The University of Southampton
Courses

# MATH1004 Introductory Mathematics for Chemists and Oceanographers

## Module Overview

This module is suitable for students with AS level Mathematics. Students with A level Mathematics with grade B or more are required to take MATH1008 instead. This module is designed for Chemistry and Earth Sciences students with AS-level mathematics only, and aims at providing them with a basic mathematical tool-kit which they can use in applications. The firs half of the module consists of revision of basic arithmetic and algebraic manipulations, line and quadratic functions and equations, trigonometry, and Pascal’s triangle and the binomial theorem. The second half includes exponentials and logarithms, and basic differentiation and integration of functions in one variable.

### Aims and Objectives

#### Learning Outcomes

##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Perform simple arithmetic and algebraic manipulations
• Sketch accurate graphs of linear and quadractic functions, and their intersections
• Use trigonometric relations to solve general triangles, and find solutions of simple trigonometric equations
• Use the properties of exponentials and logarithms in theoretical and practical problem solving contexts
• Differentiate functions on one variable
• Calculate simple definite and indefinite integrals of functions on one variable
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Apply the newly adquired mathematical toolkit in a problem solving context within your discipline

### Syllabus

1. Numbers and Units: types of numbers, arithmetic of fractions, display of numbers and standard form, units 2. Algebra: removing brackets, factorisation, algebraic fractions, formulae, indices, quadratic equations, systems of linear equations, partial fractions 3. Linear Functions: equation of a line, distances between points, intersections 4. Quadratic Equations: sketching, intersections with lines 5. Trigonometry: angles, sine/cosine/tangent, solving general triangles, unit circle, graphs of trigonometric functions, wave functions, trigonometric equations 6. Pascal’s Triangle and Binomial Theorem 7. Exponentials and Logarithms: properties, exponential and logarithmic functions, basic equations involving exponentials or logarithms 8. Derivatives: definition, important derivatives, rules for differentiation, higher derivatives, applications to graph sketching, tangent and normal line of a graph 9. Integration: definition, fundamental theorem of calculus, important integrals, properties, indefinite and definite integrals, integration by substitution, integration by partial fractions and by parts

### Learning and Teaching

#### Teaching and learning methods

Lectures (chalk and talk based on skeletal notes provided), group tutorials, private study.

TypeHours
Independent Study102
Teaching48
Total study time150

#### Resources & Reading list

A. Croft, and R. Davison (2010). Foundation Maths.

K.A. Stroud and Dexter J. Booth (2009). Foundation Mathematics.

Paul Monk and Lindsey J. Munro (2010). Maths for Chemistry.

Robert Lambourne and Michael Tinker (2000). Basic Mathematics for the Physical Sciences.

Pat Maier, Anna Barney, and Geraldine Price (2009). Study Skills for Science.

### Assessment

#### Summative

MethodPercentage contribution
Exam  (2 hours) 70%
In-class Test 20%
Problem Sheets 10%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.