MATH1400: Modelling with Differential Equations

Schedule for academic year 2011-12

• Lectures: Thursdays 12-1 (Chemistry West Block LT F) and Fridays 11-12 (RSLT 20).
• Tutorials: Fridays 12-1, 1-2 and 2-3.

Handouts:

• Outline
• Chapter 1: Introduction
• Chapter 2: Solution of first-order ODEs
• Chapter 3: Applications of first-order ODEs
• Chapter 4: Second-order linear ODEs
• Chapter 5: Applications of second-order ODEs
• All five chapters in one file
• Homework 1 (due 13th February). Solutions.
• Homework 2 (due 27th February). Solutions.
• Homework 3 (due 12th March). Solutions.
• Homework 4 (due 23rd April). Solutions.
• Homework 5 (due 8th May: 7th May is a Bank Holiday). Solutions.
• Quiz 1: 17th February
• Quiz 2: 2nd March
• Quiz 3: 16th March
• Quiz 4: 27th April
• Mock exam from 2008, (covered in the last two videos) and solutions (Note: Question 5 is not on the syllabus this year. There is an error in the solution to question 1b: it should be v'/v^2 = -1/x, leading to -1/v=-log|x|-C, and so y=x/(log|x| + C).)

Assessment:

• Please prepare your solutions for the examples sheets in advance of the tutorials. Section 1 of each sheet will be covered over the two tutorials immediately before the hand-in date.
• Please hand in your solutions to section 2 of each example sheet in the grey boxes to the left of taught student office on Level 8 in the School of Mathematics.
• Make sure you have written your name and your tutor's name on your homework, and put your work in your tutor's box.
• There are five examples sheets, worth 10% in total. Each example sheet will be graded out out 5.
• The deadline for handing in your homeworks is 5pm on the day indicated. You will lose one mark (out of five) for each day that the homework is late. If you miss the deadline for a valid reason, please make this known to me and to your tutor. Please see the School of Mathematics policy on missed and late coursework for more information.
• Homework (and solutions) will normally be returned to you at the tutorial that week or the next week. They may also be returned in the blue boxes to the right of the taught student office.
• There will be a 20 minute quiz in the second half of the tutorials on the dates listed above. The topic of each quiz will be announced in lectures beforehand.
• There will be four quizzes, worth 10% in total. Each quiz will be graded out out 10.
• If you miss a quiz for a valid reason, please make this known to me and to your tutor. There will be no quiz resits.
• There will be a two-hour exam worth 80% in total.

Videos of the lectures from 2008-09:

There are also smaller versions on LUTube:

Lecture	Link	Pages	Topic
7	Video	20-22	Chapter 2: Example of a Bernoulli equation; Chapter 3: Radioactivity.
8	Video	22-26	Chapter 3: Radioactivity; Malthusian population model.
9	Video	26-27	Chapter 3: Logistic population model; Newton's law of cooling.
10	Video	28-30	Chapter 3: Mechanics; Mixing; Chapter 4: Introduction to second-order linear ODEs.
11	Video	30-32	Chapter 4: Superposition principle; Reduction of order.
12	Video	32-35	Chapter 4: Reduction of order; linear constant coefficient ODEs.
13	Video	35-37	Chapter 4: Review of first-order linear constant coefficient ODEs.
14	Video	38-41	Chapter 4: Examples of first- and second-order linear constant coefficient ODEs; the homogeneous problem.
15	Video	41-44	Chapter 4: The homogeneous problem.
16	Video	45-48	Chapter 4: The inhomogeneous problem (presented by Oliver Harlen).
17	Video	48-52	Chapter 4: More examples of the inhomogeneous problem.
18	Video	52-55	Chapter 4: More examples of the inhomogeneous problem.
19	Video	57-61	Chapter 5: Functions of two variables; Partial derivatives and differentials. (Not on syllabus this year.)
20	Video	61-64	Chapter 5: Second derivatives; stationary points: maxima, minima and saddles. (Not on syllabus this year.)
21	Video	---	Mock exam 1.
22	Video	---	Mock exam 2.

Useful resources:

• Module Description.
• Most School of Maths/Library/University of Leeds resources are on the VLE.
• The Leeds Skills Centre has a Maths drop-in service open every day during term. They can be found at 15 Blenheim Terrace.
• Online help is available from the Skills Centre, including Maths Solutions, featuring experienced teachers demonstrating solutions to a series of maths problems that are known to challenge students.
• The Mathcentre offers general online help with basic mathematics skills (some can be downloaded onto your iPod or mobile phone!).
• MIT's OpenCourseWare offers a Differential Equations course on 18.03 Differential Equations. This includes videos of the lectures, interactive simulations, lecture notes, assignments and solutions, and exams and solutions.