Mathematics 0D2

MATH19872 Mathematics 0D2 10 Semester 2 Undergraduate Level 1 Yanghong Huang 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 aims to provide a basic course in various mathematical topics to students in Foundation Year. On completion of the course the successful student will be able to: - Calculate interpolating functions and values using linear and quadratic interpolation formulae and their inverses - Select and apply numerical differentiation formulae to approximate derivatives, and discuss the accuracy of these approximations. - Approximate integrals using the trapezium rule and Simpson's rule, and discuss the accuracy of these approximations. - For each of circles centred on the origin, circles passing through the origin, straight lines, Archimedes and logarithmic spirals, ellipses, cardioids:  --Given a curve represented by a written description, a polar-coordinate formula or a sketch, recall or derive the other two representations of the curve.  --Recall how each of the parameters of the polar form of each curve relate to the characteristics of the plotted shape.  --Scale and rotate the shape by multiplying the radius value and adding a constant to theta, respectively.  --Convert between polar and Cartesian representations (points, lines, circles and ellipses only). - Calculate the intersection points of polar curves, and use given intersection points to infer properties of the curves - Recall the definitions of a root and the residual function. - Apply the bisection method, the rule of false position and the Newton-Raphson method to solve scalar equations. For each method, explain the situations under which a root will be found and identify suitable initial values / intervals. -Evaluate geometric integrals: the area inside a polar curve or between two polar curves; the volume of revolution of a curve (or between two curves) given in Cartesian form rotated about the x-axis; the volume of revolution of a curve rotated about the y-axis; the surface area of revolution of a curve given in Cartesian form about the x-axis; the arc-length of a curve given in either polar or Cartesian coordinates. - Evaluate recurrence relations given a recurrence and initial term(s), and in simple cases evaluate later terms by identifying patterns in the sequence. - Derive and apply reduction formulae to evaluate definite and indefinite integrals. - Use the Mathematica language to achieve the above outcomes, including use of variables, functions and polar and Cartesian plots. 2: Numerical Interpolation: Linear Interpolation, Quadratic Interpolation.1: Numerical Differentiation2: Numerical Integration: The Trapezoidal Rule, Simpson's Rule.3: Polar Coordinates: Polar coordinates of points. Polar coordinates of lines and curves. Points of intersection of polar curves3: Numerical Solution of Equations: Bisection Method, Rule of False Position, Newton-Raphson method3: Areas, lengths and volumes: Area inside a polar Curve, Volume of Solid of Revolution, Arc Length, Surface Area of Solid of Revolution3: Recurrence Relations and Reduction Formulae: Recurrance relations, Reduction formulae [f(x)]^n with limits, reduction formulae x^n * f(x) with limits, reduction formulae without limits.5: Mathematica: General introduction, application to topics in syllabus. 0 Other 20% 1 Written exam 80% Coursework (Computerised Assignment) (week 7) Weighting within unit 10%Mathematica Test (week 10 unless the project is submitted in week 10, in which case, the 0D2 coursework would be submitted in week 11.) Weighting within unit 10%Examination (semester 2) 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 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 Maths With an Int FY Foundation Mandatory N CROFT, A & DAVISON, R. 2010. Foundation Maths (5th ed.) Pearson Education, Harlow. (ISBN9780273730767)BOSTOCK, L., & CHANDLER, S. 1981. Mathematics - the core course for A-level. Thornes, Cheltenham. (ISBN0859503062)BOSTOCK, L., & CHANDLER, S. 1994. Core Maths for A-level (2nd ed.). Thornes, Cheltenham. (ISBN9780748717798)STROUD, K.A, 2007. Engineering mathematics (6th ed.) Palgrave Macmillan, Baisingstoke. (ISBN9781403942463 / ISBN1403942463)JAMES, G. 2001. Modern engineering mathematics (3rd ed.). Prentice Hall, Harlow. (ISBN0130183199 / ISBN9780130183194)COOMBES, K. 1998. The Mathematica primer. Cambridge University Press, Cambridge. (ISBN0521631300 / ISBN0521637155  / ISBN9780521631303 / ISBN9780521637152) Lectures 24 Tutorials 12 0 64 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