Difference tables

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Frank Doheny

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Frank Doheny

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Ready to use

7 years, 11 months ago

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Frank Doheny 7 years, 11 months ago

Gave some feedback: Ready to use

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Frank Doheny 8 years ago

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Name	Status	Author	Last Modified
Difference tables	Ready to use	Frank Doheny	14/03/2018 21:18
Difference tables 2	Ready to use	Frank Doheny	14/03/2018 21:20

Question statement

The following set of data was generated by a polynomial.

$\begin{matrix} {x}&{f(x)} \\ \var{x0}&\var{y0}\\\var{x1}&\var{y1}\\\var{x2}&\var{y2}\\\var{x3}&\var{y3}\\\var{x4}&\var{y4}\\\var{x5}&\var{y5}\\\var{x6}&\var{y6}\\\var{x7}&\var{y7}\\\end{matrix}$

Give any introductory information the student needs.

			Name	Type	Generated Value

x0	integer	0
stp	number	0.1
x1	number	0.1
x2	number	0.2
x3	number	0.3
x4	number	0.4
x5	number	0.5
x6	number	0.6
x7	number	0.7
a	integer	3
b	integer	1
c	integer	3
d	integer	22
y0	number	22
y1	number	22.313
y2	number	22.664
y3	number	23.071
y4	number	23.552
y5	number	24.125
y6	number	24.808
y7	number	25.619
d10	number	0.313
d11	number	0.351
d12	number	0.407
d13	number	0.481
d14	number	0.573
d15	number	0.683
d16	number	0.811
d20	number	0.038
d21	number	0.056
d22	number	0.074
d23	number	0.092
d24	number	0.11
d25	number	0.128
d30	number	0.018
d31	number	0.018
d32	number	0.018

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

Statement
Advice

Parts

Gap-fill
1. Gap Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Use a difference table to show it was generated by a degree 3 polynomial and hence calculate the leading coefficient, $a$ .

$a=$ Unnamed gap

Advice

The difference table should take the form:

$\begin{matrix} {x}&{f(x)}&\delta_1&\delta_2&\delta_3 \\ \var{x0}&\var{y0}&\var{d10}&\var{d20}&\var{d30}\\\var{x1}&\var{y1}&\var{d11}&\var{d21}&\var{d31}\\\var{x2}&\var{y2}&\var{d12}&\var{d22}&\var{d32}\\\var{x3}&\var{y3}&\var{d13}&\var{d23}&\var{d32}\\\var{x4}&\var{y4}&\var{d14}&\var{d24}&\var{d32}\\\var{x5}&\var{y5}&\var{d15}&\var{d25}\\\var{x6}&\var{y6}&\var{d16}\\\var{x7}&\var{y7}\\\end{matrix}$

All the 3rd differences equal the constant $\var{d32}$

The coefficient of $x^3$ is given by the formula: $a=\frac{constant}{3!*(step-size)^3}$

$a=\frac{\var{d32}}{3!*(\var{stp})^3}=\var{a}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exam:

Numerical methods by Frank Doheny in Numerical methods.

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Taxonomy: mathcentre

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Checkpoint description

Frank Doheny 7 years ago

Frank Doheny 7 years, 11 months ago

Frank Doheny 8 years ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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Difference tables

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 7 years ago

Frank Doheny 7 years, 11 months ago

Frank Doheny 8 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`