Mathematics 0B1

MATH19801 Mathematics 0B1 10 Semester 1 Undergraduate Level 1 Colin Steele Unit coordinator Department of Mathematics 1 FHEQ level (Framework for Higher Education Qualifications) ' First part HE study/Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 The course unit unit aims to provide a basic course in calculus and algebra to students in Foundation studies with AS-level mathematics or equivalent. On completion of this unit successful students will be able to:1 - Express a (proper or improper) rational function in terms of simpler (partial) fractions. Isolate parts of a non-rational expressionwhich can be turned into partial fractions form.2 - Find information (e.g. centres, crossing-points) from the equations of straight lines and circles. On the basis of information relevant to straight-lines and circles, find the equations of straight-lines and circles.3 - Combine, as a single trigonometric ratio multiplied by a constant, two or more expressions of the form a \cos x or b \sin x.4 - Convert the coordinates of a point from plane-polar to cartesian (rectangular) coordinates or from cartesian to plane-polar coordinates.5 - Carry out simple differentiation and (indefinite and definite) integration using tables of derivative and integrals.6 - Use differentiation to locate and to classify (maximum, minimum or point of inflection) stationary points and to find the maximum or minimum value that a given function takes on a given interval.7 - Carry out differentiation of functions using the product, quotient and chain (function of a function) rules. Carry out differentiation using implicit, logarithmic and parametric differentiation.8 - Sketch simple curves seen previously. Sketch curves on the basis of their relation with curves sketched previously or on the basis of specific values of the function. Sketch a curve using locations of axis-crossings, stationary points and asymptotes. Sketch curves for different values of a parameter.9 - Use definite integration to find the areas between curves or between curves and the axes.10 - Evaluate integrals using integration by parts, integration by substitution or by re-arrangement e.g. integration using partial fractions.11 - Write down terms in a series based on the formula for a general term. Find possible general forms for a series based on a small number of terms. Find information (specific terms, sums of terms)on the basis of other information for arithmetic and geometric series. Expand a function of the form $(a + x)^n$ as a binomial series for negative or non-integer values of n. Determine whether a (simple) series will converge or diverge.12 - Write down the series expansion of a function around a given point as a Maclaurin or Taylor series.13 - Determine physical behaviour of a system by means of an derivative, integral or other quantity. Rational Functions and Partial Fractions (3 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> <li> Limitations of partial fractions (combination with non-rational functions etc)</li> </ul> Geometry and Trigonometry (3 lectures) <ul> <li> Straight Lines and Conic Sections</li> <li> Combining Trigonometric Ratios ( a cos x + b sin x = r cos (x - \alpha) etc)</li> <li> Polar Coordinates of points</li> </ul> Differentiation (4 lectures) <ul> <li> Reminder of simple differentiation</li> <li> Stationary Points</li> <li> Product, quotient and chain rules</li> <li> Implicit, logarithmic and parametric differentiation</li> </ul> Curve Sketching (4 lectures) <ul> <li> Some simple curves e.g. trig, exponentials,</li> <li> Functions of the form f(ax+b)</li> <li> Curve sketching by using function values</li> <li> Curve sketching using axis-crossings, stationary points and asymptotes</li> <li> Curves and a parameter.</li> </ul> Integration (4 lectures) <ul> <li> Reminder of simple indefinite and definite integration</li> <li> Integration and areas under / between curves</li> <li> Integration by parts</li> <li> Integration by substitution</li> <li> Integration by partial fractions</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> <li> Maclaurin and Taylor Series</li> </ul> 0 Other 30% 1 Written exam 70% Quizzes during tutorials in weeks 5, 7, 9, 11. Weighting within unit 20%Diagnostic Followup: (week 3). Weighting within unit 10%Examination. Weighting within unit 70% 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 Physics with Int FY Foundation Mandatory 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 BSc(Hons) Science w a Int FY Maths With an Int FY Foundation Mandatory N CPreparation for Calculus (International Edition): Functions and How They Change    Bruce Crauder,Benny Evans,Alan Noell,(MIE) PREP CALCULUS    W. H. Freeman    2022    ISBN: 978 Mathematical Formula Tables     ——2004     —Calculus : early transcendentals    Sullivan, Michael,    Macmillan International Higher Education    2019    ISBN: 9781319248482 Advanced engineering mathematics.    Stroud, K. A.,    Red Globe Press    2020    ISBN: 9781352010268 Engineering Mathematics    Stroud, K. A.    Bloomsbury Publishing Plc    2020    ISBN: 9781352010282 Foundation maths    Croft, Tony, 1957- author.    Pearson    2016    ISBN: 9781292095172 Foundation maths    Croft, Tony,    Pearson Education Limited    2016    ISBN: 1292095199 Engineering mathematics [electronic resource]    Stroud, K. A.,    Palgrave Macmillan    2013    ISBN: 1137031220 Foundation mathematics    Stroud, K. A.    Palgrave Macmillan    2009    ISBN: 9780230579071 Mathematics 1e WileyPLUS Student Pack    Colin Steele,Douglas Quinney,Jeremy Levesley,Gareth Woods    Web site: www.wiley.com    2021    URL: Web site: www.wiley.com… Lectures 24 Tutorials 11 0 65 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