## Mathematics 1E1 for EEE

 Unit code: MATH19681 Credit Rating: 10 Unit level: Level 1 Teaching period(s): Semester 1 Offered by School of Mathematics Available as a free choice unit?: N

None

#### Aims

The programme unit aims to provide a first semester course in calculus and algebra to students in school of Electrical and Electronic Engineering.

#### Learning outcomes

Intended learning outcomes:
Knowledge and understanding: Be familiar with the topics in the syllabus.
Intellectual skills: Be able to carry out routine operations involving the topics in the syllabus.
Transferable skills and personal qualities: Have a set of tools and methods that can be applied in the courses given in the host department or in subsequent years.
Learning and teaching processes:

Two lectures in weeks 1-12. One smallish-group tutorial in weeks 2-12.
Lectures : 24
Tutorials : 11
Hours of private study : 65
Week Lectures continue in week 6.

#### Assessment methods

• Other - 25%
• Written exam - 75%

#### Assessment Further Information

Diagnostic Follow-up Coursework (if needed) (week 4): weighting within unit 10%.
Coursework 2: weighting within unit 5%. Computerised exercise.
Coursework 3: weighting within unit 5%. Computerised exercise .
Coursework 4: weighting within unit 5%. Computerised exercise.
2 hour (semester 1) examination Weighting within unit 75%.

#### Syllabus

5 lectures : Vectors : Vectors in component form ; vector addition, subtraction and multiplication by a scalar ; parallelogram and triangle of vectors ; vector equation of a straight line ; Scalar products ; vector products.

4 lectures : Coordinate Systems : Alternate coordinate systems in 2 and 3 dimensions i.e. cartesian, plane polar, cylindrical, spherical. Transformations between systems highlighting the role of the correct quadrant / octant and concentrating on points and position vectors.

4 lectures : Complex Numbers and Hyperbolic Functions : Definition of complex numbers : algebraic operations ; modulus, argument and Argand diagram ; trigonometric and exponential forms. De moivre's Theorem Definition of hyperbolic functions. Elementary properties. Inverse functions ; Osborne's Rule.

6 lectures : Differentiation : Working definition (rate of change, physical interpretation). Differentiation rules (parametric, implicit, logarithmic etc) Derivatives of logarithmic and hyperbolic functions. Applications to maxima and minima. l'Hopital's rule (including working defn of limit). Newton Raphson Method (application of differentiation).

3 lectures : Integration : Working definition of the integral. Fundamental theorem of calculus Physical interpretation. Definite integrals and areas under curves. Revision of integration techniques (polynomials etc). Integration by parts, by substitution and by partial fractions. (partial fractions themselves part of followup). Applications of integration. (this topic also to form 4 lectures from 1E2).

KA Stroud, Engineering Mathematics, Palgrave
Croft et al., Introduction to Engineering Mathematics, Pearson

#### Study hours

• Assessment written exam - 2 hours
• Lectures - 24 hours
• Tutorials - 11 hours
• Independent study hours - 63 hours

#### Teaching staff

John Parkinson - Unit coordinator