## 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 View Timetable

Year running 2018/19

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

The content will cover such areas as:

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:
Working example problems - 40 hours
Preparing coursework - 32 hours
Revision for examination - 37 hours
Total 147 hours.

### Opportunities for Formative Feedback

Weekly resources and quizzes (formative); reflection with exam wrapper activities; problem sets and coursework; mid-term quiz.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Written Work 10 x2 hour weekly problem sets 20.00 In-course Assessment 1 assessment of 40 minutes 5.00 Total percentage (Assessment Coursework) 25.00

Resits are not available for individual coursework elements in the module. Attendance is required for coursework elements which are linked to an assessment available only at that specific time, such as fieldwork, lab reports on specific labs, and midterms.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 35.00 Standard exam (closed essays, MCQs etc) 2 hr 30 mins 40.00 Total percentage (Assessment Exams) 75.00

Resits for the exam component of the module will be assessed by the same methodology as the first attempt during the July Resit period in most cases or during the next available opportunity.