BEng/MEng Mechanical Engineering with an Integrated Foundation Year

The course unit aims to: provide a basic course in calculus and algebra to students in the Foundation Year with no post-GCSE mathematics.

On completion of this unit successful students will be able to:

1 - Define the exponential function and apply the rules of indices to simplify algebraic expressions.

2 - Use the definition of the logarithm, together with its rules, to solve logarithmic equations.

3 - Find the roots, degree, leading term and coefficients of a polynomial.

4 - Identify and solve quadratic equations using the quadratic formula.

5 - Determine the equation of a line given its gradient and a point through which it passes.

6 - Calculate the gradient of a line given: (a) two points it passes through; (b) the gradient of a line to which it is parallel/perpendicular.

7 - Find the coordinates of the intersection points of two curves.

8 - Write down the equation of a tangent to a curve at a point.

9 - Given two points in the plane, determine the equation of a circle centred at one point and passing through the other.

10 - Define the domain of a function and calculate its inverse.

11 - Determine and simplify the composition of two functions.

12 - Convert angles between degrees and radians.

13 - Using the unit circle, recall the definition of the trigonometric functions, and apply this to determine the values of these functions at commonly-encountered angles.

14 - Find the size of an angle using the inverse trigonometric functions together with geometric reasoning.

15 - Use trigonometric identities to determine all angles and side-lengths in a right-angled triangle, given a side-length and one other piece of information (side-length or angle).

16 - Use the chain/product/quotient rules to differentiate the composition/product/quotient of two functions.

17 - Apply the rules for differentiation to determine the coordinates of, and classify, the stationary points of a given function.

18 - Use integration to find the area between two curves.

Functions (3 lectures)

• Definition of a function
• Indices
• Standard functions (polynomial, exponentials, logarithms etc.)

Solution of Equations (2-3 lectures)

• Accuracy and Rounding
• Linear, Quadratic and other polynomial equations

Trigonometry (4 lectures)

• Circular measure
• Trigonometric functions
• Inverse Trig Functions
• Trigonometric Identities

Coordinate Geometry (3-4 lectures)

• Straight lines,
• circles,
• points of intersection,
• slopes and gradients

Differentiation (3 lectures)

• Definition
• Derivatives of standard functions
• Product rule
• Quotient Rule
• Chain Rule

Stationary points (2 lectures)

• Maxima and Minima
• Curve Sketching

Integration (4 lectures)

• Derivatives and anti-derivatives
• Indefinite integration, specific integrals, use of tables

Definite integrals and areas under / between curves.

Coursework 1 (week 5); Weighting within unit 10%

Coursework 2 (week 10); Weighting within unit 10%

Computer assignments; Weighting within unit 10%

End of semester 1 examination; Weighting within unit 70%

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

BOOTH, D. 1998. Foundation Mathematics (3rd ed.). Addison-Wesley, Harlow. (ISBN0201342944)

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

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