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Teaching GuideTerm Faculty of Science |
| Grao en Nanociencia e Nanotecnoloxía |
 Subjects |
| Advanced Calculus |
| Contents |
| Identifying Data | 2023/24 | |||||||||||||
| Subject | Advanced Calculus | Code | 610G04009 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 2nd four-month period |
First | Basic training | 6 | ||||||||||
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| Topic | Sub-topic |
| Unit 1: Topology in R^n | Scalar product, norm and distance. Classification of points and sets. Topology in R: bounded sets, supreme, infimo, maximum and minimum. Polar, cylindrical and spherical oordinates. Applications. |
| Unit 2: Functions of more than one variable | Scalar and vector functions. Level sets. Continuity. Applications. |
| Unit 3: Differentiation of functions of more than one variables and applications | Directional derivative. Partial derivatives: properties and practical computations. Differerential of a function. Relationship between the differential and the partial derivatives. Gradient vector, relationship with the directional derivatives. Jacobian matrix. Higher order partial derivatives. Introduction to vector calculus. Taylor's theorem for scalar functions. Critical points, classification. Hessian matrix. Extremos condicionados: reducción de la dimensión, método de los multiplicadores de Lagrange. Aplicaciones. |
| Unit 4: Integration of functions of one and more variables | Double integrals. Triples integrals. Change of variables in double and triple integrals. Applications of integrals. |
| Unit 5: Integration in curves and surfaces | Parameterized curves. Integral line. Gradient function and conservative field. Green's theorem. Parameterized surfaces. Integral of surface. Sotkes theorem. Divergence's theorem. Applications. |
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