# BEng/MEng Mechanical Engineering with an Integrated Foundation Year

Year of entry: 2024

## Course unit details:Mathematics 0B2

Unit code MATH19812 10 Level 1 Semester 2 No

### Aims

The course unit aims to provide a second semester course in calculus and algebra to students in Foundation Studies entering University with AS-level mathematics or equivalent.

### Learning outcomes

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

1) Carry out arithmetic operations (including the finding of roots) on complex numbers and represent the results in cartesian, polar and exponential forms as well as on an Argand Diagram.

2) Solve and analyse systems of linear equations using matrices.

3) Calculate improper integrals and analyse functions that are defined by integrals.

4) Solve homogeneous, separable and linear first-order Ordinary Differential Equations and analyse their properties using direction fields.

5) Carry out partial differentiation and use the chain rule to estimate errors in functions.

### Syllabus

Complex Numbers (4 lectures) :

• Definition.
• Arithmetic operations in Cartesian form.
• Argand Diagram.
• Modulus, argument and conjugate.
• Polar and Exponential forms.
• Roots of complex numbers.

Matrices (6 lectures)

• Definition
• Addition, subtraction and multiplication by a scalar
• Multiplication of two matrices
• Square matrices
• Solution of equations
• Inverse Matrices
• Determinants

Further Integration (3 lectures)

• Improper integrals
• Functions defined by integrals (error function etc)

Ordinary Differential Equations (5 lectures)

• First-order differential equations.
• General and particular solutions
• Direction fields and qualitative solutions
• Separable equations
• Linear equations and the integrating factor
• Homogeneous equations

Partial Differentiation (4 lectures)

• Definition of partial differentiation
• The chain rule for differentiation
• Total Derivatives

Using partial differentiation to estimate errors

### Assessment methods

Method Weight
Other 20%
Written exam 80%

Coursework 1 (week 4). Weighting within unit 10%

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

Examination in semester 2. Weighting within unit 80%

### Recommended reading

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

BOSTOCK, L., CHANDLER, S., & ROURKE, C. 1982. Further pure mathematics. Thornes, Cheltenham. (ISBN0859501035)

CROFT, T. & DAVISON, R, 2008. Mathematics for engineers: a modern interactive approach (3rd ed.) Pearson, Harlow.

### Study hours

Scheduled activity hours
Lectures 24
Tutorials 11
Independent study hours
Independent study 65

### Teaching staff

Staff member Role
Nikesh Solanki Unit coordinator

### Additional notes

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

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