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Teaching GuideTerm Faculty of Computer Science |
Guía Provisional
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| Grao en Intelixencia Artificial |
 Subjects |
| Calculus and Numerical Analysis |
| Contents |
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| Identifying Data | 2024/25 | |||||||||||||
| Subject | Calculus and Numerical Analysis | Code | 614G03002 | |||||||||||
| 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 |
| Functions of one variable. | Real functions of one real variable. Elementary functions. Limits. Continuity. Bisection method to solve nonlinear equations. |
| Derivatives | Derivative of a function at one point. Physical and geometrical meaning. Derivability. Calculus of derivatives. Lagrange Mean Value Theorem. Extrema. Concavity and convexity. Newton-Raphson method to solve nonlinear equations. Lagrange interpolation. Numerical differentiation. |
| Integration | Indefinite integrals: primitives. Riemann's integral. Numerical quadrature. Calculus of areas of plane regions. Calculus of volumes. |
| Functions of several variables | Functions of several variables. Visualization. Limits and continuity. Differentiability: gradient vector, approximation by the tangent plane, chain rule, directional derivative. Derivatives of higher order. Schwarz's Theorem. Extrema of real functions of several variables. |
| Numerical solution of linear systems | Condition number of a system of linear equations. Direct and iterative methods. |
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