Undergraduate Course: Mathematics for Science and Engineering 1a (MATH08060)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Course type  Standard 
Availability  Not available to visiting students 
Credit level (Normal year taken)  SCQF Level 8 (Year 1 Undergraduate) 
Credits  20 
Home subject area  Mathematics 
Other subject area  None 
Course website 
None 
Taught in Gaelic?  No 
Course description  This course is restricted to students for whom it is a compulsory part of their Degree Programme. 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. 
Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  Students MUST NOT also be taking
Introduction to Linear Algebra (MATH08057)

Other requirements  This course is restricted to students for whom it is a compulsory part of their Degree Programme.
AGrade at Higher Mathematics OR BGrade at Alevel Mathematics OR equivalent 
Additional Costs  None 
Course Delivery Information

Delivery period: 2011/12 Semester 1, Not available to visiting students (SS1)

WebCT enabled: Yes 
Quota: 330 
Location 
Activity 
Description 
Weeks 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Central  Lecture  Appleton Th 5  111  12:10  13:00      Central  Lecture  David Hume Th A  111   12:10  13:00     Central  Lecture  Appleton Th 5  111     12:10  13:00  
First Class 
Week 1, Monday, 12:10  13:00, Zone: Central. Appleton Tower, Th 5 
Additional information 
Tutorials Wed 9:00, 10:00, 11:00, 12:10 or 13:05
Appleton M2 A/B/C 
Exam Information 
Exam Diet 
Paper Name 
Hours:Minutes 


Main Exam Diet S1 (December)  Mathematics for Science and Engineering 1a (MATH08060)  3:00   
Summary of Intended Learning Outcomes
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 angleformulae, 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 loglinear and loglog 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). 
Assessment Information
Coursework 20%; examination 80% 
Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
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. 
Transferable skills 
Not entered 
Reading list 
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 online assessment and resource system.

Study Abroad 
Not entered 
Study Pattern 
Not entered 
Keywords  mse1a 
Contacts
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 

