## Quiz 4 Results

Below find the results. You are identified by the last four digits of your student number unless you are excelling. The marks are out of 2.5 percentage points. Your best eight quizzes go to the 20% mark for quizzes. The R % column is your running percentage (for best eight quizzes). The QPP is your Quiz Percentage Points. MPP is your Maple percentage points. GPP is your gross percentage points. One student didn’t write down their name for Quiz 4. They should email me.

 S/N Q1 Q2 Q3 Q4 R% QPP MPP GPP O’Sullivan, K. 2.17 2.5 2.5 2.5 96.7 9.67 3 12.7 Murphy 2.37 2.5 2.07 2.5 94.4 9.44 3 12.4 Connolly 2.17 2.5 2.5 1.8 89.7 8.97 3 12 1480 2.5 2.5 2.07 1.5 85.7 8.57 3 11.6 2073 0.99 2.5 2.5 2.5 84.9 8.49 3 11.5 5484 2.43 2.5 2.5 1 84.3 8.43 3 11.4 2327 2.5 1.72 1.2 2.5 79.2 7.92 3 10.9 2942 1.71 1.7 1.74 1.8 69.5 6.95 3 9.95 8332 2.37 1.22 2.5 0.6 66.9 6.69 3 9.69 7879 1.12 2.5 0 2.2 58.2 5.82 3 8.82 2128 2.24 0.4 2.28 0 49.2 4.92 3 7.92 2070 0.33 0.2 2.07 2.3 49 4.9 3 7.9 3703 1.71 1.2 1.85 0 47.6 4.76 3 7.76 8426 2.24 2.5 0 0 47.4 4.74 1.5 6.24 1298 0.46 1.9 1.74 0.6 47 4.7 1.5 6.2 1486 2.24 2.4 0 0 46.4 4.64 1.5 6.14 3481 1.71 0.3 1.04 1.5 45.5 4.55 3 7.55 2257 0.53 0.6 1.74 1.2 40.7 4.07 3 7.07 3872 0.26 0 2.5 1.2 39.6 3.96 3 6.96 1321 1.45 0.4 0.76 1.02 36.3 3.63 3 6.63 8425 0 0.4 1.63 1 30.3 3.03 3 6.03 2237 1.71 0 0.98 0 26.9 2.69 3 5.69 9896 1.97 0 0 0 19.7 1.97 0 1.97 8354 0.39 0 0.22 0.2 8.1 0.81 3 3.81 9555 0.53 0 0 0 5.3 0.53 0 0.53 7209 0.39 0 0 0 3.9 0.39 0 0.39 2092 0 0 0 0.2 2 0.2 1.5 1.7 4402 0 0 0 0 0 0 0 0

## Quiz 5 Question Bank

As there is no Maple Lab, the quiz will take place from 19:00-19:15 sharp.

Question bank for Quiz 5 (in Week 6) is p. 69, Q. 1-9.

It is unreasonable to do all of these. When you think you understand how to do the questions doing more is only practise which has diminishing returns.

The bonus questions will be based on the (abstract) partial differentiation in last week’s Quiz Bank, p. 50, Q.1-5.

If you have any specific difficulties with these questions, please email me. Alternatively use Maple or Wolfram Alpha to help. Your Quiz 5 Questions will be taken from these.

I thought there was more worked solutions. Here is a worked solution for Q. 5:

Winter 2013 (i) Verify that the equation

$latex 2x^3-10x-11=0$

has a root in the interval (2, 3).

(ii) Use the Newton-Raphson method to approximate this root correct to three decimal places
where $x_0 = 2.5$.

Solution: (i) Let $f(x)=2x^3-10x-11$. Note that

$f(2)=2(2)^3-10(2)-11=16-20-11<0$ and

$f(3)=2(3)^3-10(3)-11=54-30-11>0$

so there is a root in $(2,3)$.

(ii) Using

$\displaystyle x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$,

we calculate (with \$latex f'(x)=6x^2-10)

$\displaystyle x_1=2.5+\frac{2(2.5)^3-10(2.5)-11}{6(2.5)^2-10}\approx 2.673$

$\displaystyle x_2=2.673+\frac{2(2.673)^3-10(2.673)-11}{6(2.673)^2-10}\approx 2.659$,

where I used more digits than four when inputting $x_1$ into the formula for $x_2$. Further iterations yield:

$x_3\approx 2.659$,

and so, correct to three decimal places, the root is $r\approx 2.659$.

Note: I will only ask for two iterations of the Newton-Raphson method (although more is preferable ‘in the wild’).

## Week 5

We started Chapter 2 by looking Root Approximation

## Week 6

We will finish Chapter 2 by looking at Numerical Integration. We might try and make a start on Chapter 3, Laplace Transforms.

## Plan

• Week 3: Maple Lab 1 & Section 1.4
• Week 4: Section 1.4 & Section 1.5
• Week 5: Maple Lab 2 & Section 2.1
• Week 6: Section 2.2 & Sections 3.1-3.3
• Week 7: Maple Lab 3 & Sections 3.1-3.3
• Week 8: Maple Lab 4 & Section 3.4
• Week 9: Section 3.4
• Week 10: Maple Lab 5 & Section 3.4
• ————-EASTER————–
• Week 11: Maple Test & Section 3.4
• Week 12: Section 3.5
• ————-END OF LECTURES———-
• Week 13: Review Class — Summer 2015 Paper

## Maple Catch Up

If you want to do Maple catch up (if you miss a lab) you have two options:

• download the Maple file from your email, do the exercises in Maple (either in a new worksheet or on top of the original file with the exercises), save the worksheet and email me the worksheet you were working on.
• come in for a double Maple session on a ‘Maple’ night.

## Academic Learning Centre

I would urge anyone having any problems with the material to use the Academic Learning Centre. You will get best results if you come to the helpers there with specific questions.

## Study

Please feel free to ask me questions about the exercises via email or even better on this webpage. Anyone can give me exercises they have done and I will correct them. I also advise that you visit the Academic Learning Centre.

## Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..