2023/24 Undergraduate Module Catalogue
XJFY0315 Mathematics
20 creditsClass Size: 999
Module manager: Rainer Hollerbach
Email: r.hollerbach@leeds.ac.uk
Taught: Semesters 1 & 2 (Sep to Jun) View Timetable
Year running 2023/24
Co-requisites
| XJFY0100 | English for Engineering |
| XJFY0215 | Physics |
| XJFY0400 | Scientific Problem Solving |
| XJFY0500 | Chemistry |
Module replaces
XJFY0300XJFY0310This module is not approved as a discovery module
Module summary
This module aims to bridge the gap between the students’ prior knowledge of Mathematics and what is needed for their subsequent studies. It seeks to ensure that they have the mathematical background to study in English modules which are identical with corresponding University of Leeds modules.Objectives
This module aims toReview particular mathematics topics and relate them to the Engineering disciplines, in particular:
- an understanding of Derivatives, Integrals, and Series as aspects of mathematics which are relevant to Engineering.
- an understanding of Vectors and Linear Algebra as aspects of mathematics which are relevant to Engineering.
Familiarise students with the language of Mathematics
Build confidence in dealing with lectures and learning materials live and online in English
Build confidence in presenting mathematics solutions in English.
Learning outcomes
On completion of this module, students will be expected to be able to:
LO1. Demonstrate an understanding of aspects of mathematics which are most relevant to Engineering in particular, including aspects of:
1. Derivatives
2. Integrals
3. Taylor series
4. Complex numbers and functions
5. Vectors, dot and cross products
6. Linear algebra
LO2. Deploy appropriate techniques and formulae to solve mathematical problems
LO3. Solve mathematical problems in English under timed conditions using appropriate platforms where required
LO4. Present mathematical solutions in English showing workings out and formulae used.
Skills outcomes
On completion of this module students are expected to be able to:
1. Use the language of mathematics appropriately
2. Use online digital platforms such as Minerva, Teams and Gradescope to facilitate their learning
3. Understand and communicate fundamental mathematical knowledge in English
Syllabus
Derivatives:
1. A definition of derivative as rate of change of a function.
2. Standard derivatives of powers, trig, exp and log functions.
3. Product rule, quotient rule, chain rule, implicit differentiation.
4. Basic applications including maxima and minima, etc.
Integrals:
1. Definition as area under a curve, definite and indefinite integrals.
2. Fundamental theorem of calculus, integrals as anti-derivatives.
3. Methods of integration, including substitution, by parts, partial fractions, trig substitutions.
4. Additional applications, including surface areas and volumes of revolution.
Series:
1. Sequences.
2. Finite and infinite series.
3. Taylor Series.
Complex Numbers and Functions:
1. Definition of i as the square root of -1.
2. Complex numbers as quantities of the form x + i*y.
3. Basic arithmetic of complex numbers.
4. Use of the Euler identity to extend all previous functions (exp, log, trig, roots, powers) to complex variables.
Vectors:
1. Definition in terms of quantities having magnitude and direction.
2. Basic manipulations including vector addition, scalar multiplication, etc.
3. Unit vectors i, j, k, decomposition into components.
4. Dot and cross products, and applications to geometry of lines and planes.
Linear Algebra:
1. Systematic solution of simultaneous equations.
2. Definitions of matrices and matrix multiplication.
3. Applications of matrices to coordinate transformations, rotations, reflections.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| Lecture | 64 | 1.00 | 64.00 |
| Independent online learning hours | 42.00 | ||
| Private study hours | 94.00 | ||
| Total Contact hours | 64.00 | ||
| Total hours (100hr per 10 credits) | 200.00 | ||
Private study
94Opportunities for Formative Feedback
Worked examplesPast exam papers
Collective feedback from mid-term exams and past papers will be given to the students before the final exam
Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| In-course Assessment | Formative coursework will be given throughout the module in the form of example sheets and solutions | 0.00 |
| Total percentage (Assessment Coursework) | 0.00 | |
Formative coursework will be given throughout the module in the form of example sheets and solutions
Exams
| Exam type | Exam duration | % of formal assessment |
| Standard exam (closed essays, MCQs etc) | 1 hr 00 mins | 20.00 |
| Standard exam (closed essays, MCQs etc) | 1 hr 00 mins | 20.00 |
| Standard exam (closed essays, MCQs etc) | 2 hr 00 mins | 60.00 |
| Total percentage (Assessment Exams) | 100.00 | |
The two one hour exams in semester 1 and Semester 2 will be mid-term exams, testing material covered during the period of teaching immediately before the exams. The two hour exam will be the final exam, testing materials covered throughout the syllabus.
Reading list
There is no reading list for this moduleLast updated: 14/07/2023
Browse Other Catalogues
- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue
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