To surpass the subject it will be necessary to obtain, after adding the qualifications of all the activities, a minimum note of 50% of the total. To obtain the qualification of no presented, it will be sufficient that the student do not participate in the objective proof and have not been evaluated in more than 50% of the guided works. In the second opportunity the criterion to surpass the subject will be the previous or to reach a mark no less than 50% in the objective proof. Regarding successive academic courses, the process of education-learning, included the evaluation, refers to an academic course; nevertheless it allows request keep the qualification of practices of a previous course. Guided work qualifications are only kept between courses on student demand.

The students enrolled in regime of partial time and academic exemption from attendance exemption, can be evaluated in a personalised way regarding the methodologies of theory sessions, problem solving and guided works. For the students enrolled in the partial time regime it is compulsory to make the objective proof, as well as the partial proofs along the course. For the first and second opportunity the criteria of evaluation for this students, is the same that for the others and the percentage of dispenses of assistance will be of 80%.

The objective proof is equal for all the students.

The priority for obtaining qualifications "with honours", will be for the students that achieve this mark at the earliest opportunity.

Learning outcomes	Study programme competences
Integration and applications	A21	B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B12 B13
Differentiation and applications	A21	B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B12 B13
Linear algebra and applications	A21	B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B12 B13
Differential equations and applications	A21	B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B12 B13

Topic	Sub-topic
• Differentiation	o Basic Rules of Differentiation. o The Chain Rule. o Techniques Differentiation. o L'Hôpital's Rule. Taylor's Theorem. o Applications of Differentiation. o Maxima and Minima. o Optimisation Problems. o The Newton-Raphson Method.
• Integration	o Integration as Summation. o Fundamental Theorem of Calculus. o Some Basic Integrals. o Integration by Substitution. o Integration by Parts. o Integration of Rational Functions. o Geometrical Applications of Integration. o Numerical Integration. Simpson's Rule. o Improper Integrals.
• Linear Algebra	o Systems of Linear Equations o Elementary operations. o The Algebra of Matrices. o Determinants. Basic properties. o The determinant rank. o Eigenvalues and Eigenvectors. o Normal forms for matrices. o Cayley-Halmiton theorem.
• Ordinary Differential Equations.	o First Order Differential Equations. o Separable First Order Differential Equations. o Linear First Order Differential Equations. o Applications of First Order Differential Equations. o Second Order Linear Differential Equations with Constant Coefficients. o Homogeneous Linear Systems with Constant Coefficients.

Methodologies / tests	Competencies	Ordinary class hours	Student’s personal work hours	Total hours
Guest lecture / keynote speech	A21 B2 B3 B6 B13	32	64	96
Problem solving	A21 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B12	8	18	26
Supervised projects	A21 B1 B2 B3 B8 B9 B10 B12 B13	8	16	24
Objective test	B1 B2 B3 B4 B8 B9 B10 B13	3	0	3

Personalized attention		1	0	1

(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies	Description
Guest lecture / keynote speech	Desenvolvemento dos conceptos e resolución de problemas
Problem solving	Cuestionarios, boletins e exames doutros cursos que periodicamente poranse a disposición dos alumnos sobre distintos contidos e que o alumno terá que resolver.
Supervised projects	Traballo sobre temas propostos polo profesor, presentarase un resumo teórico xunto cun boletín de problemas resoltos acerca do tema correspondente
Objective test	Desenvolvemento de cuestións e problemas da materia

Methodologies	Competencies	Description	Qualification
Guest lecture / keynote speech	A21 B2 B3 B6 B13	Questions to the students.	10
Supervised projects	A21 B1 B2 B3 B8 B9 B10 B12 B13	Development of specific aspects with examples and solved problems. Competence B3 will be assessed.	10
Problem solving	A21 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B12	Delivery of exercises and solved exams. Competences A15, B2 and C3 will be assessed.	10
Objective test	B1 B2 B3 B4 B8 B9 B10 B13	Desenvolvemento de cuestións e resolución de problemas da materia	70

Assessment comments
To surpass the subject it will be necessary to obtain, after adding the qualifications of all the activities, a minimum note of 50% of the total. To obtain the qualification of no presented, it will be sufficient that the student do not participate in the objective proof and have not been evaluated in more than 50% of the guided works. In the second opportunity the criterion to surpass the subject will be the previous or to reach a mark no less than 50% in the objective proof. Regarding successive academic courses, the process of education-learning, included the evaluation, refers to an academic course; nevertheless it allows request keep the qualification of practices of a previous course. Guided work qualifications are only kept between courses on student demand. The students enrolled in regime of partial time and academic exemption from attendance exemption, can be evaluated in a personalised way regarding the methodologies of theory sessions, problem solving and guided works. For the students enrolled in the partial time regime it is compulsory to make the objective proof, as well as the partial proofs along the course. For the first and second opportunity the criteria of evaluation for this students, is the same that for the others and the percentage of dispenses of assistance will be of 80%. The objective proof is equal for all the students. The priority for obtaining qualifications "with honours", will be for the students that achieve this mark at the earliest opportunity.

Basic	LARSON (2006). CALCULO. McGrawHill

Complementary	Finney (). Cálculo. Addison-Wesley Bradley (). Cálculo. Prentice Hall Alfonsa García (). Cálculo I. CLGSA Rogawski (2014). Cálculo, una variable. Editorial Reverté Salas / Hille / Etgen (). Cálculus. Reverté NEUHAUSER (2004 ). MATEMÁTICAS PARA CIENCIAS . Pearson

Other comments
It is convenient to have studied Mathemathics in the final course of Secondary Education. For those students who have not, the nivelation course offered by the Faculty of Science is strongly recommended.