| Course: | Mathematics Applied to Technology and Enterprise | ||
| Curricular Unit (UC) |
Analysis |
Mandatory | X |
| Optional | |||
| Scientific Area | Mathematics | ||
| Year: 1st | Semester: 1st | ECTS: 6 | Total Hours: 160 |
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| Contact Hours | T: | TP: 90 | PL: | S: | OT: 5 |
| Professor in charge |
To be allocated accoring to the distribuition of Teaching Service to be approved by the Cordinating Council of Mathematics Department Area |
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T - Theoretical; TP - Theory and practice; PL - Laboratory; S - Seminar; OT - Tutorial. (*) - Variable.
- Intended learning outcomes (knowledge, skills and competences to be developed by the students):
1.To know basic functions’ properties.
2.To understand the differential calculus concepts necessary for the study of functions; to relate derivative with linear approximation and velocity.
3.To understand Taylor expansion as a key tool to approximate functions with features located at a point and to be able to generalize the notion of polynomial approximation in other contexts.
4.To associate power series with the limit of Taylor expansions, to use convergence criteria and to know power series expansions.
5.To manipulate antiderivative methods as an basic tool for integral calculus. To associate the value of the integral of a function with its average and to know the basic applications. Manipulate indefinite and improper integrals.
6.To solve separable differential equations and 1st order linear equations, as particular cases of direct integration.
7.To understand application models leading to differential equations and to interpret results in their context.
- Syllabus:
1.Functions: Basic properties of real variable functions. Topological notions, limits and continuity.
2.Diferential calculus: Lagrange's Theorem. Monotonicity and extrema in bounded and unbounded intervals. Indeterminate expressions and l’Hôpital’s rule. Taylor polynomial and Taylor power series expansion, power series and numerical series. Convergence and comparison criteria, convergence intervals and main expansions.
3.Integral calculus
Darboux integral. Mean value theorem. Indefinite integral. Fundamental theorem of calculus. Barrow’s rule. Integrations techniques. Polynomial approximation by interpolation and integration in cases of degrees 2 and 3. Integration by parts and substitution. Improper integrals.
4. Ordinary differential equations: 1st order initial value problems; Existence and uniqueness of solution. Separable variables and 1st order linear differential equations.
