Mathematics for AVT Dr Ian Drumm

1
Mathematics for AVTDr Ian Drumm
Week 2

• Aims
• Basic algebraic manipulation
• Formulae simplification and transposition
• Learning Outcomes
• Simplification, factorisation, algebraic
  fractions
• Algebraic Fractions
• Transpose formulae
• Acoustics examples

2
Simplification

• Collecting like terms
• Finding common denominators
• Using Brackets

Exercises
3
Removing brackets

• Multiplying out
• Take care with signs (- x - )
• And how expression is written

4
Removing brackets

• Laws of indices apply

Exercises
5
Removing Brackets

• Expressions of the form (ab)(cd)
• Note

6
Factorisation

• Putting terms into brackets
• Identify common factors
• Can always multiply out to check

7
Factorising

• Quadratic Expressions
• Example

-5mn, possible factors of 5 are -1 x 5, 1 x
-5 4mn, can get 4 from factors -154 hence
-1 and 5 are the values for m and n we want
8
Factorising

• Example..
• Multiply by first coefficient (i.e. 2)
• Hence can write in the form

where
Exercises
9
Algebraic fractions

• Factorise numerator and denominator
• Cancel common factors

Exercises
10
Multiplication and division of algebraic fractions

• Multiply numerators and multiply denominators
• Can invert denominator and hence multiply

11
Addition and subtraction of algebraic fractions

• Find lowest common denominator
• Hence add or subtract numerators

Exercises
12
Formulae and transposition

• Variables represent physical quantities

Ftotal force in N (Newtons), mmass in kg,
aacceleration in ms-1
e.g. if m1.2kg and a5.0ms-1 the
F(1.2)(5.0)6.0N
Youll see in later modules the above is an
equation of motion and can have more
sophisticated representations e.g. for mass,
spring, damper system..
13
Rearranging formulae

• To get equation for given variable can
• Add to both sides
• Subtract from both sides
• Multiply both sides
• Divide both sides
• Apply some function to both sides

e.g. to find from we square both sides
and subtract from both sides
14
Know you prefixes and SI Units
15
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16
Figures and accuracy

• With physical parameters limits to measured and
  predicted accuracy
• If input parameters to n figures of accuracy then
  result should be to n figures of accuracy.

5.37m is accurate to 0.01m
Given a voltage of 4.6V and a current of 7.2mA
what is the resistance in the wire?
Note result given to 2 figures of accuracy also
since .888 is gt.5 we round up
17
Tolerances

• Precision of estimate