Mathematics 0C2 (MATH19832)
Spring 2018, University of Manchester
Aim
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 Dr
Sean Prendiville's course, 0C1.)
Intended learning outcomes
 Knowledge and understanding: Be familiar with partial fractions, series and functions, differentiation and integration.
 Intellectual skills: Be able to carry out routine operations involving the topics in the syllabus.
 Transferable skills and personal qualities: Have a set of tools and
methods that can be applied in the courses given in the host
department or in subsequent years.
Syllabus
 Integration (4 lectures)
Derivatives and antiderivatives; indefinite integrals and integration using tables/inspection; definite integrals and the area under graph; integration by substitution.
 Trigonometry (4 lectures)
Trigonometric functions; addition formulas and further identities; inverse trigonometric functions; using trigonometric identities for integration.
 Sequences and series (3 lectures)
Arithmetic progressions; geometric progressions; polynomials and the binomial theorem.
 Further calculus (6 lectures)
Differential and derivative; Taylor series; implicit differentiation; integral and differential; integration by parts.
 Rational functions (5 lectures)
Proper and improper rational functions; polynomials and long division;
partial fractions decomposition; integration of rational
functions.
Assessment
 Written exam; Weighting within unit 80%. Date/time:
21.5.2018 at 9:45 am  11:45 am. 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:
Update: Here is the
Good luck with your studies!
 Class test 1; Weighting within unit 10%.
Date/time 19.2.2018 at 121pm: Held in the
lecture room Pariser C21. See the rules of the test.
Update: Class test 1 solutions.
 Class test 2; Weighting within unit 10%
Date/time 23.4.2018 at 121pm: Held in the
lecture room Pariser C21. See the rules of the test
Update: Class test 2 solutions.
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.
Tutorials
Tutorials are held every Friday 1112 at the Sackville Street
Building, room D39.
Content gone through during the lectures

29.1.2018: Revision of differentiation, antiderivatives

2.2.2018: Indefinite integral, examples

5.2.2018: Definite integral, the area under graph

9.2.2018: Integration by substitution

12.2.2018: Trigonometric functions and identities

16.2.2018: Further trigonometric identities and using them in integration

19.2.2018: Class test 1

23.2.2018: Trigonometric functions in integrations, inverse functions

26.2.2018: Inverse trigonometric functions, solving trigonometric equations

2.3.2018: Sequences, arithmetic progressions, formula for the kth
element and the sum of first n terms

5.3.2018: Geometric progressions, the sum of first n terms and
geometric series

9.3.2018: Revision on arithmetic and geometric progressions,
Pascal's triangle and the binomial theorem

12.3.2018: Examples on using binomial theorem, review of further calculus

16.3.2018: Differentials, chain rule and product rule

19.3.2018: Implicit differentiation

23.3.2018: Integration by parts

26.3.2018  15.4.2018: Easter break

16.4.2018: Revision of integration by parts, Taylor series

20.4.2018: More examples on Taylor series, starting rational functions

23.4.2018: Class test 2

27.4.2018: Reducing improper rational functions to proper
rational functions using long division

30.4.2018: Spitting proper rational functions to partial fractions
using factorisation

4.5.2018: Using what we did earlier to compute integrals of
rational functions

7.5.2018: May bank holiday

11.5.2018: Revision
Remember to fill up the
unit survey for the course. Good
luck with the exam!