and discuss the accuracy of these approximations.

- Approximate integrals using the trapezium rule and Simpson's rule, and discuss the accuracy of these approximations.

- For each of circles centred on the origin, circles passing through the origin, straight lines, Archimedes and logarithmic spirals, ellipses, cardioids:
 --Given a curve represented by a written description, a polar-coordinate formula or a sketch, recall or derive the other two representations of the curve.
 --Recall how each of the parameters of the polar form of each curve relate to the characteristics of the plotted shape.
 --Scale and rotate the shape by multiplying the radius value and adding a constant to theta, respectively.
 --Convert between polar and Cartesian representations (points, lines, circles and ellipses only).

- Calculate the intersection points of polar curves, and use given intersection points to infer properties of the curves

- Recall the definitions of a root and the residual function.

- Apply the bisection method, the rule of false position and the Newton-Raphson method to solve scalar equations. For each method, explain the situations under which a root will be found and identify suitable initial values / intervals.

-Evaluate geometric integrals: the area inside a polar curve or between two polar curves; the volume of revolution of a curve (or between two curves) given in Cartesian form rotated about the x-axis; the volume of revolution of a curve rotated about the y-axis; the surface area of revolution of a curve given in Cartesian form about the x-axis; the arc-length of a curve given in either polar or Cartesian coordinates.

- Evaluate recurrence relations given a recurrence and initial term(s), and in simple cases evaluate later terms by identifying patterns in the sequence.

- Derive and apply reduction formulae to evaluate definite and indefinite integrals.

- Use the Mathematica language to achieve the above outcomes, including use of variables, functions and polar and Cartesian plots.

2: Numerical Interpolation: Linear Interpolation, Quadratic Interpolation.

1: Numerical Differentiation

2: Numerical Integration: The Trapezoidal Rule, Simpson's Rule.

3: Polar Coordinates: Polar coordinates of points. Polar coordinates of lines and curves. Points of intersection of polar curves

3: Numerical Solution of Equations: Bisection Method, Rule of False Position, Newton-Raphson method

3: Areas, lengths and volumes: Area inside a polar Curve, Volume of Solid of Revolution, Arc Length, Surface Area of Solid of Revolution

3: Recurrence Relations and Reduction Formulae: Recurrance relations, Reduction formulae [f(x)]^n with limits, reduction formulae x^n * f(x) with limits, reduction formulae without limits.

5: Mathematica: General introduction, application to topics in syllabus.

Coursework (Computerised Assignment) (week 7) Weighting within unit 10%

Mathematica Test (week 10 unless the project is submitted in week 10, in which case, the 0D2 coursework would be submitted in week 11.) Weighting within unit 10%

Examination (semester 2) Weighting within unit 80%

CROFT, A & DAVISON, R. 2010. Foundation Maths (5th ed.) Pearson Education, Harlow. (ISBN9780273730767)

BOSTOCK, L., & CHANDLER, S. 1981. Mathematics - the core course for A-level. Thornes, Cheltenham. (ISBN0859503062)

BOSTOCK, L., & CHANDLER, S. 1994. Core Maths for A-level (2nd ed.). Thornes, Cheltenham. (ISBN9780748717798)

STROUD, K.A, 2007. Engineering mathematics (6th ed.) Palgrave Macmillan, Baisingstoke. (ISBN9781403942463 / ISBN1403942463)

JAMES, G. 2001. Modern engineering mathematics (3rd ed.). Prentice Hall, Harlow. (ISBN0130183199 / ISBN9780130183194)

COOMBES, K. 1998. The Mathematica primer. Cambridge University Press, Cambridge. (ISBN0521631300 / ISBN0521637155  / ISBN9780521631303 / ISBN9780521637152)

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  

Please see Blackboard / course unit related emails for any further updates