Objectives and Contextualisation
Reach a sufficient level in the calculation of a variable to deal with phenomena and solve the mathematical problems raised in engineering that can be described in these terms.
Support the parts of the other subjects of the degree that require mastery of real functions of a variable. Achieve a sufficient level in the use of complex numbers and above all in trigonometry.
Competences
Electronic Engineering for Telecommunication
Communication
Develop personal attitude.
Develop personal work habits.
Develop thinking habits.
Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
Work in a team.
Telecommunication Systems Engineering
Communication
Develop personal attitude.
Develop personal work habits.
Develop thinking habits.
Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
Work in a team.
Learning Outcomes
Apply, in the problems that arise in engineering, knowledge about linear algebra, geometry, differential geometry, differential and integral calculus, differential and partial derivative equations, numerical methods, numerical algorithms, statistics and optimisation.
Apply, to the problems that arise in engineering, knowledge of linear algebra, geometry, differential geometry, differential and integral calculus, differential and partial derivative equations, numerical methods, numerical algorithms, statistics and optimisation.
Communicate efficiently, orally and in writing, knowledge, results and skills, both professionally and to non-expert audiences.
Develop curiosity and creativity.
Develop scientific thinking.
Develop the capacity for analysis and synthesis.
Manage available time and resources.
Manage available time and resources. Work in an organised manner.
Prevent and solve problems.
Resolve the mathematical problems that can arise in engineering.
Work autonomously.
Work cooperatively.
Work in an organised manner.
Content
1. Complex numbers.
1.1 Trigonometric functions. Addition formulae. Identities. Trigonometric inverse functions.
1.2 Trigonometric equations.
1.3 Complex numbers. Sum, product and the invers. Square roots. Second degree equations.
1.4 Module and argument. Euler's formula.
1.5 Polynomials, roots and factorization. Fundamental theorem of Algebra.
2. Continuity
2.1 Continuity and limits.
2.2. Fundamental theorems of continuous functions. Exponential and logarithmic functions.
3. Differential calculus.
3.1 Derivatives of functions. Algebraic rules of derivation. Chain rule. Derived of the inverse.
3.2 Mean value theorem and consequences. Intervals of monotony.
3.3 Relative and absolute extremes. Optimization.
3.4 Calculation of limits using derivation.
3.5 Taylor's formula.
4. Integral Calculus.
4.1 Notion of Riemann integral.
4.2 Fundamental Theorem of Calculus. Barrow's theorem.
4.3 Calculation of primitives.
4.4 Applications of integrals (part in seminars).
5. Differential equations.
5.1 Notion of differential equation.
5.2 Solving the equations of separate variables.
5.3 First order linear equations.
5.4 Second order linear with constant coefficients.
5.5 Examples of applications of the differential equations.
