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VBA Assessment 1 – Results

Last year I didn’t have these until Week 8.

Written Assessment 1 – Results

Last year I didn’t have these until Week 9.

Week 7

We looked at finite differences.

In VBA we have VBA Assessment 1.

Week 8

We will do a (written) Shooting Method example and start looking at partial differential equations by looking at Laplace’s Equation.

In VBA we have MCQ VI and will do the Boundary Value Problems lab.

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VBA Assessment 1

VBA Assessment 1 is taking place this week, Week 6.

Tuesday 14:20-16:00 will run 14:20-16:10

Friday 09:05-10:45 will run 09:05-10:55

More information in the Week 4 weekly summary.

In the Week 5 VBA we worked on Lab 3. Those of us who did not finish the lab are advised to finish it outside class time, and are free to email me on their work if they are unsure if they are correct or not.

Written Assessment 1

Written Assessment 1 takes place Tuesday 12 March at 09:00 in the usual lecture venue.

Here is a copy of last year’s assessment. This should give you an idea of the length and format but not what questions are coming up – and replaces Section 1.6.1 of the manual.

However there are far more things I could examine.

Roughly, everything up to but not including Runge Kutta Methods (p.64). Some examples of questions I could ask include:

ODEs in Engineering

p.13, Examples 1-4; p.15, Q.1-4

General Theory

Example, p. 15; p.34 Example

Maclaurin/Taylor Series

Examples 1 & 2 on p. 24; Q. 1 on p.27

Euler Method

p.29, Examples 1-4; p. 38, Q.1-5, 8-9

Three Term Taylor Method

p. 35, Examples 1-2; p.39, Q.7, 10-14

Heun’s Method

p.38, Q. 6; p. 42, Examples 1-2l p. 47, Q.4-5

Second Order Differential Equations

p.50, Example. p.51, Example. p.55, Q. 1-3, 5-14

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VBA Assessment 1

VBA Assessment 1 will take place in Week 6, (5 & 8 March) in your usual lab time.

Tuesday 10:05-11:45 will run 10:05 to 11:55

Tuesday 14:20-16:00 will run 14:20-16:10

Friday 09:05-10:45 will run 09:05-10:55

More information in last week’s weekly summary.

In the Week 5 VBA we worked on Lab 3. Those of us who did not finish the lab are advised to finish it outside class time, and are free to email me on their work if they are unsure if they are correct or not.

Written Assessment 1

Written Assessment 1 takes place Tuesday 12 March at 09:00 in the usual lecture venue.

Here is a copy of last year’s assessment. This should give you an idea of the length and format but not what questions are coming up – and replaces Section 1.6.1 of the manual.

However there are far more things I could examine.

Roughly, everything up to but not including Runge Kutta Methods (p.64). Some examples of questions I could ask include:

ODEs in Engineering

p.13, Examples 1-4; p.15, Q.1-4

General Theory

Example, p. 15; p.34 Example

Maclaurin/Taylor Series

Examples 1 & 2 on p. 24; Q. 1 on p.27

Euler Method

p.29, Examples 1-4; p. 38, Q.1-5, 8-9

Three Term Taylor Method

p. 35, Examples 1-2; p.39, Q.7, 10-14

Heun’s Method

p.38, Q. 6; p. 42, Examples 1-2l p. 47, Q.4-5

Second Order Differential Equations

p.50, Example. p.51, Example. p.55, Q. 1-3, 5-14

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VBA Assessment 1

VBA Assessment 1 will take place in Week 6 (5 & 8 March) in your usual lab time. You will not be allowed any resources – but the library of code (p.148) and these formulae will appear on the assessment:

relevant

The following is the proposed layout of the assessment:

Q. 1: Numerical Solution of Initial Value Problem [80%]

Examples of initial value problems that might be arise include:

  • Damping

\displaystyle \frac{dv}{dt}=-\frac{\lambda}{m}v(t);           v(0)=u

  • The motion of a free-falling body subject to quadratic drag:

\displaystyle \frac{dv}{dt}=g-\frac{c}{m}v(t)^2;           v(0)=u

  • Newton Cooling

\displaystyle \frac{d\theta}{dt}=-k\cdot (\theta(t)-\theta_R);           \theta(0)=\theta_0

  • The charge on a capacitor

\displaystyle \frac{dq}{dt}=\frac{E}{R}-\frac{1}{RC}q(t);           q(0)=0

Students have a choice of how to answer this problem:

  • The full, 80 Marks are going for a VBA Heun’s Method implementation (like Lab 3).
  • An Euler Method implementation (like Lab 2), gets a maximum of 60 Marks.

You will be asked to write a program that takes as input all the problem parameters, perhaps some initial conditions, a step-size, and a final time, and implements Heun’s Method (or possibly Euler’s Method): similar to Exercise 1 on p. 122 (except possibly implementing Heun’s Method) and also Exercise 1 on p.128 (except without the “conditional” derivative).

If you can write programs for each of the four initial value problems above you will be in absolutely great shape for this assessment.

Q. 2: Using your Program [20%]

You will then be asked to use your program to answer a number of questions about your model. For example, assuming Heun’s Method is used, consider the initial value problem (3.7) on p. 119.

  1. Given, v_0=0.2, m=3, \lambda=1.5, h=0.01, approximate v(0.3).
  2. Given, v_0=0.4, m=30, \lambda=1.5, h=0.1, investigate the behaviour of v(t) for large t.
  3. Given v_0=0.2, m=0.1, \lambda=1.5, h=0.5, T=10, run the Heun program. Comment on the behaviour of v(t). Run the same program except with h=0.05. Comment on the behaviour of v(t).
  4. Given, v_0=0, m=3, \lambda=1.5, h=0.1, T=2, run the Heun program. Comment on the behaviour of v(t).

Week 4

We finished off a Three Term Taylor Method example and spoke again about Heun’s Method.

We also introduced second order differential equations and saw how to attack them numerically. In particular we looked at a real pendulum.

In VBA we worked on Lab 3. Those of us who did not finish the lab are advised to finish it outside class time, and are free to email me on their work if they are unsure if they are correct or not.

Week 5

In the morning class we will finish looking at second order differential equations.

In the afternoon we will begin a quick study of Runge-Kutta Methods.

In VBA we have MCQ III and look at Lab 4, on Second Order Differential Equations.

Local vs Global Error

LocalvGlobal

Assessment

The following is a proposed assessment schedule:

  1. Week 6, 20% First VBA Assessment, Based (roughly) on Weeks 1-4
  2. Week 7, 20 % In-Class Written Test, Based (roughly) on Weeks 1-5
  3. Week 11, 20% Second VBA Assessment, Based (roughly) on Weeks 6-9
  4. Week 12, 40% Written Assessment(s), Based on Weeks 1-11

Study

Study should consist of

  • doing exercises from the notes
  • completing VBA exercises

Student Resources

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

Ungraded Concept MCQ League Table

To add a bit of interest to the Ungraded Concept MCQs, I will keep a league table.

Unless you are excelling, you are identified by the last five digits of your student number. AW is the number of attendance warnings received.

league2

Please ask questions in the lab about questions you have gotten wrong.

 

Week 3

We backtracked a little and found the Maclaurin Series

\displaystyle \ln(\sec x)\approx \frac{1}{2}x^2+\frac{1}{12}x^4.

We then did some further study on the Euler Method. The global error with the Euler Method is \mathcal{O}(h) and we need to reduce this by coming up with a better method or adjusting the Euler Method.

We looked at the Three Term Taylor Method as a better method. To employ the Three Term Taylor Method we need implicit differentiation, which means more pen-and-paper work.

We could avoid implicit differentiation by looking at Huen’s Method, which is an adjustment of Euler’s Method in that it uses lines.

In VBA we finished off the Euler Method Lab 2 and looked at P. 122, Exercise 1. The first group also started P. 123, Exercise 2, but the later groups instead used the time for some theory revision.

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I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Week 2

We developed the Euler Method for approximating the solution of differential equations. As we will need Taylor Series to analyse the error in this approximation — and improve Euler’s Method — we started looking at that. We kind of rushed it, but we used it to analyse the Euler Method.

In VBA we started programming the Euler Method to solve the problem of a damper. We did MCQ 1.

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I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Week 1

In Week 1, by briefly looking at a number of examples (many of which we have seen before), we had a review of some central ideas from approximation theory such as approximation, measurement error, accuracy & precision, iteration, convergence, meshing, error, etc.

We started looking at where ordinary differential equations come into Engineering.

In VBA we had a quick review lab, focussing on plotting data, command buttons, message boxes, input boxes, If-statements and do-loops.

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Week 10

We looked at finite differences for the Heat Equation. This completes the examinable written material.

In VBA we implemented same.

Week 11 — 2nd 20% VBA Assessment

In the 09:00 class we will have a revision session, geared towards the 20% VBA Assessment 2. This will look at the 20% VBA Assessment 2 Tutorial Sheet It might therefore be a good idea to go through this before next week.

In the 12:00 class we will have a revision session, geared towards the 40% Written Assessment 2. This will look at the 40% Written Assessment 2 Tutorial Sheet It might therefore be a good idea to go through this before next week.

Formulae will be provided in the VBA 2 Assessment.

To understand how your student numbers generate constants (see below) see this VBA Test 2 from last year (do not read this as a sample – it included e.g. the Heat Equation which you will not be examined on (in VBA) and the Laplace’s Equation might be slightly simpler than what ye will have).

See last week’s Weekly Summary for the Format of the VBA Assessment 2.

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Week 9

We finished talking about Laplace’s Equation and started talking about the Heat Equation.

In VBA we looked at finite difference methods for Laplace’s Equation. This completes the examinable VBA material. The Heat Equation that we cover in Week 10 will not be examinable. 

Week 10

We will look at finite differences for the Heat Equation. This completes the examinable written material.

In VBA we will implement same.

Read the rest of this entry »

VBA Assessment 1 – Results

Have been emailed.

Written Assessment 1 – Results

I would hope to have these with ye early next week.

Week 8

We continued our look at Finite Differences for differential equations, including Laplace’s Equation.

In VBA we looked at the shooting method (and Goal Seek) and finite differences for boundary value problems.

Week 9

We will continue our look at Laplace’s Equation.

In VBA we will look at Laplace’s Equation.

Assessment

The following is the proposed assessment schedule:

  1. Week 6, 20% First VBA Assessment, More Info Below
  2. Week 7, 20 % In-Class Written Test, More Info in Week 5
  3. Week 11, 20% Second VBA Assessment, More Info in Week 9
  4. Week 12, 40% Written Assessment(s), More Info in Week 10

Study

Study should consist of

  • doing exercises from the notes
  • completing VBA exercises

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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