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DRPS : Course Catalogue : School of Mathematics : Mathematics

# Undergraduate Course: Mathematics for Science and Engineering 1b (MATH08061)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 8 (Year 1 Undergraduate) Availability Not available to visiting students SCQF Credits 20 ECTS Credits 10 Summary **THIS COURSE IS FOR RETAKING STUDENTS ONLY** AP's, GP's, limits, power series, radius of convergence. Basic differentiation: rate of change, simple derivatives, rules of differentiation, maxima/minima. Derivatives of powers, polynomials, rational functions, circular functions. Chain rule. Differentiation of exponential and related functions, differentiation of inverse functions, parametric and implicit differentiation, higher derivatives. Partial differentiation, directional derivatives, chain rule, total derivative, exact differentials. L'Hopital's rule. Taylor's Theorem and related results. Maclaurin series. Basic integration: anti-derivatives, definite and indefinite integrals. Fundamental Theorem of Calculus. Substitution. Area, arc-length, volume, mean values, rms values and other summation applications of integration. Integration by parts. Limits and improper integrals. Differential equations. General and particular solutions, boundary values. Separable differential equations. First order linear differential equations with constant coefficients. Course description This syllabus is for guidance purposes only : AP's, GP's, limits, power series, radius of convergence. Differentiation. Rates of change, definition of derivative, slope, speed, acceleration, maximum and minimum values. Techniques of differentiation. Rules. Derivatives of powers, polynomials, rational functions, circular functions. Chain rule. Differentiation of exponential and related functions, parametric and implicit differentiation, higher derivatives. Integration, basics and Fundamental Theorem of Calculus. Techniques of integration. Applications of Integration. Volumes of solids of revolution, mean values, rms, arclength and surface area. Improper integrals Taylor's Theorem and related results. Maclaurin series, L'H\^opital's rule, interpolation. Calculus of vectors. Partial Differentiation, directional derivatives, chain rule, total derivative, exact differentials. ODE's. Classification of DE's. Ordinary/Partial, independent/dependent variables, order, linear/nonlinear, homogeneous/nonhomogeneous. Solving DE's. General and particular solutions, boundary values. First order ODE's. Separable, linear, exact solutions.
 Pre-requisites Co-requisites Prohibited Combinations Students MUST NOT also be taking Calculus and its Applications (MATH08058) Other requirements This course is restricted to students for whom it is a compulsory part of their Degree Programme. A-Grade at Higher Mathematics OR B-Grade at A-level Mathematics OR equivalent
 Academic year 2016/17, Not available to visiting students (SS1) Quota:  50 Course Start Semester 2 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 33, Seminar/Tutorial Hours 21, Supervised Practical/Workshop/Studio Hours 10, Summative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 129 ) Additional Information (Learning and Teaching) Students must pass exam and course overall. Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 % Additional Information (Assessment) Coursework 20%, Examination 80% Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S2 (April/May) Mathematics for Science and Engineering 1b (MATH08061) 3:00 Resit Exam Diet (August) Mathematics for Science and Engineering 1b 3:00
 Series : 1. Ability to sum arithmetic and geometric series 2. Understanding the nature of power series and the radius of convergence 3. Ability to undertake simple calculations using the geometric, binomial, exponential and trigonometric series 4. Ability to construct Maclaurin and Taylor series Differentiation : 1. Understanding and application of derivative as a rate of change; understanding its graphical interpretation 2. Ability to differentiate polynomials in standard form and all powers of x, including higher derivatives 3. Ability to use the product, quotient and chain rules 4. Ability to use differentiation to solve optimisation problems 5. Ability to differentiate and integrate each of the trigonometric functions. 6. Ability to differentiate inverse functions including those for sin and tan 7. Understanding of simple calculus properties of hyperbolic functions 8. Ability to differentiate implicit functions 9. Ability to calculate simple partial derivatives 10. Ability to calculate directional derivatives 11. Ability to perform differentiation following the motion 12. Ability to construct and use differential expressions 13. Ability to understand the notation used in thermodynamic Integration : 1. Ability to evaluate an integral by anti-differentiation 2. Understanding an integral as a sum 3. Ability to integrate polynomials in standard form and all powers of x 4. Ability to use simple rearrangements (trigonometric and partial fractions) and simple substitution 5. Ability to construct integrals using the summation definition, with applications 6. Ability to integrate squares and products of sin and cos 7. Ability to integrate 1/(ax+b) and f'/f; ability to differentiate and integrate exp(x) 8. Ability to evaluate integrals in terms of inverse circular and hyperbolic functions 9. Ability to use integration by parts 10. Ability to use substitutions of various types 11. Ability 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 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
 Students will be assumed to have acquired their personal copy of : "Modern Engineering Mathematics", 4th Edition by Glyn James. ISBN: 9781780166476 CU.James: Modern Maths Pack 2011. Note that this is a special edition for Edinburgh University Students. It is only available from Blackwell's bookshop on South Bridge in Edinburgh. It includes essential access to the on-line assessment and resource system.
 Graduate Attributes and Skills Not entered Keywords mse1b
 Course organiser Dr Antony Maciocia Tel: (0131 6)50 5994 Email: A.Maciocia@ed.ac.uk Course secretary Ms Marieke Blair Tel: (0131 6)50 5048 Email: M.Blair@ed.ac.uk
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