## Mathematics 0C2

 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

None

#### Aims

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

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