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Unit code: | MATH19832 |
Credit Rating: | 10 |
Unit level: | Level 1 |
Teaching period(s): | Semester 2 |
Offered by | School of Mathematics |
Available as a free choice unit?: | N |
Requisites
NoneAims
To provide an elementary second-semester course in calculus and algebra to students entering the university with no post-GCSE mathematics in the Foundation Year.
Learning outcomes
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
Assessment methods
- Other - 20%
- Written exam - 80%
Assessment Further Information
Coursework 1 (week 4); Weighting within unit 10%
Coursework 2 (week 10); Weighting within unit 10%
2 hour end of semester 2 examination; Weighting within unit 80%
Syllabus
Complex Numbers (5 lectures) :
- Definition.
- Arithmetic operations in Cartesian form.
- Argand Diagram.
- Modulus, argument and conjugate.
- Polar and Exponential forms.
Sequences and Series (4 lectures)
- The notation of series
- Arithmetic and Geometric Series
- The role of convergence
- Binomial Series
Further Differentiation (4 lectures)
- Taylor and Maclaurin Series
- Implicit Differentiation
- Logarithmic Differentiation
- Parametric Differentiation
Further Integration (4-5 lectures)
- Reminder of basic integration
- Integration by parts
- Integration by substitution
- Improper integrals
Rational Functions and Partial Fractions (4-5 lectures)
- Simple Rational Functions (including distinction of proper / improper)
- Forms for Partial Fractions
- Techniques for finding partial fraction coefficients
Integration using partial fractions
Recommended reading
BOOTH, D. 1998. Foundation Mathematics (3rd ed.). Addison-Wesley, Harlow. (ISBN0201342944)
CROFT, A & DAVISON, R. 2010. Foundation Maths (5th ed.) Pearson Education, Harlow. (ISBN9780273730767)
STROUD, K., & BOOTH, D.J, 2009. Foundation mathematics. Palgrave Macmillan, Basingstoke. (ISBN9780230579071 / ISBN0230579078)
Study hours
- Lectures - 24 hours
- Tutorials - 11 hours
- Independent study hours - 65 hours
Teaching staff
Tuomas Sahlsten - Unit coordinator