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Second Order Differential Equation
02 March 2014 19:55
Form :
Method :
Substitute into the equation
Auxiliary Equation
Cases :
I. +
II. +
III.…read more

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Substitute:
into the initial equation
Equate coefficients
f(x) = exponential function of the form
NB if h(x) is part of the auxiliary equation substituting it will give zero, instead use
Substitute:
into the initial equation
Equate coefficients
f(x) = trigonometric function of the form
Substitute:
into the initial equation
Equate coefficients
Differential Equations Page 3…read more

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Substitution
17 March 2014 22:23
Example: This equation can't be solved
straight away because it contains
x and y coefficients
1
The substitution is made with e as it
does not change with differentiation
2
3
Sub 2 &3 into 1
Differential Equations Page 4…read more

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Differential Equations Page 5…read more

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Modulus Argument Form
17 March 2014 23:02
Im
Where
z can be written in the form
Re z=r
Where
and is dependant on which quadrant z lies in
Complex Numbers Page 1…read more

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De Moivre's Theorem
17 March 2014 23:07
Theorem:
Euler's Relation
Proof for De Moivre's Theorem by Mathematical Induction
Cases
I.
=
=
II.…read more

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March 2014 12:27
Complex Numbers Page 3…read more

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Trigonometric Identities
18 March 2014 12:32
Expression for and in terms of cosine and since of multiples of
Method:
Group terms and use
Group terms and use
Expansion of cos(n) and as powers of an
Complex Numbers Page 4…read more

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Expansion of cos(n) and as powers of an
Use:
for
for
Complex Numbers Page 5…read more

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