# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2013/2014 -- ARCHIVE as at 1 September 2013 for reference onlyTHIS PAGE IS OUT OF DATE

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# Undergraduate Course: Mathematical Methods 2 (MATH08032)

 School School of Mathematics College College of Science and Engineering Course type Standard Availability Available to all students Credit level (Normal year taken) SCQF Level 8 (Year 1 Undergraduate) Credits 10 Home subject area Mathematics Other subject area Mathematics for Physical Science & Engineering Course website https://info.maths.ed.ac.uk/teaching.html Taught in Gaelic? No Course description *In 2011-12, this course is available only to students retaking it and will be assessed on an 'exam only' basis.* Hyperbolic functions, inverse trigonometric functions. Differentiation of inverse functions and its use in integration. Integration by parts. Separable differential equations. First order linear differential equations with constant coefficients. Direction fields, Euler's method, trapezium and Simpson's rule with extrapolation, Newton-Raphson method. Implicit, parametric and polar functions. Introduction to partial differentiation, directional derivative, differentiation following the motion, differentials and implicit functions. Limits and improper integrals, substitution.
 Pre-requisites Students MUST have passed: Mathematical Methods 1 (MATH08029) OR Practical Calculus (MATH08001) Co-requisites Prohibited Combinations Students MUST NOT also be taking Mathematics for Informatics 2a (MINF08002) OR Mathematics for Informatics 2b (MATH08047) Other requirements None Additional Costs None
 Pre-requisites None Displayed in Visiting Students Prospectus? No
 Not being delivered
 Further function types: understanding 1. the definition and properties of hyperbolic functions 2. the definition and properties of inverse trigonometric functions and using them to solve trigonometric problems 3. implicit functions and ability to graph them 4. parametric functions and ability to graph them 5. how to translate between cartesian and polar coordinates and draw simple polar curves Further Differentiation: ability 1. to understand inverse functions and to differentiate hose for sin and tan 2. to use hyperbolic functions, including simple calculus properties 3. to differentiate implicit functions 4. to calculate simple partial derivatives 5. to calculate directional derivatives 6. of perform differentiation following the motion 7. to construct and use differential expressions 8. to use Newton-Raphson's method 9. to understand the notation used in thermodynamics Further Integration: ability 1. to evaluate integrals in terms of inverse circular functions 2. to use integration by parts 3. to use substitutions of various types 4. to calculate arc-lengths and areas for parametric functions Differential equations: ability 1. to identify and solve separable differential equations 2. to solve linear homogeneous first-order differential equations with constant coefficients 3. to find particular solutions for linear differential equations with constant coefficients, for simple right-hand sides 4. to fit initial and boundary conditions Numerical calculus: ability 1. to use the composite trapezium rule 2. to use Simpson's rule 3. to apply Richardson's Extrapolation to trapezium and Simpson's rules 4. to draw direction fields and sketch solution curves 5. to use Euler's Method for differential equations Limits and Continuity: ability 1. to use L'Hopital's Rule 2. to use the limits of combinations of log, polynomial and exponential functions 3. to evaluate 'improper' integrals
 Coursework: 15% Degree Examination: 85%
 None
 Academic description Not entered Syllabus Not entered Transferable skills Not entered Reading list Not entered Study Abroad Not entered Study Pattern Not entered Keywords mm2
 Course organiser Dr Noel Smyth Tel: (0131 6)50 5080 Email: N.Smyth@ed.ac.uk Course secretary Ms Marieke Blair Tel: (0131 6)50 5048 Email: M.Blair@ed.ac.uk
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