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Teaching GuideTerm University College of Technical Architecture |
| Grao en Arquitectura Técnica |
 Subjects |
| Mathematics I |
| Contents |
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| Identifying Data | 2019/20 | |||||||||||||
| Subject | Mathematics I | Code | 670G01001 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 1st four-month period |
First | Basic training | 6 | ||||||||||
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| Topic | Sub-topic |
| SUBJECT 1.- FUNCTIONS OF ONE VARIABLE | 1.1.- Definition and basic concepts. 1.2.- Limit of a function at a point. Properties. Operations. Infinite limits and limits at infinity. 1.3.- Continuity. Discontinuities. Properties of continuous functions. 1.4.- Derivative. Properties. Geometrical meaning. Chain rule. Taylor polynomial. 1.5.- Interpolation. |
| SUBJECT 5.- STATISTICS AND PROBABILITY | 5-1 STATISTICS: 5-1.1 Statistics descriptive for one variable. 5-1.2 Previous concepts. Frequency tables. 5-1.3 Graphic representation. Characteristic measurement, position, dispersion 5-1.4 Statistics descriptive for several variables. 5-1.5 Bidimensional variable. Frecuency distribution. Graphic representation. Regression and correlation 5-2 PROBABILITY: 5-2.1 Probability. Random experiment. Sample space. Events. Probability definition. 5-2.2 Conditional probability. Independent events. Product and total probabilities rules. Bayes’ theorem. 5-2.3 Probability distribution. Aleatory variable discrete and continuous. Expectation and variance. 5-2.4 Binomial distribution. Normal distribution 5-2.5 Introduction to statistical inference |
| SUBJECT 3.- INTEGRATION OF FUNCTIONS | 3.1.- Concept of primitive. Properties. 3.2.- Methods of integration. Primitive calculus. 3.3.- Improper integrals. 34.- Geometrical applications. Areas, volumes, lengths. 3.5.- Numerical integration. |
| SUBJECT 4.- DIFFERENTIAL EQUATIONS. NUMERICAL METHODS. | 4.1.- Definition and basic concepts. 4.2.- First order differential equations: separated variables, homogeneous, linear. 4.3.- Numerical methods: Euler, Runge-Kutta. |
| SUBJECT 2.- FUNCTIONS OF SEVERAL REAL VARIABLES | 2.1.- Definitions and basic concepts. 2.2.- Limit. Properties. Operations. 2.3.- Continuity. 2.4.- Differentiation. Partial derivatives. Properties. 2.5.- Tangent plane and normal straight. 2.6.- Relative extremes with and without constrains. Lagrange multipliers method. |
| Attached: Computer programm MAXIMA | Problems may be solved assisted by the computer programm Maxima |
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