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 ASlevel in the UK.

### Aims and Objectives

#### 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 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, scussion 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: 120 • Private Study hours: 180 • Total study time: 180 hours

TypeHours
Supervised time in studio/workshop48
Follow-up work90
Preparation for scheduled sessions36
Revision18
Lecture72
Total study time300

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

### Assessment

#### Summative

MethodPercentage contribution
Assignment 40%
Assignment 60%

#### Referral

MethodPercentage contribution
Assignment 40%
Assignment 60%

#### Repeat Information

Repeat type: Internal & External