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Applications of Mathematics

The resources below have come from a variety of sources; they have been gathered to provide examples of the use of GCE mathematics outside of theclassroom. The Mathematical Content section is followed by a section listing the Resources.

Asterisked items contain exercises; italic items are on-line.

MATHEMATICAL CONTENT



Content is divided into the following sections:

    Core

       Algebra and functions
       Coordinate geometry in the (x, y) plane
       Sequences and series
       Trigonometry
       Exponentials and logarithms
       Differentiation
       Integration
       Numerical Methods
       Vectors

    Non-Core

       Further Pure Mathematics
       Decision and DiscreteMathematics
       Mechanics
       Probability and Statistics

Algebra and functions

      Quadratic functions and their graphs
           Tractive Effort,Acceleration and Braking
       Discriminant of a quadratic function
           Tractive Effort,Acceleration and Braking
       Completing the square
           Tractive Effort,Acceleration and Braking
       Simultaneous Equations
            Mathematical Modelling in Economics
           Mathematics in the Electronic Systems Industry
       Simultaneous equations: analytical solution by substitution
       of one linear and one quadratic equation
            Ventilation Systems

Coordinate geometry in the (x, y)plane
       Equation of a straight line
            Telemetry

Sequences and series

      Benford's Law
      Computer Science
      Mathematical Modelling in Populations
      Mathematics in the Aviation Industry
      Arithmetic Series
           Mathematical Modelling in Traffic Flows
      Geometric Series
           Mathematical Modelling in Traffic Flows

Trigonometry

     Mathematical Modelling in Navigation
     Trigonometry - Applications with Sources
     Cosine Rule
         Sports Measurement

Exponentials and logarithms

     Exponentials
         Mathematical Modelling in Economics
      ex as a limit
         Mathematics inCommunications Engineering
         Mission Improbable
      Logarithms
          Benford's Law
       Exponential growth and decay
          Mathematical Modelling in Crop Growth
          Mathematical Modelling in Populations

Differentiation

      Random Transmitters
      Product rule
         Mathematics in Communications Engineering
      Chain rule
         Random Transmitters
         Tractive Effort, Acceleration and Braking
      Applications of differentiation to
      maxima and minima and stationary points
           Mathematics inCommunications Engineering
           Random Transmitters

Integration

    Integration of trigonometric functions
       Mathematical Modelling in Crop Growth
    Integration by substitution
       Tractive Effort, Acceleration and Braking
    Integration using partial fractions
       Mathematical Modelling in Populations
       Tractive Effort, Acceleration and Braking
    Analytic solution of first order differential equation
    with separable variables
       Mathematical Modelling In Populations
       Mathematics in the Aviation Industry
       Tractive Effort, Acceleration and Braking

Numerical Methods

    none

Vectors

    Mathematics in the Aviation Industry
    Mathematics in the Electronic Systems Industry
    National Air Traffic Services
    Scalar Product
       Mathematics in the Aviation Industry
       National Air Traffic Services

Further Pure Mathematics

    Integration involving trigonometry (beyond Core)
         Antenna
         Mathematical Modellingin Navigation
    Matrices
       Mathematics in the Electronic Systems Industry
       Mathematical Modellingin Tournaments

Decision and Discrete Mathematics

    Algorithms
       Computer Science
    Codes
       Computer Science
       Mathematics in Communications Engineering
    Difference Equations
       Mathematical Modelling in Populations
    Graphs
       Mathematical Modelling in Tournaments

Mechanics

    Forces
       Joint Moments and MuscleForces
       Mathematics in the Electronic Systems Industry
    Rigid Bodies
       Centre of Mass
           Joint Moments and MuscleForces
       Moments
           Joint Moments and MuscleForces
           Mathematics inthe Electronic Systems Industry
       Moments of Inertia
           Joint Moments and MuscleForces
    Kinematics
       Constant Acceleration
           Mathematics and RailwaySignalling

Probability and Statistics

    Probability
       Independent Events
           Mission Improbable
           National Air Traffic Services
           Random Transmitters
       Bayes Theorem
           Mathematical Modelling InHeredity
           Tennis
       Expectation
           Mathematical Modelling inGambling
    ContinuousDistributions
       Normal Distribution
           Benford's Law
           Mathematics inCommunications Engineering
           Mathematical Modellingin Insurance
           Mission Improbable
    Discrete Distributions
       Binomial Distribution
           Mathematics in Communications Engineering
           Mission Improbable
       Poisson Distribution
           Mathematical Modellingin Insurance
           Real-Life Examples inMedical Statistics
    Hypothesis Tests
       Chi-Squared Test of Association
           Real-Life Examples inMedical Statistics
    Bivariate Data
       Least-Squares Linear Regession
           Mathematics inthe Electronic Systems Industry


RESOURCES



Antenna*
2-page Word document.

Benford's Law*
(comprehension exercise) - 2-pageWord document.

Bibliography of printed (and some other) materials
1-page Word document.

Computer Science
12-page Word document.

JointMoments and Muscle Forces
2-page Worddocument.

Mathematical Modelling in Crop Growth*
(worksheet) - 5-page Word document.

Mathematical Modelling in Economics*
(worksheet)
- 7-page Word document.

Mathematical Modelling in Gambling *
(worksheet)- 8-page Word document.

Mathematical Modelling in Heredity*
(worksheet) - 8-page Word document.

Mathematical Modelling in Insurance*
(worksheet)
- 6-page Word document.

Mathematical Modelling in Navigation*
(worksheets) - 11-page Word document.

Mathematical Modelling in Populations*
(worksheets) - 19-page Word document.

Mathematical Modelling in Tournaments*
(worksheets) - 14-page Word document.

Mathematical Modelling in Traffic Flows*
(worksheet) - 7-page Word document.

Mathematics and Railway Signalling
4-page Word document.

Mathematics in Communications Engineering*
(developed from Mission Improbable)
3-page Word document.

Mathematics in the Aviation Industry*
3-page Word document
(a 4-page Word document giving a critique of this resource is available).

Mathematics in the Electronic Systems Industry*
3-page Word document.

Mission Improbable
(probability in communications engineering)
19-slide Word presentation

National Air Traffic Services
8-page Word document.

Plus (mathematical magazine)
http://www.plus.maths.org.uk

Random Transmitters
(developed from Mission Improbable)
2-page Word document
(a 2-page Word document giving a critique of this resource is available).

Real-Life Examples in Medical Statistics*
2-page Word document.

Sports Measurement
4-page Word document.

Telemetry
9-slide PowerPoint presentation
with 1-page Word background document.

Tennis
(an example of mathematics in the news) - http://news.independent.co.uk/world/science_medical/story.jsp?story=481351

Tractive Effort, Acceleration and Braking
(applications in the railway industry)
8-page Word document.

Trigonometry - Applications with Sources
(references to published material)
1-page Word document

Ventilation Systems
3-page Word document.

Primary Mathematics Challenge