Mathematics 0C2

MATH19832 Mathematics 0C2 10 Semester 2 Undergraduate Level 1 Tuomas Sahlsten Unit coordinator 1 FHEQ level (Framework for Higher Education Qualifications) ' First part HE study/Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 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. 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 Complex Numbers (5 lectures) :<ul> <li> Definition.</li> <li> Arithmetic operations in Cartesian form.</li> <li> Argand Diagram.</li> <li> Modulus, argument and conjugate.</li> <li> Polar and Exponential forms.</li></ul>Sequences and Series (4 lectures)<ul> <li> The notation of series</li> <li> Arithmetic and Geometric Series</li> <li> The role of convergence</li> <li> Binomial Series</li></ul>Further Differentiation (4 lectures)<ul> <li> Taylor and Maclaurin Series</li> <li> Implicit Differentiation</li> <li> Logarithmic Differentiation</li> <li> Parametric Differentiation</li></ul>Further Integration (4-5 lectures)<ul> <li> Reminder of basic integration</li> <li> Integration by parts</li> <li> Integration by substitution</li> <li> Improper integrals</li></ul>Rational Functions and Partial Fractions (4-5 lectures)<ul> <li> Simple Rational Functions (including distinction of proper / improper)</li> <li> Forms for Partial Fractions</li> <li> Techniques for finding partial fraction coefficients</li></ul>Integration using partial fractions 0 Other 20% 1 Written exam 80% Coursework 1 (week 4); Weighting within unit 10%    Coursework 2 (week 10); Weighting within unit 10%    End of semester 2 examination; Weighting within unit 80% BEng(Hons) Eng w a Int FY BEng(Hons) Eng w a Int FY Foundation Recommended BEng(Hons) Eng w a Int FY Mech Eng with an Int FY Foundation Mandatory BEng(Hons) Eng w a Int FY Aero Eng with an Int FY Foundation Mandatory BEng(Hons) Eng w a Int FY Civ Eng with an Int FY Foundation Mandatory BEng(Hons) Eng w a Int FY EEM Eng with an Int FY Foundation Mandatory BEng(Hons) Eng w a Int FY Chem Eng with an Int FY Foundation Mandatory BEng(Hons) Eng w a Int FY Comp Sci with an Int FY Foundation Mandatory BSc(Hons) Science w a Int FY BSc(Hons) Science w a Int FY Foundation Recommended BSc(Hons) Science w a Int FY Chem with an Int FY Foundation Mandatory BSc(Hons) Science w a Int FY EarthPlanetSciwithintFY Foundation Mandatory BSc(Hons) Science w a Int FY EnvSci with an Int FY Foundation Mandatory BSc(Hons) Science w a Int FY Mat Sci with Int FY Foundation Mandatory N CROFT, A & DAVISON, R. 2010. Foundation Maths (5th ed.) Pearson Education, Harlow. (ISBN9780273730767) Lectures 22 Tutorials 11 0 67 This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates