To pass this course it will be necessary to obtain (after adding the
qualifications of all the activities) a minimum mark of 50% of the
total and 50% of the multiple-choice test. To obtain the mark "not presented", it will be sufficient that
the students do not participate in the multiple-choice test and have not been
evaluated in more than 50% of the problem solving and supervised works.
To pass the course in the second opportunity, either the above criterion
is fullfiled or a mark higher than 50% in the multiple choice test is
obtained. Final marks are not kept from successive academic years.
However, it is possible to keep the marks of the supervised works of the previous academic year, if the teacher agrees to this, having the student previously demanded it.

The students which are part-time enrolled (and so they are granted
with an attendance exemption), can be evaluated in a personalized way
regarding the methodologies of the lectures, problem solving and
supervised works. For those students which are part-time enrolled, it is
compulsory to make the multiple-choice test, as well as the partial test
along the course. For the first and second opportunity the criteria of
evaluation for these students is the same as the criterion for full-time
enrolled students (where the attendance waiver will
be of 80%).

The
priority for obtaining qualifications "with honors" will be for the
students that achieve this mark in the first opportunity.

Contingency plan (due to Covid19):
If the multiple-choice test is not made face-to-face, it will have a percentage of 30% and the other methodologies 70%

Learning outcomes	Study programme competences
The study, representation and interpretation of elementary functions of one and several variables	A21	B1 B2 B3 B4
Integration and applications	A21	B1 B2 B3 B5 B6 B7
Skillful use of primitive calculation techniques and their applications	A21	B1 B2 B3 B8 B9 B10
Solve systems of linear equations and operate with matrix calculus	A21	B1 B2 B3 B12
State and solve simple models involving equations and systems of differential equations.	A21	B1 B2 B3 B13
Differentiation and applications	A21	B1 B2 B3
Linear algebra and applications	A21	B1 B2 B3
Differential equations and applications	A21	B1 B2 B3

Topic	Sub-topic
• Differentiation	o Basic Rules of Differentiation. o The Chain Rule. o Differentiation techniques. 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.
• 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.
• 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.

Methodologies / tests	Competencies	Ordinary class hours	Student’s personal work hours	Total hours
Guest lecture / keynote speech	A21 B1 B2 B3	32	64	96
Problem solving	A21 B1 B2 B3 B4 B5 B6	8	18	26
Supervised projects	A21 B1 B2 B3 B4 B7 B8 B9	8	16	24
Multiple-choice questions	B2 B3 B4 B10 B12 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	Concept development and problem solving Contingency plan (due to Covid19): Microsoft Teams: lectures will be taught regularly in the schedule fixed by the Faculty of Science.
Problem solving	A variety of problems (from textbooks and exams of past academic years) will be periodically made available to students on different topics of this course. The students will have to solve them to acquire the required skills to pass this course. Contingency plan (due to Covid19): Microsoft Teams: seminars in small groups will be taught regularly in the schedule fixed by the Faculty of Science.
Supervised projects	Working on topics proposed by the teacher, a theoretical summary will be presented along with a collection of problems resolved on the corresponding topic. Contingency plan (due to Covid19): Microsoft Teams: seminars in small groups will be taught regularly in the schedule fixed by the Faculty of Science.
Multiple-choice questions	Mathematical solution of questions and problems related to the topics of this course. Contingency plan (due to Covid19): The multiple-choice test will be carried out by using the platforms Moodle and Microsoft Teams.

Methodologies	Competencies	Description	Qualification
Supervised projects	A21 B1 B2 B3 B4 B7 B8 B9	Development of specific aspects with examples and solved problems. Competence B3 will be assessed.	10
Problem solving	A21 B1 B2 B3 B4 B5 B6	Delivery of exercises and solved exams. Competences A15, B2 and C3 will be assessed.	20
Multiple-choice questions	B2 B3 B4 B10 B12 B13	Multiple-choice questions	60
Guest lecture / keynote speech	A21 B1 B2 B3	Questions to the students.	10

Assessment comments
To pass this course it will be necessary to obtain (after adding the qualifications of all the activities) a minimum mark of 50% of the total and 50% of the multiple-choice test. To obtain the mark "not presented", it will be sufficient that the students do not participate in the multiple-choice test and have not been evaluated in more than 50% of the problem solving and supervised works. To pass the course in the second opportunity, either the above criterion is fullfiled or a mark higher than 50% in the multiple choice test is obtained. Final marks are not kept from successive academic years. However, it is possible to keep the marks of the supervised works of the previous academic year, if the teacher agrees to this, having the student previously demanded it. The students which are part-time enrolled (and so they are granted with an attendance exemption), can be evaluated in a personalized way regarding the methodologies of the lectures, problem solving and supervised works. For those students which are part-time enrolled, it is compulsory to make the multiple-choice test, as well as the partial test along the course. For the first and second opportunity the criteria of evaluation for these students is the same as the criterion for full-time enrolled students (where the attendance waiver will be of 80%). The priority for obtaining qualifications "with honors" will be for the students that achieve this mark in the first opportunity. Contingency plan (due to Covid19): If the multiple-choice test is not made face-to-face, it will have a percentage of 30% and the other methodologies 70%

Basic	LARSON (2006). CALCULO. McGrawHill W. Keith Nicholson (2019). Linear Algebra with Applications. Lyryx Learning Team

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 studied a mathematics course in the last academic year at high school. For those students who have not, the leveling course offered by the Faculty of Science is strongly recommended.