Undergraduate Course: Analytical Techniques for Civil Engineers 2 (CIVE08016)
|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
|Summary||This course includes lectures on the representation of engineering functions, modelling of simple continuous and multi-dimensional continuous systems, and the use of statistical techniques in Civil Engineering.
Section 1. Calculus and Differential Equations
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: non-uniform 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 &ęs 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.
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 y-on-x and x-on-y, 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.
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.
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)
||Other requirements|| None
Information for Visiting Students
Course Delivery Information
|Not being delivered|
| 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.
|There are many suitable references for this course, including:|
Advanced Engineering Mathematics Kreyszig, E John Wiley and Sons.
|Graduate Attributes and Skills
|Additional Class Delivery Information
||Tutorials to be arranged.
|Keywords||Calculus, Differential Equations, Statistics, Probability
|Course organiser||Dr Jin Sun
Tel: (0131 6)51 9028
|Course secretary||Miss Lucy Davie
Tel: (0131 6)51 7073