Quiz 5 Results

Below find the results.  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.

S/N Q1 Q2 Q3 Q4 Q5 R% QPP MPP GPP
O’Sullivan, K. 2.17 2.5 2.5 2.5 2.5 97.4 12.2 3 15.2
Murphy 2.37 2.5 2.07 2.5 2.5 95.5 11.9 3 14.9
Connolly 2.17 2.5 2.5 1.8 2.1 88.6 11.1 3 14.1
Fahey 2.5 2.5 2.07 1.5 2.5 88.6 11.1 3 14.1
2073 0.99 2.5 2.5 2.5 2.5 87.9 11 3 14
5484 2.43 2.5 2.5 1 1.9 82.6 10.3 3 13.3
2327 2.5 1.72 1.2 2.5 1.9 78.6 9.82 3 12.8
2128 2.24 0.4 2.28 2.5 2.3 77.8 9.72 3 12.7
2942 1.71 1.7 1.74 1.8 1.8 70 8.75 3 11.8
8332 2.37 1.22 2.5 0.6 1.9 68.7 8.59 3 11.6
3703 1.71 1.2 1.85 1.4 2.3 67.7 8.46 3 11.5
2070 0.33 0.2 2.07 2.3 2.5 59.2 7.4 3 10.4
7879 1.12 2.5 0 2.2 1.5 58.6 7.32 3 10.3
1486 2.24 2.4 0 0 2.5 57.1 7.14 1.5 8.64
3481 1.71 0.3 1.04 1.5 2.4 55.6 6.95 3 9.95
8426 2.24 2.5 0 0 1.2 47.5 5.94 1.5 7.44
2257 0.53 0.6 1.74 1.2 1.6 45.4 5.67 3 8.67
1298 0.46 1.9 1.74 0.6 0.8 44 5.5 1.5 7
1321 1.45 0.4 0.76 1.02 1.2 38.6 4.83 3 7.83
8425 0 0.4 1.63 1 1.8 38.6 4.83 3 7.83
3872 0.26 0 2.5 1.2 0 31.7 3.96 3 6.96
2237 1.71 0 0.98 0 1.2 31.1 3.89 3 6.89
8354 0.39 0 0.22 0.2 1.7 20.1 2.51 3 5.51
9896 1.97 0 0 0 0 15.8 1.97 0 1.97
7209 0.39 0 0 0 0 3.12 0.39 0 0.39
2092 0 0 0 0.2 0 1.6 0.2 1.5 1.7
4402 0 0 0 0 0 0 0 0 0

Maple Lab

The Maple Lab takes place in C128.

The following is the proposed schedule for Weeks 8, 9, 11, 12 (but this is subject to change):

Group 1 – Starts at 18:00 and Finishes at 20:50:

Wednesdays 18:00-19:05 – Maple Lab in room C128

Wednesdays 19:15-19:30 – Weekly Quiz in C212

Wednesdays 19:30-20.50 – Theory class in room C128

Group 2 – Starts at 19:15 and Finishes at 22:00:

Wednesdays 19:15-19:30 – Weekly Quiz in C128

Wednesdays 19:30-20:50 – Theory class in room C212

Wednesdays 20.55-22:00 – Maple Lab in room C128

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

Quiz 6 Question Bank

Question bank for Quiz 6 (in Week 8) is as follows:

  • P. 80-81, Q. 1-6 [Q. 5 you won’t be asked to calculate the integral]

You will be asked to approximate two integrals:

  1. Using Midpoint or Trapezoidal Rule [will be one or the other]
  2. Using Simpson’s Rule

I expect this quiz to be tight for time.

If you have any specific difficulties with these questions, please email me. Alternatively use Maple or Wolfram Alpha to help. Your Quiz 4 Questions will be taken from these.

Quiz 6 runs from 19:15 to 19:30 sharp on Wednesday 22 March.

Week 7

We finished Chapter 2 by looking at Numerical Integration. We made a start on Chapter 3, Laplace Transforms.

Week 8

We will finish Chapter 2 by looking at Numerical Integration. We will continue working on Laplace Transforms.

Example

We never finished the following in class:

The normalised sinc function is a function used in signal processing defined by

\displaystyle \text{sinc}(x)=\frac{\sin \pi x}{\pi x}

for x\neq 0 and \text{sinc}(0) = 0.

i. Show that the equation

\displaystyle\text{sinc}(x)=\frac12

can be written as

2\sin(\pi x)-\pi x=0.

ii. Show that f(x)=2\sin(\pi x)-\pi x has a root in [0.5, 1].

iii. Hence use the Newton Raphson-Method twice with seed x_0 = 0.5 to
approximate this root correct to three significant figures.

iv. Check your answer by showing that

\displaystyle\text{sinc}(r)\approx \frac12.

where r = x_2 is your answer to part iii.

Solution: We did parts i. – ii. in class. For part iii. we will use the formula:

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

We have

f'(x)=2\cos(\pi x)\cdot \pi-\pi;

Therefore

\displaystyle x_1=0.5-\frac{2\sin(\pi(0.5))-\pi(0.5)}{2\pi \cos(\pi(0.5))-\pi}

=0.6366197724

\displaystyle \Rightarrow x_2=x_1-\frac{2\sin(\pi(x_1))-\pi(x_1)}{2\pi\cos(\pi(x_1))-\pi}\approx 0.605

For part iv. we calculate

\displaystyle \text{sinc}(0.605)=\frac{\sin(\pi(0.605))}{\pi(0.605)}=0.4978\approx \frac12.

Plan: Catch-up

Things are changed slightly due to the missed class in Week 6. At the moment we are three hours behind. I will figure this out in the next week or so.

  • 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 [Class Missed]
  • Week 7: Section 2.2 & Section 3.1
  • Week 8: Maple Lab 3 & Sections 3.2-3.3
  • Week 9: Maple Lab 4 & Section 3.4
  • Week 10: Section 3.4
  • ————-EASTER————–
  • Week 11: Maple Lab 5 & Section 3.4 
  • Week 12: Maple Test & Section 3.4 [Missing 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..

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