Undergraduate Course: Engineering Mathematics 2B (SCEE08010)
Course Outline
School  School of Engineering 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 8 (Year 2 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  This course is in two parts, taught simultaneous with one lecture per week.
The first part, mathematical methods, covers: Multivariate integration and vector calculus for engineering. Gradient, tangent plane, normals; Scalar and vector fields; divergence and curl; conservative fields and potential; vector differential identities; simple applications from properties of continua and electromagnetism. Repeated multiple integration (change of order of integration); integration in noncartesian coordinates, Jacobian; line integrals (link to potential and work); surface integrals (flux); divergence, Green's and Stokes' theorems; applications and physical interpretations;
The second part, quantitative methods, covers: descriptive statistics and the presentation of statistical data; probability theory; discrete and continuous probability density functions; hypothesis testing (including 1way ANOVA); regression and experimental design.

Course description 
Mathematical Methods:
 Vector Calculus:
* Basic concepts, Transformations [1 lecture]
* Gradient [0.5 lecture]
* Divergence and curl [1.5 lectures]
 Integration:
* Double Integrals [3 lectures]
* Line integrals [1.5 lectures]
* Green's Theorem [0.5 lecture]
* Surface Integrals [2 lectures]
* Volume Integrals [1 lecture]
* Gauss' Theorem [0.5 lecture]
* Stokes' Theorem [0.5 lecture]
Quantitative Methods:
 Descriptive Statistics [1 lecture]
 Graphical presentation of data [1 lecture]
 Probability theory [1 lecture]
 Discrete distributions [1 lecture]
 Continuous distributions [1 lecture]
 Hypothesis testing: ttest [ 1 lecture]
 Hypothesis testing: power of the test, 1 way ANOVA [1 lecture]
 Linear Regression including tests for regression line [1 lecture]
 Nonlinear and multivariate regression [1 lecture]
 Experimental design [1 lecture]
The mathematical methods material will be supported by tutorial classes every other week. These will alternate with quantitative methods laboratory classes using the R statistical software.

Information for Visiting Students
Prerequisites  Mathematics units passed equivalent to Mathematics for Science and Engineering 1a and Mathematics for Science and Engineering 1b. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2020/21, Available to all students (SV1)

Quota: None 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 20,
Seminar/Tutorial Hours 5,
Supervised Practical/Workshop/Studio Hours 5,
Formative Assessment Hours 2,
Summative Assessment Hours 10,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
56 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Written Exam 80%:
Coursework 20%:
Students must pass both the Exam and the Coursework.
Their will be a total of 2 coursework reports, one on vector calculus and one on qualitative methods.

Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)   1:30   Resit Exam Diet (August)   1:30  
Learning Outcomes
1. An understanding of vector fields, their divergence and curl. 2. An ability to use the basic vector differential identities. 3. A competence in evaluating repeated and multiple integrals. 4. An understanding of line integrals, their calculation and relation to the potential of a conservative field. 5. An ability to calculate integrals, such as flux, over simple curved surfaces. 6. An ability to use the divergence theorem and Stokes's theorem in simple situations, and a realization of their great practical importance. 7. An understanding of the presentation of statistical data using graphical methods and descriptive statistics. 8. A knowledge of probability theory. 9. An understanding of common discrete and continuous probability distributions. 10. An ability to describe and test statistical hypotheses using appropriate tests. 11. An ability to both lines of best fit and loglaws using regression techniques, including the interpretation of the slope and intercept of the line. 12. An understanding of the use of replication and randomization to control error in experiments and the use of Analysis of Variance techniques to determine significant factors.

Reading List
Students are expected to own a copy of :
1. Advanced Modern Engineering Mathematics by Glyn James, Prentice Hall, ISBN 9780273719236
Students are recommended to download a copy of the free, open source, R statistics package from www.rproject.org
Reading list
1. Sarah Stowell. Using R for Statistics. Apress, 2014. ISBN 9781484201404.
2. Brian Dennis. The R Student Companion. Chapman & Hall/CRC Press, 2012. ISBN 9781439875407
3. William Navidi, Statistics for Engineers and Scientists, McGrawHill, 2014. ISBN 9781259251603

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  Vector calculus,Multiple integrals,Line integrals,Statistical method,Regression,Data presentation 
Contacts
Course organiser  Dr Nicholas Polydorides
Tel: (0131 6)50 2769
Email: N.Polydorides@ed.ac.uk 
Course secretary  Miss Jennifer Yuille
Tel: (0131 6)51 7073
Email: Jennifer.Yuille@ed.ac.uk 

