## XJFY0300 Mathematics 1

### 15 creditsClass Size: 330

Module manager: Professor Rainer Hollerbach
Email: r.hollerbach@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2021/22

Module replaces

XJFY0360 Mathematics 1

This module is not approved as a discovery module

### Objectives

- To review particular mathematics topics and relate them to the Engineering disciplines.
- To further develop an understanding of Derivatives, Integrals, and Series as aspects of mathematics which are relevant to Engineering.
- To build confidence in presenting mathematics solutions in English.

Learning outcomes
- An understanding of aspects of mathematics which are most relevant to Engineering; in particular derivatives, integrals and series.
- Ability to understand mathematics problems presented in English.
- Ability to present mathematics solutions in English.

### Syllabus

Derivatives:
- A definition of derivative as rate of change of a function
- Standard derivatives of powers, trig, exp and log functions
- Product rule, quotient rule, chain rule, implicit differentiation
- Basic applications including maxima and minima, related rates, etc.

Integrals:
- Definition as area under a curve, definite and indefinite integrals
- Fundamental theorem of calculus, integrals as anti-derivatives
- Methods of integration, including substitution, by parts, partial fractions
- Basic applications, including surface areas and volumes of revolution

Series:
- Sequences, Series and Taylor Series.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 48 1.00 48.00 Independent online learning hours 32.00 Private study hours 70.00 Total Contact hours 48.00 Total hours (100hr per 10 credits) 150.00

### Private study

Independent Online Learning

Independent Online Learning activities will include reviewing lecture notes and other material on the VLE. Typically recommended 2 hrs reviewing online material per teaching week.

Private study

Private study tasks relate to the content of the course including background reading such as text books and worksheets, and also the preparation of any assessed pieces of work.

Please note: all delivery types and number of hours are subject to variation, depending on immediate delivery needs. An 'hour' refers to one session in the timetable which is approximately 45 minutes long.

Worked examples.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Problem Sheet Mid-Semester Test 25.00 Total percentage (Assessment Coursework) 25.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) (S2) 2 hr 00 mins 75.00 Total percentage (Assessment Exams) 75.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated