Course: 2024/2025

Calculus I

(16472)

Requirements (Subjects that are assumed to be known)

None

Skills and learning outcomes

Description of contents: programme

1. REAL VARIABLE FUNCTIONS
1.1 The real line: sets of numbers, properties, absolute values
1.2 Elementary functions and curves
1.3 Polar coordinates
2. LIMITS AND CONTINUITY
2.1 Limits of functions. Properties and fundamental theorems
2.2 Continuity of functions
2.3 Fundamental theorems
3. DERIVATIVES AND THEIR APPLICATIONS
3.1 Definition, properties, and derivatives of elementary functions.
3.2 Meaning of the derivative. Extrema.
4 LOCAL STUDY OF A FUNCTION
4.1 Graphic representation
4.2 Taylor polynomial and its applications
5. SEQUENCES AND SERIES OF REAL NUMBERS
5.1 Sequences of numbers
5.2 Series of positive numbers
5.3 Absolute and conditional convergence
6. SEQUENCES AND SERIES OF FUNCTIONS
6.1 Sequences and series of functions.
6.2 Taylor series
7. INTEGRATION IN ONE VARIABLE
7.1 Calculus of primitives
7.2 Fundamental Theorem of Calculus
7.3 Applications

Learning activities and methodology

THEORETICAL-PRACTICAL CLASSES. [44 hours with 100% classroom instruction, 1.76 ECTS]
Knowledge and concepts students must acquire. Students receive course notes and
will have basic reference texts to facilitate following the classes and carrying
out follow up work. Students partake in exercises to resolve practical problems
and participate in workshops and evaluation tests, all geared towards
acquiring the necessary capabilities.
TUTORING SESSIONS. [4 hours of tutoring with 100% on-site attendance, 0.16 ECTS]
Individualized attendance (individual tutoring) or in-group (group tutoring)
for students with a teacher.
STUDENT INDIVIDUAL WORK OR GROUP WORK [98 hours with 0 % on-site, 3.92 ECTS]
FINAL EXAM. [4 hours with 100% on-site, 0.16 ECTS]
Global assessment of knowledge, skills and capacities acquired throughout the
course.
METHODOLOGIES
THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual
support in which the subject`s main concepts are developed while providing
material and bibliography to complement student learning.
PRACTICAL CLASS. Resolution of practical cases and problems, posed by the
teacher, and carried out individually or in a group.
TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or
in-group (group tutoring sessions) for students with a teacher as a tutor.

Assessment System

- % end-of-term-examination 60
- % of continuous assessment (assigments, laboratory, practicals...) 40

Extraordinary call: regulations

Basic Bibliography

- D. PESTANA, J.M. RODRÍGUEZ, E. ROMERA, E. TOURÍS, V. ÁLVAREZ, A. PORTILLA. Curso práctico de Cálculo y Precálculo. Ariel (Planeta). 2019
- S.L. SALAS, E. HILLE & G.J. Etgen . Calculus: One and Several Variables. Wiley. 2006

Additional Bibliography

- B.P. DEMMIDOVICH. Problemas y ejercicios de Anlálisis Matemático. Paraninfo. 1980
- G.L. BRADLEY, K.J. SMITH. Calculus. Pearson. 2012
- M. SPIVAK. Calculus. Cambridge University Press. Fourth edition, 2008
- T.M. APOSTOL. Calculus vol. 1. Wiley. 1991

The course syllabus may change due academic events or other reasons.