## Mathematics 1E2

 Unit code: MATH19682 Credit Rating: 10 Unit level: Level 1 Teaching period(s): Semester 2 Offered by School of Mathematics Available as a free choice unit?: N

None

#### Aims

The course unit aims to provide a second semester course in calculus and algebra to students in school of Electrical and Electronic Engineering and the school of Chemistry.

#### 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

#### Assessment methods

• Other - 20%
• Written exam - 80%

#### Assessment Further Information

Coursework 1 (week 4) Weighting within unit 5%. Computerised exercise followed by class for relevant individuals.
Coursework 2 (week 6-7) Weighting within unit 5%. Computerised exercise followed by class for relevant individuals.
Coursework 3 (week 9) Weighting within unit 5%. Computerised exercise followed by class for relevant individuals.
Coursework 4 (week 11-12) Weighting within unit 5%. Computerised exercise followed by class for relevant individuals.
2 hour (semester 2) examination Weighting within unit 80%

#### Syllabus

4 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 follows on from the 3 lectures from 1E1).

2 lectures : Series : Simple Series : convergence of geometric series : Maclaurin and Taylor Series

8 lectures : Multivariate Calculus : Functions of two or more variables. Partial Differentiation. Gradient. Chain Rule. Multiple integration and line integration. Taylor Series in two variables. Maxima and minima in two dimensions.

8 lectures: Ordinary Differential Equations : Concept, order and role of conditions. 1st order linear equations with constant coefficients (Emphasizing a complementary function / particular integral approach but making mention of integrating factors. Natural and Forced response (including the case of resonance). 2nd order linear equations with constant coefficients, characteristic polynomials. Mathematical and physical interpretation of solutions (time-constant etc).

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 - 0 hours

#### Teaching staff

Raphael Assier - Unit coordinator