An introduction to the DE module
Can you solve these?
1.
dT
= −k (T − 20 )
dt
2.
( t + 5)
3.
104
4.
d 2Q
dQ
+ 100
+ 10000Q = 1000sin100t
2
dt
dt
5.
df
= 0.02r ,
dt
6.
dθ
= g ( 2 cos θ − 1)
dt
dv
+ 5v = 9.8 ( t + 5 )
dt
d 2x
dx
+ 2 × 105
+ 106 x = 0
2
dt
dt
dr
= r −8 f
dt
And can you suggest situations they might model?
(All these examples are taken from the DE textbook by John Berry, Ted Graham, Roger
Porkess and Peter Mitchell.)
The modelling cycle
An introduction to the
Differential Equations module
Andrew Rogers
King Edward VI Camp Hill Boys’ School
Assumptions about audience
• May be offering Further Maths for the first
time
• May be reconsidering choices of FM units
• May have little experience of this part of
maths, or be rusty
• Have a basic understanding of Mechanics
• Enjoy doing mathematics!
Format of session
•
•
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•
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Solve some differential equations
Discuss the specification
Look at some exam papers
Briefly look at the coursework
Discuss the skills candidates should
develop
Specification
• Assumed knowledge
Specification
• Objectives
• Assessment
Specification
• Modelling with differential equations
• It is an A2 applied unit
• It can contribute to Further Maths
qualifications only, and cannot contribute to
(single) Mathematics
1
Specification
Specification
• First order differential equations
Specification
• Second and higher order DEs
Specification
• Simultaneous DEs
• Numerical methods
Specification
Exam W08 Question 1
• Most of these things can be found in
other Board’s specifications somewhere,
but this unit brings it all together
2
Exam W08 Question 2
Exam W08 Question 3
Exam W08 Question 4
Coursework
• Aim: candidates should learn how differential
equations can be used to solve real-world
problems, and follow the modelling cycle
• Two slightly different assessment sheets
• Free choice of tasks but new centres are
encouraged to use one of those published by
MEI
• We use “Cascades” because we can throw
water about
Cascades!
Cascades!
3
Cascades!
Cascades!
Why is this REALLY useful?
Thank you for listening
• Candidates will learn to solve DEs which arise
in biology, physics, chemistry, electronics,
engineering, economics…
• Candidates will meet and use the modelling
cycle in some depth
• Through the coursework, candidates meet
experimental design in some depth
• Candidates will refine their curve sketching
skills
• Candidates will meet some further numerical
processes
• amrogers1@gmail.com for further
information or comments
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