Mathematics 0C2 (MATH19832)
Spring 2020, University of Manchester
Welcome
Welcome to the
Mathematics 0c2 course in the University of
Manchester! The aim of the course is to provide an elementary secondsemester
course in calculus and algebra to students entering the university
with no postGCSE mathematics in the Foundation Year. Syllabus can
be found from the university website:
MATH19832
(This course follows directly on from Mathematics 0C1.)
We will continue where Mathematics 0C1 ended, in particular, we will
give further techniques in differentiation and integration, which
can be useful in applications. Moreover, we will introduce notions
like sequences and series, which appear commonly in mathematics
and nature. We will also define the notion of a complex number,
which extend our notion of real numbers and have some beautiful
geometric properties and appears commonly in problems in physics.
Succeeding in the Course Unit
What do I need to do to succeed in this course unit? There are 13 Intended Learning Outcomes (ILOs) for this course, which are listed as follows. On completion of this unit successful students will be able to:
 Define complex numbers and sketch them using the Argand Diagram
 Perform arithmetic operations on complex numbers and compute their moduli, arguments and conjugates
 Express complex numbers in their polar and exponential forms and perform computations using these expressions
 Define arithmetic, geometric and binomial sequences, evaluate their sums and compute convergent series
 Define binomial coefficients, write binomial formula and apply it in integration exercises
 Write Taylor and Maclaurin Series and apply them to compute limits
 Apply implicit, logarithmic and parametric differentiation in differentiation exercises
 Write integration by parts and integration by substitution formulae and apply them in integration exercises
 Compute examples of improper integrals
 Express improper rational functions as proper rational functions
 Find partial fraction coefficients for proper rational functions
 Apply the algorithms of simplifying improper rational functions
to compute their integrals
It is helpful to follow them as the assessment (class tests and final
exam) will be based on them and you can come back to this list to
check what is expected and if there is something to be improved.
Good luck with the course!
Assessment
 Written exam; Weighting within unit 80%. Date/time:
TBA. You can use the Mathematical
formula tables, which are provided by the examinations office, you
can view them from here (pdf).
See past exam papers:
Note that last year we introduced complex numbers to the syllabus
and some further integration topics. Thus some previous years (until 2018) exams do
not exactly reflect the content of the course.
 Class test 1; Weighting within unit 10%.
Date/time: Tuesday 18th February, 2020, at 11 am. Held in the
lecture room Renold E7. See the rules of the test.
 Class test 2; Weighting within unit 10%
Date/time: Tuesday 21nd April, 2020, at 11 am. Held in the
lecture room Renold E7. See the rules of the test
Workbook

Workbook (pdf), which we will
use in the course. This includes exercises and examples, which
we will fill during the classes. I highly recommend printing a
copy of this workbook and keeping it with you during the lectures.
Lectures
The lectures will take place on Tuesdays at 11:00 in Renold building room
E7 and Fridays at 12:00 in the Sackville Street building room
F41. In the lectures we will go through the workbook in
visualiser and sometimes on blackboard, filling some of the
exercises and examples. I highly recommend to attend the
lectures as they provide excellent support for the studies.
In case you miss a lecture, there are still
lecture
podcasts available, which can be accessed from
here
(requires sign in). However, sometimes the podcast does not
record properly or a blackboard is used so it may not be able to
see all the content gone through lectures from the podcasts.
Tutorials
There are two possible tutorial sessions for this course: either
Tuesday 1011 am in George Begg C002, or Friday 1112 am in George Begg C002.
In these sessions we go through some of the exercises carefully linked below, with emphasis on
how to come up with the solution in the actual exam situation.
Moreover, the sessions provide an excellent opportunity to ask questions about the course and we can go
through together some harder parts of the course.
I recommend to attempt the exercises yourself before looking at the solutions!
Content gone through during the lectures
 Week 1: Quadratic equation, definition of complex numbers,
arithmetic operations, complex plane
 Week 2: Arguments of complex numbers, polar and exponential form
 Week 3: Examples of using exponential form
 Week 4: Class test (Tuesday lecture) and arithmetic progressions
 Week 5: More on arithmetic progressions and geometric progressions
 Week 6: Binomial theorem and revision of differentiation,
implicit differentiation
 Week 7: Logarithmic and parametric differentiation, Taylor series
 Week 8: Integration by substitution and parts, improper integrals
 Week 9: Continuing integration examples
 Easter break
 Week 10: Class test (Tuesday lecture) and starting rational functions
 Week 11: Continuing reducing partial
fractions, integrating partial fractions
 Week 12: Revision
Remember to fill up the
unit survey for the course. Good
luck with the exam!