2017/18 Undergraduate Module Catalogue
LLLC0113 Mathematics and Statistics for Earth and Environment
30 creditsClass Size: 20
Module manager: Ellen Avery
Email: e.r.avery@leeds.ac.uk
Taught: Semesters 1 & 2 (Sep to Jun) View Timetable
Year running 2017/18
This module is not approved as a discovery module
Objectives
-To present the mathematical methods within algebra, trigonometry and vectors which are the foundation of mathematics for scientists.-To present the mathematical methods of differential and integral calculus and to provide an introduction to differential equations and to vectors
-Starting from basic rules, definitions and axioms, to enable students to build a working toolbox of mathematical techniques, concepts and facts for solving problems in pre-calculus mathematics.
-To enable students to use mathematical techniques for differentiating and integrating functions, for solving differential equations and for working with vector quantities.
-To enable students to understand and use statistical methods and to present the ways of gathering and displaying data as well as an awareness of bias and to use analytical techniques to explain, justify and predict from data sets
-To link examples of mathematical methods and applications relevant to the Earth and Environmental Sciences when appropriate.
Learning outcomes
Students will be able to demonstrate knowledge and understanding of:
-The mathematical methods within algebra, trigonometry and vectors which are the foundation of mathematics for scientists
-The mathematical methods of differential and integral calculus and of some simple solution methods for various types of differential equation.
-Vector operations
-Statistical operations
Skills outcomes
-Select and apply appropriate mathematical methods to solve abstract and real-world problems.
-Show confidence in manipulating mathematical expressions, setting up and solving equations and constructing simple proofs.
Syllabus
Revision of basic arithmetic, algebra, equations and Pythagoras theorem. Manipulation of Surds; Co-ordinate geometry of the straight line; gradients, lengths and perpendicularity; Solution of equations by graphs; Probability laws - addition and multiplication; Collecting and recording data, measures of spread and central tendency; Differentiation of algebraic functions; Trigonometry, Sin, Cos, Tan and their graphs.
Maxima and minima values using differentiation; Sin x, cos x, tan x, e×, log x; Differentiation of products, quotients and functions of a function; Integration of standard functions; Definite and indefinite integrals; Integration by parts and by substitution; Area under a curve and between curves, volumes of revolution; Use of functional notation; Formulation and solution of differential equations by separating the variables.
Vectors in 3 dimensions; vector equation of a line; differentiation and integration of vectors and links to applications in science and engineering.
Complex Numbers: Argand diagram, Cartesian and polar forms, complex conjugate modulus.
Simple statistical analysis; Mean, Mode, Median, Standard Deviation and links to errors in data sets.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| Workshop | 40 | 1.00 | 40.00 |
| Lecture | 40 | 2.00 | 80.00 |
| Independent online learning hours | 33.00 | ||
| Private study hours | 147.00 | ||
| Total Contact hours | 120.00 | ||
| Total hours (100hr per 10 credits) | 300.00 | ||
Private study
Private Study:Reading - 38 hours
Working example problems - 40 hours
Preparing coursework - 32 hours
Revision for examination - 37 hours
Total 147 hours.
Opportunities for Formative Feedback
Weekly quizzes (formative); coursework (20%); 2 mid-term quizzes (10%)Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| Written Work | 12x2 hour weekly problem sets | 20.00 |
| In-course Assessment | 2 assessments of 40 minutes each | 10.00 |
| Total percentage (Assessment Coursework) | 30.00 | |
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) | 2 hr 00 mins | 30.00 |
| Standard exam (closed essays, MCQs etc) | 2 hr 30 mins | 40.00 |
| Total percentage (Assessment Exams) | 70.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 11/06/2015
Browse Other Catalogues
- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue
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