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DRPS : Course Catalogue : School of Mathematics : Mathematics

# Undergraduate Course: Mathematics for Science and Engineering 1a (MATH08060)

 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** **STUDENTS MUST BE REGISTERED AS EXAM ONLY** Basic rules of algebra and algebraic manipulation, suffix and sigma notation, binomial expansion, parametric representation, numbers and errors. Functions, graphs, periodicity; polynomials, factorization, rational functions, partial fractions, curve sketching. The circular, hyperbolic and logarithmic functions and their inverses. Implicit functions, piecewise functions, algebraic functions. Sequences and series; permutations and combinations, Binomial theorem. Polynomials and their roots, partial fractions. Complex numbers: Cartesian, polar form and de Moivre's theorem; connection with trigonometric and hyperbolic functions; the complex logarithm; loci. Basic vector algebra; scalar product, vector product, triple product and geometry. Matrices, inverses and determinants, linear equations and elimination. Rank, eigenvalues, eigenvectors, symmetric matrices. Course description This syllabus is for guidance purposes only : Numbers: Numbers, rules of arithmetic, inequalities, modulus, intervals. Algebraic manipulation, suffix and sigma notation, Binomial expansion. Coordinates, lines, circles and parametric representation. Numbers and accuracy, significant figures, rounding errors. Functions: Functions. Inverse functions, composition, symmetry. Linear and quadratic functions. Polynomials, factorization, division, roots, curve sketching. Rational Functions. Partial Fractions, asymptotes. Circular functions. Trig identities, amplitude and phase, inverse trig functions, polar coordinates. Exponential, logarithm, hyperbolic and inverse hyperbolic functions. Implicit functions, piecewise functions, algebraic functions. Complex Numbers: Argand diagram, arithmetic, modulus and argument, polar form, Euler's formula, relation with circular and hyperbolic functions, logarithm of a complex number. Powers of a complex number, De Moivre, powers of trig functions and multiple angles. Loci in complex plane. Vectors: Basic definitions. Scalars, vectors, Cartesian coordinates, complex numbers, addition, components, scalar product, vector product, triple product. Vectors and geometry of lines and planes. Matrices: Definitions, basic operations, multiplication. Determinants Inverse Matrix Linear equations, elimination methods Rank Eigenvalues, eigenvectors, symmetric matrices.
 Pre-requisites Co-requisites Prohibited Combinations Students MUST NOT also be taking Mathematics for the Natural Sciences 1a (MATH08072) OR Engineering Mathematics 1a (MATH08074) 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:  0 Course Start Semester 1 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 100 %, Coursework 0 %, Practical Exam 0 % Additional Information (Assessment) Examination only Feedback Not entered No Exam Information
 Revision of basic arithmetic and algebra : 1. Ability to manipulate numbers and symbols 2. Ability to round numbers and calculate decimal places and significant figures 3. Ability to use suffix and sigma notation 4. Ability to expand expressions using the binomial theorem 5. Ability to enumerate permutations and combinations and evaluate binomial coefficients Functions : 1. Understanding concept of functions. 2. Ability to graph functions, using appropriate calculus techniques 3. Understanding periodicity, evenness and oddness and using it to solve computational and graphical problems 4. Ability to graph f(ax+b), given the graph of f(x) 5. Ability to evaluate and graph piecewise functions 6. Ability to complete the square for quadratics and to solve quadratic equations 7. Ability to factor polynomials with integer roots 8. Ability to divide polynomials and construct partial fractions, graphing the result 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. Understanding of 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 Trigonometric functions : 1. Ability to evaluate all six ratios from given information 2. Ability to use addition formulae and multiple angle-formulae, including their reversals 3. Ability to calculate amplitude, period and phase for sinusoidal functions 4. Ability to use inverse trigonometric functions. Hyperbolic functions, Logarithms and Exponentials : 1. Understanding the definition of a log as the inverse of exponentiation and ability to solve simple problems using this 2. Ability to use the log rules 3. Ability to manipulate exponential functions 4. Ability to use hyperbolic and inverse hyperbolic functions 5. Ability to use log-linear and log-log graphs, including understanding of exponential processes Complex numbers : 1. Ability to perform simple arithmetic in Cartesian form, including calculation of conjugate and modulus 2. Ability to represent complex numbers on an Argand Diagram 3. Ability to represent simple straight lines and circles in complex number notation 4. Ability to calculate with the polar form 5. Ability to use de Moivre's Theorem to calculate powers 6. Ability to use Euler's formula to find simple roots and fractional powers Vectors : 1. Understanding position and free vectors 2. Ability to distinguish between directed line segments and vectors 3. Ability to compute the dot product, compute angles and recognise orthogonality 4. Ability to resolve vectors 5. Ability to calculate the equations of lines and planes in 3D 6. Ability to calculate the vector product and the scalar and vector triple products 7. Ability to solve various intersection problems involving lines and planes Matrix algebra : 1. Ability to add, multiply and compute the transpose 2. Ability to solve linear equations using Gaussian elimination 3. Ability to compute the inverse (2x2, 3x3) 4. Ability to compute the determinant (2x2, 3x3) 5. Understanding the link between matrix, determinant and solution of equations 6. Ability to solve homogeneous equations 7. Understanding of rank, eigenvectors and eigenvalues. 8. The ability to compute eigenvectors and eigenvalues (2x2, 3x3).
 Students will be assumed to have acquired their personal copy of : "Mathematics for Science and Engineering 1", adapted from Modern Engineering Mathematics, 4th Edition by Glyn James. ISBN: CU.James: Modern Maths Pack 2013. 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 mse1a
 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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