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Teaching GuideTerm Faculty of Science |
| Grao en Nanociencia e Nanotecnoloxía |
 Subjects |
| Fundamentals of Mathematics |
| Contents |
| Identifying Data | 2023/24 | |||||||||||||
| Subject | Fundamentals of Mathematics | Code | 610G04001 | |||||||||||
| 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 |
| Unit 0: Sets of numbers. | Real numbers. Complex numbers. |
| Unit 1: Differential calculus of one variable. | Differentiable functions. Chain's rule. Increasing and decreasing functions. Local extrema. Concavity and convexity. Inflection points. Graph representation of functions. Newton's method. Taylor's polynomial. Applications. |
| Unit 2: Integral calculus of one variable. | Definite integral. Fundamental theorem of Calculus. Integration rules. Computation of flat areas and volumes. Numerical integration: trapezoid's method. Improper integrals. Applications. |
| Unit 3: Vector spaces. Linear algebra. | Matrix algebra. Solving linear system equations. Gauss' method. Vector spaces. Diagonalization. Eigenvalues and eigenvectors. Applications. |
| Unit 4: Sequences and series. | Numerical sequences. Numerical series. Function sequences. Function series. Series of Taylor. Series of Fourier. Applications. |
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