The University of Southampton
Courses

# GSCI0010 Mathematics for Scientists

## Module Overview

This module is designed to provide students with the mathematics knowledge and skills required for a successful transition to degree-level study in disciplines related to the chemical and biological sciences. The material covered is at a level corresponding to pre-university qualifications such as AS Level in the UK.

### Aims and Objectives

#### Module Aims

• Stimulate interest in and to promote the study of mathematical processes that will enhance the student’s studies in the sciences. • Develop understanding of mathematical techniques and their application through use of basic number, algebra, trigonometry, matrices, logarithms and calculus. • Extend the range of mathematical skills available to students and enable them to gain confidence in the use of mathematical techniques. • Prepare learners for application of mathematical techniques appropriate to their selected area of study in higher education.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• recall, select and use knowledge of mathematical techniques appropriate to the study of the sciences;
• demonstrate knowledge and understanding of mathematical processes.
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• apply mathematical processes, skills and knowledge to some real scientific situations and to solve simple problems;
• interpret data and a variety of graphs and communicate information mathematically.
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• apply mathematical methods to solve simple problems.

### Syllabus

Topic 1 :Revision Revision of numerical & algebraic skills Note: Numerical fractions, algebraic fractions, cancelling & crossmultiplication, transposition of formulae, indices and surds. Topic 2: Equations and Polynomials • Set up and solve simple equations as well as linear simultaneous equations in two unknowns using substitution and elimination • Set up and solve quadratic equations using factorisation and formula. Note: Do not need to be able to use completing the square. Apply to examples as used in Chemistry Topic 3: Indices and Logarithms • Understand rational indices (positive, negative & zero) including indices expressed as fractions and use them to simplify algebraic expressions • Be able to express a number in the form x´10n • Understand the relationship between indices and logs with special reference to log10 and loge (ln) • Use the laws of logarithms to simplify expressions • Be able to change the base of logs • Be familiar with graphs of e x and e-x use logs to solve equations of the form ax = b and a 2x + ax + b = 0 Topic 4: Graphs • use coordinates to plot graphs of algebraic equations • find gradients and equations of straight lines • understand the relationship between gradients of parallel and perpendicular lines • plot graphs of pairs of equations Topic 5: Linear laws • use the equation of the straight line y = mx+ c in determining a linear law • determine non-linear laws reducible to linear form, such as y = ax 2 + b, y = Topic 6: Trigonometry • be aware of the 6 trigonometric functions, and use sin, cos and tan to solve problems in 2D and 3D • know forms of graphs for sin, cos and tan and understand the derivation of the positive and negative values • know the values of sin, cos and tan for common angles in the range 0o £x £ 360 o e.g. 0o, 30o, 45o,etc in surd form • be able to use the sine and cosine rules • know that area of triangle = ½ bh = ½ absinC • understand definition of a radian and be able to convert degrees«radians • use formulae s = rq and A = ½r 2q Topic 7: Statistics • promote understanding of statistical terms, the ways of gathering and displaying data as well as an awareness of bias • use analytical techniques to explain, justify and predict from data Topic 8: Matrices • add subtract and multiply matrices • identify null and identity matrices • evaluate determinant of 2x2 matrices • understand and use AA-1 = A -1A = I • formulate and solve linear simultaneous equations for 2 unknowns as matrix equations and solve using the inverse matrix method Topic 9: Differentiation • understand the gradient of a curve at a point as the limit of the gradients of a sequence of chords • Notes: should understand how to find derivatives of simple functions from first principles • use the derivative of x n, lnx, ex, sinx, cosx, tanx and constant multiples, sums/differences of these • find gradient of a curve at a point • find equation of tangent/normal to a curve at a point • use the product and quotient rules • use the chain rule to differentiate functions of the form f(g(x)) • understand that a derivative gives a rate of change • find the second derivative of a function • locate stationary points and distinguish between maxima and minima (by any method) Note: should know that not all stationary points are maxima or minima but don't need to know conditions for points of inflexion Topic 10: Integration • understand integration as the reverse of differentiation; integrate xn (including n = -1) ex sinx cosx sin2x together with sums/differences and constant multiples of these • use integration to find a region bounded by a curve and two ordinates or by two curves • use the trapezium rule and Simpson's rule to obtain approximate values for definite integrals • apply integration to find volumes of revolution about the x-axis

### Learning and Teaching

#### Teaching and learning methods

Teaching methods include: • lectures, to include worked examples and question/answer sessions; • ativities guided through work packs; • discussion and workshops. Learning activities include: • Lectures and group taught sessions; • individual work on examples, supported by tutor input, discussion and workshop sessions; • work pack activities and additional worksheets; • open book sessments to support learning in this module; . • private study and use of recommended text books; • resources hosted on the Virtual Learning Environment. Study Time allocation: • Contact Hours: 96 • Private Study hours: 54 • Total study time: 150 hours

TypeHours
Revision14
Preparation for scheduled sessions10
Supervised time in studio/workshop24
Lecture72
Follow-up work20
Total study time150

Any GCSE text book offering Higher level work will be beneficial for some of the more basic aspects of the course. Selected chapters from any AS level standard text book will provide useful practise and revision.

Mathematics Wed sites - recommended resources listed on the VLE.

Anthony Croft and Robert Davison (5th). Foundation Maths.

### Assessment

#### Summative

MethodPercentage contribution
Examination  (120 minutes) 60%
Mid-Sessional Test  (120 minutes) 40%

#### Referral

MethodPercentage contribution
Examination  (120 minutes) 60%
Mid-Sessional Test  (120 minutes) 40%

#### 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:

##### Approved Calculators

All students will be required to have a university approved calculator

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.

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