Undergraduate Course: Analytical Techniques for Civil Engineers 2 (CIVE08016)
Course Outline
School 
School of Engineering 
College 
College of Science and Engineering 
Course type 
Standard 
Availability 
Available to all students 
Credit level (Normal year taken) 
SCQF Level 8 (Year 2 Undergraduate) 
Credits 
10 
Home subject area 
Civil 
Other subject area 
None 
Course website 
None

Taught in Gaelic? 
No 
Course description 
This course includes lectures on the representation of engineering functions, modelling of simple continuous and multidimensional continuous systems, and the use of statistical techniques in Civil Engineering. 
Information for Visiting Students
Prerequisites 
None 
Displayed in Visiting Students Prospectus? 
Yes 
Course Delivery Information

Delivery period: 2010/11 Semester 1, Available to all students (SV1)

WebCT enabled: Yes 
Quota: None 
Location 
Activity 
Description 
Weeks 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
King's Buildings  Lecture   111      11:10  12:00  King's Buildings  Lecture   111   11:10  12:00     King's Buildings  Tutorial  Tutorials  211   12:10  13:00    or 12:10  13:00 
First Class 
Week 1, Tuesday, 11:10  12:00, Zone: King's Buildings. Lecture Theatre 1, Daniel Rutherford Building 
Additional information 
Tutorials to be arranged. 
Exam Information 
Exam Diet 
Paper Name 
Hours:Minutes 
Stationery Requirements 
Comments 
Main Exam Diet S1 (December)  Analytical Techniques for Civil Engineers 2  1:30  12 sides / 2 x graph   Resit Exam Diet (August)   1:30  12 sides / 2 x graph  
Summary of Intended Learning Outcomes
By the end of the course students should be able to:
 solve a variety of statistical problems that they will encounter in other courses in the 2nd and later years;
 to model and solve some common civil engineering problems via the use of calculus;
 calculate the safety margins and probability of failure of simple structures given statistical information about the strengths and loadings. 
Assessment Information
Examination only. 
Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
LECTURES
Section 1. Calculus and Differential Equations
L1 Introduction
Calculus in modern Civil Engineering: the needs of the practising engineer. The meaning of a differential: elementary examples and revision.
L2 Differentiation techniques
Review of differentiation techniques: product, quotient, function of a function, successive, implicit, logarithmic (all with examples).
L3 Partial differentiation
Partial derivatives, total differential, rates of change with partial derivatives, maxima minima and saddles (all with examples).
L4 Integration
Definitions and fundamentals, integration by parts, examples.
L5 Introduction to differential equations
Definition and nature of solutions, ordinary and partial DEs,. First order ordinary differential equations: civil engineering examples.
L6 Second order ordinary differential equations
Simple harmonic motion, complementary function and the variety of particular integrals. Second order ODEs as a paradigm for all ODE and PDE solutions. Complementary function and particular integral
L7 Second and third order ordinary differential equations
General second order ODE: damped vibrations, structural members in tension. Third order ODEs: nonuniform torsion.
L8 Fourth order ordinary differential equations
Fourth order ODEs: beam bending on Winkler foundation, local axisymmetric bending of a cylindrical shell, particular integrals, boundary conditions, special cases.
L9 Fourier series
Fourier series and analysis
L10 Partial differential equations I
Introduction, differential operators, boundary value problems, Classic PDEs: heat conduction, Laplace&©s equation, Bending of elastic plates. Summary and perspectives based on Civil Engineering applications.
Section 2. Statistics
L11 Introduction to basic statistics and probability
Nature and causes of uncertainty in Civil Engineering. Risk. Representation of random samples. Course content.
L12 Description of random data
Mean, median, mode, sample variance, sample standard deviation, percentiles, quartiles, population variance.
L13 Probability
Definitions, Venn diagrams, notation, independence, Bayes' theorem, tree diagrams.
L14 Discrete distributions  1
Binomial distribution, combinations and permutations, probability bar charts, frequency histograms, cumulative frequency function.
L15 Discrete distributions  2
Poisson distribution. Hypothesis testing.
L16 Continuous distributions
Definitions, probability distribution, probability density function, Normal Distribution, tables.
L17 Normal distribution
Central limit theorem, use of tables, examples
L18 Lognormal and other distributions
Lognormal, exponential, Pearson distributions and examples
L19 Regression and correlation analysis: 1
Least squares method, regression line, regression of yonx and xony, confidence limits and assessment procedure, correlation coefficient, example.
L20 Regression and correlation analysis: 2
Procedure for goodness of fit test, correlation and causation, application to engineering problems, example.
L21 Summary and review
A review of the material covered and its context within the courses.
TUTORIALS
Calculus
Tutorial 1 Differentiation
Problems of differentiation of common functions and their combinations.
Tutorial 2 Integration and first order linear differential equations
Revision of integration. Solution of first order linear differential equations.
Tutorial 3 Second order differential equations
Solution of first order linear differential equations.
Tutorial 4 Third order, fourth order and partial differential equations
Solution of higher order and partial differential equations.
Statistics
Tutorial 5 Probability and discrete distributions
Simple calculations of probabilities, tree diagrams, conditional probability, testing simple hypotheses, statistics of discrete distributions, modelling of data.
Tutorial 6 Regression and correlation analysis
Calculation of regression lines, estimation of prediction error, correlation coefficient, confidence limits, use of regression analysis in practical engineering problems.
Tutorial 7 Continuous distributions
Statistics of the normal distribution and use of distribution tables. Exponential distribution and other simple continuous distributions.

Transferable skills 
Not entered 
Reading list 
There are many suitable references for this course, including:
Advanced Engineering Mathematics Kreyszig, E John Wiley and Sons.

Study Abroad 
Not entered 
Study Pattern 
Not entered 
Keywords 
Not entered 
Contacts
Course organiser 
Dr Martin Gillie
Tel: (0131 6)50 7204
Email: M.Gillie@ed.ac.uk 
Course secretary 
Mrs Sharon Potter
Tel: (0131 6)51 7079
Email: Sharon.Potter@ed.ac.uk 

