|Subject||NUMERICAL AND ESTATISTICAL METHODS||Code||00707006|
|General description||First part is an introduction to Numerical Methods. We present the main techniques about interpolation and curve fitting, and numerical integration. We also study algorithms to obtain numerical solutions of systems of linear and non-linear equations. Second part is devoted to Statistics. We focus our study on exploratory data analysis, Probability and Distribution Theory and Statistical Inference.|
|Tribunales de Revisión||
|The students understand the main concepts of numerical and statistical methods, and they apply them in solving mathematical problems appearing in engineerings.||B5655
|Students show skills and abilities in analysis, synthesis, critical reasoning and decision making.||B5656
|Students apply the studied concepts in the elaboration of correct argumentations and reasonings. They are able to face up with situations where they need new mathematical knowledge and techniques. They have developed their autonomous learning skills.||C5
|Students are able to communicate mathematical ideas and information in oral and written form.||B5656
|PART I: NUMERICAL METHODS||1: NUMERICAL SOLUTION OF NONLINEAR EQUATIONS IN ONE VARIABLE.
Iterative methods: bisection, fixed point and Newton-Raphson. Analysis of error.
2: POLYNOMIAL INTERPOLATION AND APPLICATIONS.
Lagrange interpolation polynomial. Hermite interpolation. Cubic splines.
3: LEAST SQUARES DATA FITTING.
Regression line. Linear models. Nonlinear models.
4: NUMERICAL INTEGRATION METHODS.
Rules of rectangles, midpoint, trapezoids and Simpson
|PART II: STATISTICAL METHODS||1: DESCRIPTIVE STATISTICS.
Data types and graphical representation. Scatter plots and correlation coefficient.
Basic calculation of probabilities: intersections, unions and conditional probability. Bayes' theorem.
3: RANDOM VARIABLES AND PROBABILITY DISTRIBUTITONS.
Probability distribution of discrete and continuous random variables. Some models: uniform, binomial, Poisson, normal and other probability distributitons.
4: STATISTICAL INFERENCE.
Confidence intervals and hypothesis testing.
|Methodologies :: Tests|
|Class hours||Hours outside the classroom||Total hours|
|Problem solving, classroom exercises||20||20||40|
|Practicals using information and communication technologies (ICTs) in computer rooms||12||12||24|
|(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.|
|Problem solving, classroom exercises||Students are taught how the should act -and they act themselves- in solving numerical and statistical problems appearing in Engineering.|
|Practicals using information and communication technologies (ICTs) in computer rooms|
|Assignments||They consist of various activities: responding questionnaires, uploading exercises, homework assignments, and/or team works. Many of these activities can be done electronically via moodle.|
|Lecture||Students are given the instruction on theoretical concepts and practical methods needed to solve problems.|
|Assignments||To be evaluated: knowledge and comprehension of the subject, and correct interpretation of results. Works done in "unauthorized groups" will be graded 0 points. In the case of non-contact activities, the in-person explanation of the submitted works may be required, as well as proposing to make some modification. Works and assignments are not re-evaluated in the second call.||20%|
|Mixed tests||"Mixed" means that tests are written and may also require the use of computer programs. Two tests will be done, one for each part A and B, and each of them is worth 40% of total. Aspects to be evaluated: knowledge and comprehension of the subjetc, correct use of mathematical and statistical language, correct writing and interpretation of results, and ability in the use of computer software.||80%|
|Other comments and second call|
In all tests: the use of mobile phones and other electronic devices is strictly forbidden, and will result in grade zero. Only the material specifically allowed by the instructors may be used.
Second call. Students may choose between these two options:
- maintain/preserve the grades obtained in all works and assignments (20%) and repeat one or both written tests. If either part A or B is not repeated in the second call, the grade corresponding to that part obtained in the first call will be maintained in the second call.
- remove/withdraw all works and assigments from the calculation of the final grade, in this case each of the written tests will be worth 50%.
|Contingency plan due to COVID-19 emergency conditions that prevents from presence based teaching|
|COVID-19 Teaching Guide Addendum Access Link|
|Sources of information|
|Access to Recommended Bibliography in the Catalog ULE|
ARRIAZA GÓMEZ, A.J. y otros, Estadística básica con R y R-Commander, Universidad de Cádiz, 2006
BURDEN, R.L y FAIRES, J.D., Métodos Numéricos, Thomson, 2006
Chapra, S.C., Canale, R.P., Métodos Numéricos para Ingenieros, McGraw-Hill, 2007
MILTON, S., Probabilidad y estadística con aplicaciones para ingeniería y ciencias computacionales, McGraw-Hill, 2004
DEVORÉ, J.L. , Probabilidad y Estadística para Ingeniería y Ciencias, Thomson, 2005
WALPOLE R. & MYERS R. & MYERS S., Probabilidad y Estadística para ingenieros, Prentice-Hall, 1999
CORDERO BARBERO, Alicia, y otros, Problemas resueltos de métodos numéricos, Thomson, 2006
ARRIAZA GÓMEZ, A.J. y otros, Sitio web del libro Estadística básica con R y R-Commander, http://knuth.uca.es/ebrcmdr/, 2008
|Subjects that it is recommended to have taken before|