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Educational guide | |||||||||||||||||||||||||||||||||||||||
IDENTIFYING DATA | 2024_25 | |||||||||||||||||||||||||||||||||||||||
Subject | CALCULUS | Code | 00809010 | |||||||||||||||||||||||||||||||||||||
Study programme |
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Descriptors | Credit. | Type | Year | Period | ||||||||||||||||||||||||||||||||||||
6 | Compulsory | First | Second |
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Language |
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Prerequisites | ||||||||||||||||||||||||||||||||||||||||
Department | MATEMATICAS |
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Coordinador |
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mcarv@unileon.es jgomp@unileon.es |
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Lecturers |
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Web | http://matematicas.unileon.es | |||||||||||||||||||||||||||||||||||||||
General description | Mathematical methods in mechanical engineering: Vector calculus, differential equations and differentoial geometry | |||||||||||||||||||||||||||||||||||||||
Tribunales de Revisión |
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Competencias |
Code | |
A16337 | |
A16338 | |
A16339 | |
A16340 | |
A16341 | |
A16342 | |
A16343 | |
B5121 | |
B5122 | |
B5125 | |
B5131 | |
B5132 | |
B5134 | |
B5135 | |
B5141 | |
B5142 | |
C1 | CMECES1 That students have demonstrated possession and understanding of knowledge in an area of study that is based on general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study |
C4 | CMECES4 That students can transmit information, ideas, problems and solutions to both a specialised and non-specialised audience |
C5 | CMECES5 That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy |
Learning aims |
Competences | |||
C1 |
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C4 |
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C5 |
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B5121 |
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B5122 |
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B5125 |
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B5131 |
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B5132 |
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B5134 |
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B5135 |
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B5141 |
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B5142 |
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A16337 |
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A16338 |
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A16339 |
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A16340 |
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A16341 |
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A16342 |
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A16343 |
Contents |
Topic | Sub-topic |
I. Geometry | 1.- Conics 2.- Quadric surfaces 3.- Vectorial functions: Parametric curves 4.- Curvature 5.- Surfaces in 3D space 6.- First Fundamental Form |
II. Vector Calculus | 7.- Differential Operators 8.- Path integrals 9.- Multiple integral 10.- Green's Theorem 11.- Surface integral 12.- Stokes' Theorem 13.- Gauss Divergence Theorem |
III. Differential Equations | 14.- Ordinary differential equations. 15.- A first look at mathematical models 16.- First order equations 17.- Exact equations. Separable equations. 18.- First order linear equations 19.- Higher order differential equations 20.- Linear homogeneous equations of higher order 21.- Non-homogeneous linear equations. Variation of parameters 22.- Mass-spring linear models 23.- Differential models for linear circuits. |
IV. Systems of Linear Differential Equations | 24.- Homogeneous systems of linear equations 25.- Non-homogeneous systems 26.- Qualitative behavior of non-linear systems 27.- 2D Phase portraits |
Planning |
Methodologies :: Tests | |||||||||
Class hours | Hours outside the classroom | Total hours | |||||||
Problem solving, classroom exercises | 30 | 15 | 45 | ||||||
Personal tuition | 1 | 9 | 10 | ||||||
Lecture | 30 | 15 | 45 | ||||||
Extended-answer tests | 6 | 44 | 50 | ||||||
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. |
Methodologies |
Description | |
Problem solving, classroom exercises | Problem solving in the classroom |
Personal tuition | |
Lecture | As usual |
Personalized attention |
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Assessment |
Description | Qualification | ||
Extended-answer tests | At least an ordinary evaluation | 95% | |
Others | Some students can be requested to an oral examination. | up to 50% | |
Other comments and second call | |||
<p>Students qualify after obtaining at least 50% global.</p><div><br /></div><div>Second call (University agenda): Students can qualify at second call in the same way than first.</div> |
Sources of information |
Access to Recommended Bibliography in the Catalog ULE |
Basic |
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Complementary |
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Recommendations |
Subjects that it is recommended to have taken before | |||
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