To surpass the asignatura will be necessary to obtain, added the qualifications of all the activities, a minimum note of 50% of the total and 50% objective test. To obtain the qualification of no presented, sera sufficient that the student do not participate in the objective proof and have not been evaluated in the Works tutelados in but of 50%. In the proof of second opportunity the criterion to surpass the asignatura will be the previous or obtain a no inferior note to 50% in the objective proof. By what refers to successive academic courses, the process of education-learning, included the evaluation, refers to an academic course, and therefore volveria to begin with a new course, included all the activities and procedures of evaluation that went programmed for said course; nevertheless it allows request keep the qualification of practices of a previous course.

The students enrolled in regimen of partial time and academic exemption from attendance exemption,can be evaluated of personalised way regarding the methodologies of Session maxistral, Solution of problems and Works tutelados. The students enrolled in regimen of partial time is compulsory to present to the objective proof, asi as to the partial proofs along the course. For the first and second opportunity the criteria of evaluation for this alumnado, 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.

They have priority in the granting of matrícula of honour the students at the earliest opportunity.

Learning outcomes	Study programme competences
O estudo, representación e interpretación de funcións elementais de unha e varias variables.	A15 A16 A20 A24 A25 A27	B1 B2 B3 B6	C1 C3 C6
Utilizar con destreza as técnicas de cálculo de primitivas e as súas aplicacións.	A20 A24 A25 A27	B1 B2 B3 B6	C1 C3 C6
Resolver sistemas de ecuacions lineais e operar con cálculo matricial	A20 A24 A25 A27	B1 B2 B3 B6	C1 C3 C6
Plantexar e resolver modelos sinxelos que conleven ecuacións e sistemas de ecuacións diferenciais.	A20 A24 A25 A27	B1 B2 B3 B6	C1 C3 C6

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. Integración numérica: método de Simpson. Integrales impropias.
• 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	A15 A16 A24 A25 B1 B2 B3 C1 C3 C6	32	64	96
Problem solving	A15 A20 B1 B2 B3	8	18	26
Supervised projects	A15 A27 B2 B3 B6	8	16	24
Objective test	B2 B3	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	desarrollo dos conceptos e resolución de problemas
Problem solving	Cuestionarios, boletins e exámenes de outros cursos que periódicamente se poñen a disposición dos alumnos sobre distintos contiidos e que o alumno terá que resolver.
Supervised projects	Traballo sobre temas propostos por o profesor, presentarase un resumo teórico xunto con un boletín de problemas resoltos acerca do tema correspondente
Objective test	proba orientada a evaluación dos contidos teóricos que se traballan nas sesions maxistrales

Methodologies	Competencies	Description	Qualification
Guest lecture / keynote speech	A15 A16 A24 A25 B1 B2 B3 C1 C3 C6	Questions to the students.	10
Objective test	B2 B3	Development of cuestions and problems. Competencie C6 will be assessed.	70
Supervised projects	A15 A27 B2 B3 B6	Development of specific aspects with examples and solved problems. Competence B3 will be assessed.	10
Problem solving	A15 A20 B1 B2 B3	Delivery of exercises and solved exams. Competences A15, B2 and C3 will be assessed.	10

Assessment comments
To surpass the asignatura will be necessary to obtain, added the qualifications of all the activities, a minimum note of 50% of the total and 50% objective test. To obtain the qualification of no presented, sera sufficient that the student do not participate in the objective proof and have not been evaluated in the Works tutelados in but of 50%. In the proof of second opportunity the criterion to surpass the asignatura will be the previous or obtain a no inferior note to 50% in the objective proof. By what refers to successive academic courses, the process of education-learning, included the evaluation, refers to an academic course, and therefore volveria to begin with a new course, included all the activities and procedures of evaluation that went programmed for said course; nevertheless it allows request keep the qualification of practices of a previous course. The students enrolled in regimen of partial time and academic exemption from attendance exemption,can be evaluated of personalised way regarding the methodologies of Session maxistral, Solution of problems and Works tutelados. The students enrolled in regimen of partial time is compulsory to present to the objective proof, asi as to the partial proofs along the course. For the first and second opportunity the criteria of evaluation for this alumnado, 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. They have priority in the granting of matrícula of honour the students at the earliest opportunity.

Basic	LARSON (2006). CALCULO. McGrawHill

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

Other comments
It is convenient to have knowledges of mathematics of 2 bachillerato, if it does not have them recommends  do the course of nivelación.  .