Mathematical Methods (M1M1)
Click on the topics below to view or print PDF files of the course material.
If you can't do this from any of the Maths department machines please tell me.
This page will be updated each time new material is handed out.
RECENT ADDITIONS INCLUDE
January Test plus solutions. Treasure Hunt Roll of honour. EVERYTHING to do with this course. Let me know of any
omissions.
Syllabus:
The course supplies a firm grounding to A-level topics such as differentiation, integration, complex numbers and series expansions.
- Functions: Polynomial, rational, exponential, logarithmic, trigonometric and hyperbolic functions. Odd, even and inverse functions.
- Limits: basic properties and evaluation. Continuity & discontinuous functions.
- Differentiation: First principles, differentiability; logarithmic and implicit differentiation; higher derivatives; Leibniz's formula; stationary
points and points of inflexion; curve sketching; parametric representation, polar co-ordinates.
- Power Series Expansions: The Mean Value Theorem. Taylor's Theorem with remainder. Infinite power series, radius of convergence. Ratio test;
Taylor and Maclaurin Series. De l'Hopital's rule.
- Integration: definition as Riemann limit; indefinite & definite integrals; the fundamental theorem of calculus; integration by substitution and
by parts; partial fractions; Existence of improper and infinite integrals. Integrals over areas and volumes.
- Complex Numbers: definition; the complex plane; standard and polar representation; de Moivre's Theorem; exp(z) and log(z)
- First order differential equations. Separable, homogeneous and linear equations. Special cases.
Linear higher order equations with constant coefficients,
Scanned lectures:
Lecture recordings should be available on the Panopto site,
here in folder
JMestelAY14-15. Let me know if you have problems.
Office Hour
Monday 10:30 →11.00
Tuesday 12 → 12:30
Friday 10.00 (JMC only)
The M1M1 Treasure Hunt!
For the last two years, a series of clues were given throughout the
term, which should enable you to locate the M1M1 treasure (and
maybe also enjoy the little stories).
The 2014 Treasure Hunt starts HERE.
The 2012 hunt can be found HERE.
The 2013 Hunt can be found HERE.
Progress tests:
The subject material of the tests varies slightly from year to year
according to when exactly in the course it took place.
Examination papers:
- 2002/03 exam
- 2003/04 exam
- 2004/05 exam
- 2005/06 exam
- 2006/07 exam
- 2007/08 exam
- 2008/09 exam,
- 2009/10 exam, and here
are the solutions.
- 2010/11 exam with solutions. On the
whole, question 1 was very badly done - I am staggered by how many
people think you can ignore modulus signs when integrating.
- 2011/12 exam with solutions.
The mark scheme is just a draft, and may be adjusted by
the markers, but it gives some indication of the expected difficulty of
each part.
The overall performance was a bit disappointing, many
failing on A-level material. Very few people correctly drew the curves
in Q1.
Many people having identified that L(d) was just a derivative, decided
to
try to evaluate it from first principles, usually unsuccessfully.
Of course it's easy to make mistakes under exam conditions.
- 2012/2013 exam with solutions.
I marked question 1, which was on the whole done very well. With
hindsight, I may have awarded too many marks for part (d), but I decided
to stick with the scheme as indicated. Please note that the mark scheme
for Questions 2-4 may be adjusted slightly by the markers at their
discretion.
- 2013/2014 exam with solutions.
- 2014/2015 exam with solutions.
Hot off the press. The mark scheme is not final, but gives some idea of
what is expected.