 # DEGREE REGULATIONS & PROGRAMMES OF STUDY 2018/2019 University Homepage DRPS Homepage DRPS Search DRPS Contact
DRPS : Course Catalogue : School of Engineering : Civil

# 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 SCQF Credits 10 ECTS Credits 5 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. 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: 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 &�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 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. 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.
 Pre-requisites Co-requisites Prohibited Combinations Other requirements None
 Pre-requisites None
 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 Not entered Additional Class Delivery Information Tutorials to be arranged. Keywords Calculus, Differential Equations, Statistics, Probability
 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
 Navigation Help & Information Home Introduction Glossary Search DPTs and Courses Regulations Regulations Degree Programmes Introduction Browse DPTs Courses Introduction Humanities and Social Science Science and Engineering Medicine and Veterinary Medicine Other Information Combined Course Timetable Prospectuses Important Information