Undergraduate Course: Analytical Techniques for Civil Engineers 2 (CIVE08016)
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 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. 
Course description 
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 equation: elementary examples and revision.
L2 Introduction to differential equations
Definition and nature of solutions, ordinary and partial DEs,. First order ordinary differential equations: civil engineering examples.
L3 and 4 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
L5, 6 and 7 Second and higher order ordinary differential equations
General second order ODE: damped vibrations, structural members in tension. Third order ODEs: nonuniform torsion. Fourth order ODEs: beam bending on Winkler foundation, local axisymmetric bending of a cylindrical shell, particular integrals, boundary conditions, special cases.
L8 and 9 Fourier series and analysis
L10 and11 Partial differential equations I
Introduction, differential operators, boundary value problems, Classic PDEs: heat conduction, Laplace &©s equation, Bending of elastic plates.
L12 and 13 Partial differential equations II
Solution of PDEs and examples based on Civil Engineering applications.
Section 2. Statistics
L14 Introduction to basic statistics and probability
Nature and causes of uncertainty in Civil Engineering. Risk. Representation of random samples. Course content. Description of random data
Mean, median, mode, sample variance, sample standard deviation, percentiles, quartiles, population variance.
L15 Probability
Definitions, Venn diagrams, notation, independence, Bayes' theorem, tree diagrams.
L16 and 17 Discrete distributions  1
Binomial distribution, combinations and permutations, probability bar charts, frequency histograms, cumulative frequency function. Discrete distributions  2
Poisson distribution. Hypothesis testing.
L18 Continuous distributions
Definitions, probability distribution, probability density function, Normal Distribution, tables.
L19 Lognormal and other distributions
Lognormal, exponential, distributions and examples
L20 and 21 Regression and correlation analysis: 1
Least squares method, regression line, regression of yonx and xony, confidence limits and assessment procedure, correlation coefficient, example. Regression and correlation analysis: 2
Procedure for goodness of fit test, correlation and causation, application to engineering problems, example.
L22 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 and 4 Second order differential equations
Solution of first order linear differential equations.
Tutorial 5 and 6 Third order, fourth order and partial differential equations
Solution of higher order and partial differential equations.
Statistics
Tutorial 7 and 8 Probability and discrete distributions
Simple calculations of probabilities, tree diagrams, conditional probability, testing simple hypotheses, statistics of discrete distributions, modelling of data.
Tutorial 9 Continuous distributions
Statistics of the normal distribution and use of distribution tables. Exponential distribution and other simple continuous distributions.
Tutorial 10 Regression and correlation analysis
Calculation of regression lines, estimation of prediction error, correlation coefficient, confidence limits, use of regression analysis in practical engineering problems.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Information for Visiting Students
Prerequisites  None 
Course Delivery Information
Not being delivered 
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 and differential equations;
 calculate the safety margins and probability of failure of simple structures given statistical information about the strengths and loadings.

Reading List
There are many suitable references for this course, including:
Advanced Engineering Mathematics Kreyszig, E John Wiley and Sons. 
Additional Information
Graduate Attributes and Skills 
Not entered 
Additional Class Delivery Information 
Tutorials to be arranged. 
Keywords  Calculus, Differential Equations, Statistics, Probability 
Contacts
Course organiser  Dr Jin Sun
Tel: (0131 6)51 9028
Email: J.Sun@ed.ac.uk 
Course secretary  Miss Lucy Davie
Tel: (0131 6)51 7073
Email: Lucy.Davie@ed.ac.uk 

