Advanced mathematics for engineering and applied sciences
Run by School of Computer Science and Electronic Engineering
20.000 Credits or 10.000 ECTS Credits
Semester 1 & 2
Organiser: Dr Liyang Yue
Overall aims and purpose
This module aims to provide:
- a grounding in engineering mathematics.
- an understanding of the fundamental mathematics underlying all engineering.
- experience dealing with the mathematical structures under-pinning engineering systems.
- a revision of and practice with elementary algebra.
Indicative content includes:
Differentiation: Revision of notation for sets and functions. Revision of basic algebra techniques. The limit of a real function at a point. Derivative as gradient: tangent lines. Rules of differentiation. Polynomial, exponential, logarithmic, and inverse functions. Local maxima, minima, points of inflection. Using MATLAB to sketch graphs of functions. Parametric curves; polar coordinates. Solution of equations by iteration
Integration: Integration as anti-differentiation. The area under a curve. Integration by parts and by substitution. Methods of numerical integration. Mean and root-mean-square values. The method of partial fractions. Integrals of the form f’(x)/f(x) and f’(x).f(x). Distance, velocity and acceleration. Parametric curves: arc length and area. Maclaurin and Taylor series expansions. Arithmetic with Maclaurin series.
Number Systems: Integers, rationals and real numbers. Fractions ↔ infinite decimal expansions. j = √( -1), solving quadratic equations. Complex arithmetic; Argand diagram. Revision of trigonometric functions. Complex functions: bilinear; exp; log. exp(jθ) = cos(θ) + j.sin(θ). De Moivre’s theorem: n-th roots
Functions of two variables: Examples of real functions of two variables. Using software to sketch surfaces. Partial differentiation and tangent planes. Maxima, minima and saddle points. Solution of exact differential equations. Maclaurin series for f(x,y).
Probability and Statistics: Arrangement of data; histograms; mean; mode; and median. Dispersion; range; standard deviation. Normal distribution; standardized normal curve. ; Probability; Independence; Mutually exclusive events; Probability density functions; The binomial distribution; The Poisson distribution; The Gaussian distribution.
Matrices: Matrix definition; Operations on Matrices; Determinants; Matrix inversion; Solutions of linear equations using matrices;
Vectors and vector fields: Vector definition; Operations on vectors. Vectors in 2D and 3D; Representation of lines and planes using vectors; Scalar and vector products of two vectors; Angle between two vectors; Scalar fields; Vector fields; Gradient of a scalar field
Equivalent to 40%. Uses key areas of theory or knowledge to meet the Learning Outcomes of the module. Is able to formulate an appropriate solution to accurately solve tasks and questions. Can identify individual aspects, but lacks an awareness of links between them and the wider contexts. Outputs can be understood, but lack structure and/or coherence.
Equivalent to the range 70%+. Assemble critically evaluated, relevent areas of knowledge and theory to constuct professional-level solutions to tasks and questions presented. Is able to cross-link themes and aspects to draw considered conclusions. Presents outputs in a cohesive, accurate, and efficient manner.
Equivalent to the range 60%-69%. Is able to analyse a task or problem to decide which aspects of theory and knowledge to apply. Solutions are of a workable quality, demonstrating understanding of underlying principles. Major themes can be linked appropriately but may not be able to extend this to individual aspects. Outputs are readily understood, with an appropriate structure but may lack sophistication.
Apply the basic rules and techniques of integral calculus and its application in engineering.
Demonstrate the basics, rules and techniques for partial differentiation.
Use basic operations of matrix algebra, determinants and their application in solving systems of linear equations.
Use of software packages for statistical, probabilistic and matrix calculations.
Apply the basic rules and techniques of differential calculus and its application in engineering.
Demonstrate the basics, rules and techniques of complex number algebra and its application in engineering.
Apply theory of probability and statistics to calculate averages, data spread and the probability of different events.
Apply basic operations in vector algebra (Cartesian and geometric representations) to represent lines and planes, calculate the gradient of a scalar field using partial derivatives.
|End of semester examination||35.00|
|In-class test 1||10.00|
|In-class test 2||10.00|
|In-class test 3||10.00|
|In-class test 4||10.00|
Teaching and Learning Strategy
2 x 2 hours Lectures (lecturing+ student in-class practice style), over 24 weeks
Exercise questions and solutions are available to students for private study after each lecture.
- Literacy - Proficiency in reading and writing through a variety of media
- Numeracy - Proficiency in using numbers at appropriate levels of accuracy
- Computer Literacy - Proficiency in using a varied range of computer software
- Information retrieval - Able to access different and multiple sources of information
- Critical analysis & Problem Solving - Able to deconstruct and analyse problems or complex situations. To find solutions to problems through analyses and exploration of all possibilities using appropriate methods, rescources and creativity.
Subject specific skills
- Apply underpinning concepts and ideas of engineering;
- Solve problems logically and systematically;
- Use both verbal and written communication skills to different target audiences;
- Analyse and display data using appropriate methods and mathematical techniques;
- Demonstrate familiarity with relevant subject specific and general computer software packages.
- Knowledge and understanding of facts, concepts, principles & theories
- Problem solving strategies
- Knowledge and understanding of mathematical principles
Courses including this module
Compulsory in courses:
- H612: BEng Computer Systs Eng (3 yrs) year 1 (BENG/CSE)
- H61B: BEng Computer Sys Engineering (4yr with Incorp Foundation) year 1 (BENG/CSE1)
- H610: BENG Electronic Engineering (3 yrs) year 1 (BENG/ELE)
- H62B: BEng Electronic Engineering (4yr with Incorp Foundation) year 1 (BENG/ELE1)
- H61F: BEng Electronic Engineering year 1 (BENG/ELEF)
- H621: BEng Electronic Engineering with International Experience year 1 (BENG/ELEIE)
- H6W3: BSc Electronic Engineering and Music year 1 (BSC/EEM)
- H611: BSc Electronic Engineering year 1 (BSC/ELE)
- H63B: BSc Electronic Engineering (4yr with Incorp Foundation) year 1 (BSC/ELE1)
- H622: BSc Electronic Engineering with International Experience year 1 (BSC/ELEIE)
- H661: MEng Control and Instrumentation Engineering year 1 (MENG/CIE)
- H617: MEng Computer Systs Eng (4 yrs) year 1 (MENG/CSE)
- H619: MEng Computer Systems Engineering (with International Exper) year 1 (MENG/CSEIE)
- H61P: Computer Systems Engineering with Industrial Placement year 1 (MENG/CSEP)
- H601: MEng Electronic Engineering (4 yrs) year 1 (MENG/EE)